Finite Group Databasebeta

← C31×#14534 #21471293

Subgroups — C31×#14534 #21471293

Order 7936.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#392C211yesmaximal, characteristic
2C2×C31×#390C211yesmaximal, characteristic, complemented
3C2×C31×#390C211yesmaximal, characteristic, complemented
4C2×C31×#388C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#386C211yesmaximal, characteristic, complemented
7C2×C31×#385C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1437C211yesmaximal, characteristic, complemented
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C42×C31C2211yescharacteristic
38C22×C42×C31C2211yescharacteristic
39C31×#392C418yescomplemented
40C31×#390—24no—
41C31×#390—24no—
42C31×#388—24no—
43C31×#386—24no—
44C31×#386—24no—
45C31×#385—24no—
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C25×C31C2311yescharacteristic
59C25×C31C2311yescharacteristic
60C25×C31C2311yescharacteristic
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—41no—
70C22×D4×C31—41no—
71C22×D4×C31—41no—
72C22×D4×C31—41no—
73C22×D4×C31—41no—
74C22×D4×C31—41no—
75C22×D4×C31—41no—
76C22×D4×C31—41no—
77C22×D4×C31—41no—
78C22×D4×C31—41no—
79C22×D4×C31C2×C414yes—
80C22×D4×C31C2×C414yes—
81C22×D4×C31C2×C414yescomplemented
82C23×C4×C31—22no—
83C23×C4×C31—22no—
84C23×C4×C31—22no—
85C23×C4×C31—41no—
86C23×C4×C31—41no—
87C23×C4×C31—41no—
88C23×C4×C31—41no—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—41no—
106C2×C4⋊C4×C31—41no—
107C2×C4⋊C4×C31—41no—
108C2×C4⋊C4×C31—41no—
109C2×C4⋊C4×C31D414yescomplemented
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—22no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—41no—
131C2×C22⋊C4×C31—41no—
132C2×C22⋊C4×C31—41no—
133C2×C22⋊C4×C31—41no—
134C2×C22⋊C4×C31—41no—
135C2×C22⋊C4×C31—41no—
136C2×C22⋊C4×C31—41no—
137C2×C22⋊C4×C31—41no—
138C2×C22⋊C4×C31—41no—
139C2×C22⋊C4×C31—41no—
140C2×C22⋊C4×C31—41no—
141C2×C22⋊C4×C31—41no—
142C2×C22⋊C4×C31—41no—
143C2×C22⋊C4×C31—41no—
144C2×C22⋊C4×C31—41no—
145C2×C22⋊C4×C31—41no—
146C2×C22⋊C4×C31—41no—
147C2×C22⋊C4×C31—41no—
148C2×C22⋊C4×C31C2×C414yes—
149C2×C22⋊C4×C31C2×C414yescomplemented
150C2×C22⋊C4×C31C2×C414yescomplemented
151C2×C22⋊C4×C31D414yescomplemented
152C2×C42×C31—22no—
153C2×C42×C31—22no—
154C2×C42×C31—22no—
155C2×C42×C31—41no—
156C2×C42×C31—41no—
157C2×C42×C31—41no—
158C31×#95—22no—
159C31×#95—22no—
160C31×#95—22no—
161C31×#95—22no—
162C31×#95—22no—
163C31×#95—22no—
164C31×#95—22no—
165C31×#95—41no—
166C31×#95—41no—
167C31×#95—41no—
168C31×#95C2×C414yescomplemented
169C31×#95D414yescomplemented
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31—21no—
187C24×C31—21no—
188C24×C31—21no—
189C24×C31—21no—
190C24×C31—21no—
191C24×C31—21no—
192C24×C31—21no—
193C24×C31—21no—
194C24×C31—21no—
195C24×C31—21no—
196C24×C31—21no—
197C24×C31—21no—
198C24×C31—21no—
199C24×C31—21no—
200C24×C31—21no—
