Finite Group Databasebeta

← C31×#25076 #21481835

Subgroups — C31×#25076 #21481835

Order 7936.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#466C211yesmaximal, characteristic, complemented
2C2×C31×#459C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic, complemented
4C22×C31×#102C211yesmaximal, characteristic, complemented
5C31×#2433C211yesmaximal, characteristic, complemented
6C31×#2361C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2041C211yesmaximal, characteristic, complemented
10C31×#2011C211yesmaximal, characteristic, complemented
11C31×#1982C211yesmaximal, characteristic, complemented
12C31×#1925C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1874C211yesmaximal, characteristic, complemented
15C31×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic, complemented
20C23×C8×C31C2211yescharacteristic
21C2×C31×#127C2211yescharacteristic
22C2×C31×#127C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#120—21no—
26C2×C31×#120—21no—
27C2×C4×D4×C31—21no—
28C2×C4×D4×C31C2211yescharacteristic, complemented
29C22×C4⋊C4×C31C2211yescharacteristic
30C31×#466—24no—
31C31×#459—24no—
32C31×#447—24no—
33C2×C31×#107C2211yescharacteristic, complemented
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C2×C31×C4⋊C8C2211yescharacteristic, complemented
36C2×C31×#102—24no—
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#392—21no—
49C31×#392—21no—
50C31×#390C2211yescharacteristic
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic, complemented
53C31×#389C2211yescharacteristic, complemented
54C31×#388—21no—
55C31×#386—21no—
56C31×#385—21no—
57C4×C4⋊C4×C31C2211yescharacteristic, complemented
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—21no—
68C22×D4×C31—22no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31—22no—
75C22×D4×C31—41no—
76C22×D4×C31—41no—
77C22×D4×C31C2311yescharacteristic
78C22×D4×C31C2311yescharacteristic
79C22×D4×C31C2311yescharacteristic
80C22×D4×C31C2311yescharacteristic
81C23×C4×C31—21no—
82C23×C4×C31—21no—
83C23×C4×C31C2311yescharacteristic
84C2×D8×C31—22no—
85C2×D8×C31—22no—
86C2×D8×C31—22no—
87C2×D8×C31—22no—
88C2×D8×C31—22no—
89C2×D8×C31—22no—
90C2×D8×C31—41no—
91C2×D8×C31—41no—
92C2×D8×C31—41no—
93C22×C8×C31—22no—
94C22×C8×C31—22no—
95C22×C8×C31—41no—
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C22×C8×C31C2311yescharacteristic
100C31×#127—22no—
101C31×#127—22no—
102C31×#127—41no—
103C31×#127—41no—
104C31×#121—22no—
105C31×#121—22no—
106C31×#121—22no—
107C31×#121D414yescomplemented
108C31×#120—44no—
109C31×#120—44no—
110C4×D4×C31—22no—
111C4×D4×C31—41no—
112C4×D4×C31—44no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—41no—
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C22⋊C4×C31D411yescharacteristic
132C2×C42×C31—21no—
133C2×C42×C31C2311yescharacteristic
134C2×C42×C31C2311yescharacteristic
135C31×#107—22no—
136C31×C4⋊C8—22no—
137C31×C4⋊C8—41no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—41no—
147C31×#102D414yescomplemented
148C31×C22⋊C8—22no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95D411yescharacteristic
152C31×#95D411yescharacteristic
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—42no—
160C24×C31—42no—
161C24×C31—42no—
162C24×C31—81no—
163C24×C31—81no—
164C24×C31C2×D411yescharacteristic
165C2×D4×C31—28no—
166C2×D4×C31—24no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—44no—
189C2×D4×C31—44no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—44no—
193C2×D4×C31—42no—
194C2×D4×C31—42no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
197C2×D4×C31—42no—
198C2×D4×C31—42no—
199C2×D4×C31—42no—
200C2×D4×C31—42no—
201C2×D4×C31—42no—
202C2×D4×C31—42no—
203C2×D4×C31—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—81no—
208C2×D4×C31—81no—
209C2×D4×C31—81no—
210C2×D4×C31—81no—
211C2×D4×C31C2×D412yes—
212C2×D4×C31C2×D412yes—
213C2×D4×C31#4112yes—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—42no—
223C22×C4×C31—42no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31—81no—
227C22×C4×C31—81no—
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31#4112yes—
235C22×C4×C31C2411yescharacteristic
236D8×C31—44no—
237D8×C31—44no—
238D8×C31—44no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C2×C8×C31—21no—
250C2×C8×C31—44no—
251C2×C8×C31C2×D412yes—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—42no—
259C4⋊C4×C31—42no—
260C4⋊C4×C31C2×D412yes—
261C4⋊C4×C31C