201C24×C31—21no—
202C24×C31—21no—
203C24×C31—21no—
204C24×C31—21no—
205C24×C31—21no—
206C24×C31—21no—
207C24×C31—21no—
208C24×C31—21no—
209C24×C31—21no—
210C24×C31C22×C412yes—
211C24×C31C22×C412yes—
212C24×C31C22×C412yes—
213C24×C31C2×D412yes—
214C24×C31#4112yes—
215C24×C31C2411yescharacteristic
216C2×D4×C31—28no—
217C2×D4×C31—28no—
218C2×D4×C31—28no—
219C2×D4×C31—28no—
220C2×D4×C31—44no—
221C2×D4×C31—44no—
222C2×D4×C31—44no—
223C2×D4×C31—44no—
224C2×D4×C31—44no—
225C2×D4×C31—44no—
226C2×D4×C31—44no—
227C2×D4×C31—44no—
228C2×D4×C31—44no—
229C2×D4×C31—44no—
230C2×D4×C31—44no—
231C2×D4×C31—44no—
232C2×D4×C31—44no—
233C2×D4×C31—44no—
234C2×D4×C31—44no—
235C2×D4×C31—44no—
236C2×D4×C31—44no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31—21no—
282C22×C4×C31—21no—
283C22×C4×C31—21no—
284C22×C4×C31—21no—
285C22×C4×C31—21no—
286C22×C4×C31—21no—
287C22×C4×C31—21no—
288C22×C4×C31—21no—
289C22×C4×C31—21no—
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—21no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31—21no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—21no—
304C22×C4×C31—21no—
305C22×C4×C31—21no—
306C22×C4×C31—21no—
307C22×C4×C31—44no—
308C22×C4×C31—44no—
309C22×C4×C31—44no—
310C22×C4×C31—44no—
311C22×C4×C31—44no—
312C22×C4×C31—44no—
313C22×C4×C31—44no—
314C22×C4×C31C22×C412yes—
315C22×C4×C31C22×C412yes—
316C22×C4×C31C22×C412yes—
317C22×C4×C31C22×C412yes—
318C22×C4×C31C2×D412yes—
319C22×C4×C31C2×D412yes—
320C22×C4×C31C2×D412yes—
321C22×C4×C31C2×D412yes—
322C22×C4×C31C2×D412yes—
323C22×C4×C31C2×D412yes—
324C22×C4×C31C2×D412yes—
325C22×C4×C31C2×D412yes—
326C22×C4×C31#4112yes—
327C22×C4×C31#4112yes—
328C4⋊C4×C31—44no—
329C4⋊C4×C31—44no—
330C4⋊C4×C31—44no—
331C22⋊C4×C31—28no—
332C22⋊C4×C31—28no—
333C22⋊C4×C31—44no—
334C22⋊C4×C31—44no—
335C22⋊C4×C31—44no—
336C22⋊C4×C31—44no—
337C22⋊C4×C31—44no—
338C22⋊C4×C31—44no—
339C22⋊C4×C31—44no—
340C22⋊C4×C31—44no—
341C22⋊C4×C31—44no—
342C22⋊C4×C31—44no—
343C22⋊C4×C31—44no—
344C22⋊C4×C31—44no—
345C42×C31—44no—
346C42×C31—44no—
347#14534C3111yesmaximal, characteristic, direct product factor, Sylow
348C23×C31—22no—
349C23×C31—22no—
350C23×C31—22no—
351C23×C31—22no—
352C23×C31—22no—
353C23×C31—22no—
354C23×C31—22no—
355C23×C31—22no—
356C23×C31—22no—
357C23×C31—22no—
358C23×C31—22no—
359C23×C31—22no—
360C23×C31—22no—
361C23×C31—22no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—22no—
367C23×C31—22no—
368C23×C31—22no—
369C23×C31—22no—
370C23×C31—22no—
371C23×C31—22no—
372C23×C31—22no—
373C23×C31—22no—
374C23×C31—22no—
375C23×C31—22no—
376C23×C31—22no—
377C23×C31—22no—
378C23×C31—22no—
379C23×C31—22no—
380C23×C31—41no—
381C23×C31—41no—
382C23×C31—41no—
383C23×C31—41no—
384C23×C31—41no—
385C23×C31—41no—
386C23×C31—41no—
387C23×C31—41no—
388C23×C31—41no—
389C23×C31—41no—
390C23×C31—41no—
391C23×C31—41no—
392C23×C31—41no—
393C23×C31—41no—
394C23×C31—41no—
395C23×C31—41no—
396C23×C31—41no—
397C23×C31—41no—
398C23×C31—41no—
399C23×C31—41no—
400C23×C31—41no—
401C23×C31—41no—
402C23×C31—41no—
403C23×C31—41no—
404C23×C31—41no—
405C23×C31—41no—
406C23×C31—41no—
407C23×C31—41no—
408C23×C31—41no—
409C23×C31—41no—
410C23×C31—41no—
411C23×C31—41no—
412C23×C31—41no—
413C23×C31—41no—
414C23×C31—41no—
415C23×C31—41no—
416C23×C31—41no—
417C23×C31—41no—
418C23×C31—41no—
419C23×C31—41no—
420C23×C31—41no—
421C23×C31—41no—
422C23×C31—41no—
423C23×C31—41no—
424C23×C31—41no—
425C23×C31—41no—
426C23×C31—41no—
427C23×C31—41no—
428C23×C31—41no—
429C23×C31—41no—
430C23×C31—41no—
431C23×C31—41no—
432C23×C31—41no—
433C23×C31—41no—
434C23×C31—41no—
435C23×C31—41no—
436C23×C31—41no—
437C23×C31—41no—
438C23×C31—41no—
439C23×C31—41no—
440C23×C31—41no—
441C23×C31—41no—
442C23×C31—41no—
443C23×C31—41no—
444C23×C31—41no—
445C23×C31—41no—
446C23×C31—41no—
447C23×C31—41no—
448C23×C31—41no—
449C23×C31—41no—
450C23×C31—41no—
451C23×C31—41no—
452C23×C31C4×D414yes—
453C23×C31C23×C411yescharacteristic
454C23×C31C22×D411yescharacteristic
455C23×C31C22×D411yescharacteristic
456C23×C31C22×D411yescharacteristic
457C23×C31C2×#4111yescharacteristic
458C23×C31C2×#4111yescharacteristic
459C23×C31C2×#4111yescharacteristic
460C23×C31H(5,𝔽2)11yescharacteristic
461C23×C31H(5,𝔽2)11yescharacteristic
462C23×C31H(5,𝔽2)11yescharacteristic
463C23×C31H(5,𝔽2)11yescharacteristic
464C23×C31H(5,𝔽2)11yescharacteristic
465C23×C31H(5,𝔽2)11yescharacteristic
466C23×C31H(5,𝔽2)11yescharacteristic
467C23×C312−1+411yescharacteristic
468D4×C31—416no—
469D4×C31—416no—
470D4×C31—416no—
471C2×C4×C31—22no—
472C2×C4×C31—22no—
473C2×C4×C31—22no—
474C2×C4×C31—22no—
475C2×C4×C31—22no—
476C2×C4×C31—22no—
477C2×C4×C31—22no—
478C2×C4×C31—22no—
479C2×C4×C31—22no—
480C2×C4×C31—22no—
481C2×C4×C31—22no—
482C2×C4×C31—22no—
483C2×C4×C31—22no—
484C2×C4×C31—22no—
485C2×C4×C31—22no—
486C2×C4×C31—22no—
487C2×C4×C31—22no—
488C2×C4×C31—22no—
489C2×C4×C31—22no—
490C2×C4×C31—22no—
491C2×C4×C31—22no—
492C2×C4×C31—22no—
493C2×C4×C31—22no—
494C2×C4×C31—22no—
495C2×C4×C31—22no—
496C2×C4×C31—22no—
497C2×C4×C31—22no—
498C2×C4×C31—22no—
499C2×C4×C31—22no—
500C2×C4×C31—22no—
501C2×C4×C31—22no—
502C2×C4×C31—22no—
503C2×C4×C31—22no—
504C2×C4×C31—22no—
505C2×C4×C31—22no—
506C2×C4×C31—22no—
507C2×C4×C31—416no—
508C2×C4×C31—41no—
509C2×C4×C31—41no—
510C2×C4×C31—41no—
511C2×C4×C31—41no—
512C2×C4×C31—41no—
513C2×C4×C31—41no—
514C2×C4×C31—41no—
515C2×C4×C31—41no—
516C2×C4×C31—41no—
517C2×C4×C31—41no—
518C2×C4×C31—41no—
519C2×C4×C31—41no—
520C2×C4×C31—41no—
521C2×C4×C31—41no—
522C2×C4×C31—41no—
523C2×C4×C31—41no—
524C2×C4×C31—41no—
525C2×C4×C31—41no—
526C2×C4×C31—41no—
527C2×C4×C31—41no—
528C2×C4×C31—41no—
529C2×C4×C31—41no—
530C2×C4×C31—41no—
531C2×C4×C31—41no—
532C2×C4×C31—41no—
533C2×C4×C31—41no—
534C2×C4×C31—41no—
535C2×C4×C31—41no—
536C2×C4×C31—41no—
537C2×C4×C31—41no—
538C2×C4×C31—41no—
539C2×C4×C31—41no—
540C2×C4×C31—41no—
541C2×C4×C31—41no—
542C2×C4×C31—41no—
543C2×C4×C31—41no—
544C2×C4×C31—41no—
545C2×C4×C31—41no—
546C2×C4×C31—41no—
547C2×C4×C31—41no—
548C2×C4×C31—41no—
549C2×C4×C31—41no—
550C2×C4×C31—41no—
551C2×C4×C31—41no—
552C2×C4×C31—41no—
553C2×C4×C31—41no—
554C2×C4×C31C4×D414yes—
555C2×C4×C31C4×D414yes—
556C2×#392C2×C3111yescharacteristic
557C2×#390C2×C3111yescharacteristic, complemented
558C2×#390C2×C3111yescharacteristic, complemented
559C2×#388C2×C3111yescharacteristic, complemented
560C2×#386C2×C3111yescharacteristic, complemented
561C2×#386C2×C3111yescharacteristic, complemented
562C2×#385C2×C3111yescharacteristic, complemented
563#1440C2×C3111yescharacteristic, complemented
564#1439C2×C3111yescharacteristic, complemented
565#1439C2×C3111yescharacteristic, complemented
566#1438C2×C3111yescharacteristic, complemented
567#1438C2×C3111yescharacteristic, complemented
568#1437C2×C3111yescharacteristic, complemented
569#1436C2×C3111yescharacteristic, complemented
570#1436C2×C3111yescharacteristic, complemented
571C22×C31—24no—
572C22×C31—24no—
573C22×C31—24no—
574C22×C31—42no—
575C22×C31—42no—
576C22×C31—42no—
577C22×C31—42no—
578C22×C31—42no—
579C22×C31—42no—
580C22×C31—42no—
581C22×C31—42no—
582C22×C31—42no—
583C22×C31—42no—
584C22×C31—42no—
585C22×C31—42no—
586C22×C31—42no—
587C22×C31—42no—
588C22×C31—42no—
589C22×C31—42no—
590C22×C31—42no—
591C22×C31—42no—
592C22×C31—42no—
593C22×C31—42no—
594C22×C31—42no—
595C22×C31—42no—
596C22×C31—42no—
597C22×C31—42no—
598C22×C31—42no—
599C22×C31—42no—
600C22×C31—81no—
601C22×C31—81no—
602C22×C31—81no—
603C22×C31—81no—
604C22×C31—81no—
605C22×C31—81no—
606C22×C31—81no—
607C22×C31—81no—
608C22×C31—81no—
609C22×C31—81no—
610C22×C31—81no—
611C22×C31—81no—
612C22×C31—81no—
613C22×C31—81no—
614C22×C31—81no—
615C22×C31—81no—
616C22×C31C2×C4×D411yescharacteristic
617C22×C31C2×C4×D411yescharacteristic
618C22×C31C2×C4×D411yescharacteristic
619C22×C31#51811yescharacteristic
620C22×C31#51811yescharacteristic
621C22×C31#51811yescharacteristic
622C22×C31#52011yescharacteristic
623C22×C31#53411yescharacteristic
624C22×C31#53411yescharacteristic
625C22×C31#53511yescharacteristic
626C22×C31#53511yescharacteristic
627C22×C31#53511yescharacteristic
628C22×C31#53711yescharacteristic
629C22×C31#53811yescharacteristic
630C22×C31#53811yescharacteristic
631C22×C31#53811yescharacteristic
632C22×C31#53811yescharacteristic
633C22×C31#54011yescharacteristic
634C22×C31#54211yescharacteristic
635C22×C31D4211yescharacteristic
636C22×C31D4211yescharacteristic
637C22×C31D4211yescharacteristic
638C22×C31#54611yescharacteristic
639C22×C31#54611yescharacteristic
640C22×C31#54711yescharacteristic
641C22×C31#54811yescharacteristic
642C22×C31#55011yescharacteristic
643C22×C31#55011yescharacteristic
644C22×C31#55111yescharacteristic
645C22×C31#55311yescharacteristic
646C22×C31#55911yescharacteristic
647C22×C31#56011yescharacteristic
648C22×C31#56011yescharacteristic
649C22×C31#56211yescharacteristic
650C22×C31#56211yescharacteristic
651C4×C31—24no—
652C4×C31—24no—
653C4×C31—42no—
654C4×C31—42no—
655C4×C31—42no—
656C4×C31—42no—
657C4×C31—42no—
658C4×C31—42no—
659C4×C31—42no—
660C4×C31—42no—
661C4×C31—81no—
662C4×C31—81no—
663C23×D4C22×C3111yescharacteristic
664C23×D4C22×C3111yescharacteristic
665C23×D4C22×C3111yescharacteristic
666C24×C4C22×C3111yescharacteristic
667C22×C4⋊C4C22×C3111yescharacteristic
668C22×C4⋊C4C22×C3111yescharacteristic
669C22×C4⋊C4C22×C3111yescharacteristic
670C22×C22⋊C4C22×C3111yescharacteristic
671C22×C22⋊C4C22×C3111yescharacteristic
672C22×C22⋊C4C22×C3111yescharacteristic
673C22×C22⋊C4C22×C3111yescharacteristic
674C22×C22⋊C4C22×C3111yescharacteristic
675C22×C22⋊C4C22×C3111yescharacteristic
676C22×C22⋊C4C22×C3111yescharacteristic
677C22×C22⋊C4C22×C3111yescharacteristic
678C22×C22⋊C4C22×C3111yescharacteristic
679C22×C22⋊C4C22×C3111yescharacteristic
680C22×C22⋊C4C22×C3111yescharacteristic
681C22×C22⋊C4C22×C3111yescharacteristic
682C22×C22⋊C4C22×C3111yescharacteristic
683C22×C22⋊C4C22×C3111yescharacteristic
684C22×C42C22×C3111yescharacteristic
685C22×C42C22×C3111yescharacteristic
686#392C4×C3118yescomplemented
687#390—24no—
688#390—24no—
689#388—24no—
690#386—24no—
691#386—24no—
692#385—24no—
693C2×#95C22×C3111yescharacteristic
694C2×#95C22×C3111yescharacteristic
695C2×#95C22×C3111yescharacteristic
696C2×#95C22×C3111yescharacteristic
697C2×#95C22×C3111yescharacteristic
698C2×#95C22×C3111yescharacteristic
699C2×#95C22×C3111yescharacteristic
700C2×#95C22×C3111yescharacteristic
701C2×#95C22×C3111yescharacteristic
702C2×#95C22×C3111yescharacteristic
703C2×#95C22×C3111yescharacteristic
704C2×#95C22×C3111yescharacteristic
705C2×C31—44no—
706C2×C31—82no—
707C2×C31—82no—
708C2×C31#232111yescharacteristic
709C2×C31#232111yescharacteristic
710C2×C31#232411yescharacteristic
711C2×C31#235811yescharacteristic
712C2×C31#236111yescharacteristic
713C2×C31#236611yescharacteristic
714C2×C31#237711yescharacteristic
715C2×C31#266911yescharacteristic
716C2×C31#267311yescharacteristic
717C2×C31#267611yescharacteristic
718C2×C31#268211yescharacteristic
719C2×C31#271011yescharacteristic
720C2×C31#271411yescharacteristic
721C2×C31#273011yescharacteristic
722C2×C31#279711yescharacteristic
723C25C23×C3111yescharacteristic
724C25C23×C3111yescharacteristic
725C25C23×C3111yescharacteristic
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4C2×C4×C3114yes—
745C22×D4C2×C4×C3114yes—
746C22×D4C2×C4×C3114yescomplemented
747C23×C4—22no—
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—41no—
751C23×C4—41no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4C23×C3111yescharacteristic
755C23×C4C23×C3111yescharacteristic
756C23×C4C23×C3111yescharacteristic
757C23×C4C23×C3111yescharacteristic
758C23×C4C23×C3111yescharacteristic
759C23×C4C23×C3111yescharacteristic
760C23×C4C23×C3111yescharacteristic
761C23×C4C23×C3111yescharacteristic
762C23×C4C23×C3111yescharacteristic
763C23×C4C23×C3111yescharacteristic
764C23×C4C23×C3111yescharacteristic
765C23×C4C23×C3111yescharacteristic
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4D4×C3114yescomplemented
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4C2×C4×C3114yes—
814C2×C22⋊C4C2×C4×C3114yescomplemented
815C2×C22⋊C4C2×C4×C3114yescomplemented
816C2×C22⋊C4D4×C3114yescomplemented
817C2×C42—22no—
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—41no—
821C2×C42—41no—
822C2×C42—41no—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—41no—
831#95—41no—
832#95—41no—
833#95C2×C4×C3114yescomplemented
834#95D4×C3114yescomplemented
835C31#1453411yescharacteristic, direct product factor, Sylow
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24C22×C4×C3112yes—
877C24C22×C4×C3112yes—
878C24C22×C4×C3112yes—
879C24C2×D4×C3112yes—
880C24#41×C3112yes—
881C24C24×C3111yescharacteristic
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4C22×C4×C3112yes—
981C22×C4C22×C4×C3112yes—
982C22×C4C22×C4×C3112yes—
983C22×C4C22×C4×C3112yes—
984C22×C4C2×D4×C3112yes—
985C22×C4C2×D4×C3112yes—
986C22×C4C2×D4×C3112yes—
987C22×C4C2×D4×C3112yes—
988C22×C4C2×D4×C3112yes—
989C22×C4C2×D4×C3112yes—
990C22×C4C2×D4×C3112yes—
991C22×C4C2×D4×C3112yes—
992C22×C4#41×C3112yes—
993C22×C4#41×C3112yes—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C42—44no—
1012C42—44no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23C4×D4×C3114yes—
1118C23C23×C4×C3111yescharacteristic
1119C23C22×D4×C3111yescharacteristic
1120C23C22×D4×C3111yescharacteristic
1121C23C22×D4×C3111yescharacteristic
1122C23C2×#41×C3111yescharacteristic
1123C23C2×#41×C3111yescharacteristic
1124C23C2×#41×C3111yescharacteristic
1125C23C31×H(5,𝔽2)11yescharacteristic
1126C23C31×H(5,𝔽2)11yescharacteristic
1127C23C31×H(5,𝔽2)11yescharacteristic
1128C23C31×H(5,𝔽2)11yescharacteristic
1129C23C31×H(5,𝔽2)11yescharacteristic
1130C23C31×H(5,𝔽2)11yescharacteristic
1131C23C31×H(5,𝔽2)11yescharacteristic
1132C23C31×2−1+411yescharacteristic
1133D4—416no—
1134D4—416no—
1135D4—416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—416no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4C4×D4×C3114yes—
1220C2×C4C4×D4×C3114yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22C2×C4×D4×C3111yescharacteristic
1267C22C2×C4×D4×C3111yescharacteristic
1268C22C2×C4×D4×C3111yescharacteristic
1269C22C31×#51811yescharacteristic
1270C22C31×#51811yescharacteristic
1271C22C31×#51811yescharacteristic
1272C22C31×#52011yescharacteristic
1273C22C31×#53411yescharacteristic
1274C22C31×#53411yescharacteristic
1275C22C31×#53511yescharacteristic
1276C22C31×#53511yescharacteristic
1277C22C31×#53511yescharacteristic
1278C22C31×#53711yescharacteristic
1279C22C31×#53811yescharacteristic
1280C22C31×#53811yescharacteristic
1281C22C31×#53811yescharacteristic
1282C22C31×#53811yescharacteristic
1283C22C31×#54011yescharacteristic
1284C22C31×#54211yescharacteristic
1285C22D42×C3111yescharacteristic
1286C22D42×C3111yescharacteristic
1287C22D42×C3111yescharacteristic
1288C22C31×#54611yescharacteristic
1289C22C31×#54611yescharacteristic
1290C22C31×#54711yescharacteristic
1291C22C31×#54811yescharacteristic
1292C22C31×#55011yescharacteristic
1293C22C31×#55011yescharacteristic
1294C22C31×#55111yescharacteristic
1295C22C31×#55311yescharacteristic
1296C22C31×#55911yescharacteristic
1297C22C31×#56011yescharacteristic
1298C22C31×#56011yescharacteristic
1299C22C31×#56211yescharacteristic
1300C22C31×#56211yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C2—44no—
1314C2—82no—
1315C2—82no—
1316C2C31×#232111yescharacteristic
1317C2C31×#232111yescharacteristic
1318C2C31×#232411yescharacteristic
1319C2C31×#235811yescharacteristic
1320C2C31×#236111yescharacteristic
1321C2C31×#236611yescharacteristic
1322C2C31×#237711yescharacteristic
1323C2C31×#266911yescharacteristic
1324C2C31×#267311yescharacteristic
1325C2C31×#267611yescharacteristic
1326C2C31×#268211yescharacteristic
1327C2C31×#271011yescharacteristic
1328C2C31×#271411yescharacteristic
1329C2C31×#273011yescharacteristic
1330C2C31×#279711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C31×#390C2semidirect
3. C2×C31×#390C2semidirect
4. C2×C31×#388C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#386C2semidirect
7. C2×C31×#385C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1438C2semidirect
12. C31×#1438C2semidirect
13. C31×#1437C2semidirect
14. C31×#1436C2semidirect
15. C31×#1436C2semidirect
39. C31×#392C4semidirect
81. C22×D4×C31C2×C4semidirect
109. C2×C4⋊C4×C31D4semidirect
149. C2×C22⋊C4×C31C2×C4semidirect
150. C2×C22⋊C4×C31C2×C4semidirect
151. C2×C22⋊C4×C31D4semidirect
168. C31×#95C2×C4semidirect
169. C31×#95D4semidirect
347. #14534C31direct (N × H)
557. C2×#390C2×C31semidirect
558. C2×#390C2×C31semidirect
559. C2×#388C2×C31semidirect
560. C2×#386C2×C31semidirect
561. C2×#386C2×C31semidirect
562. C2×#385C2×C31semidirect
563. #1440C2×C31semidirect
564. #1439C2×C31semidirect
565. #1439C2×C31semidirect
566. #1438C2×C31semidirect
567. #1438C2×C31semidirect
568. #1437C2×C31semidirect
569. #1436C2×C31semidirect
570. #1436C2×C31semidirect
686. #392C4×C31semidirect
746. C22×D4C2×C4×C31semidirect
774. C2×C4⋊C4D4×C31semidirect
814. C2×C22⋊C4C2×C4×C31semidirect
815. C2×C22⋊C4C2×C4×C31semidirect
816. C2×C22⋊C4D4×C31semidirect
833. #95C2×C4×C31semidirect
834. #95D4×C31semidirect
835. C31#14534direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C31×#3852
C31×#14402
C31×#14392
C31×#14382
C31×#14372
C31×#14362
#1453431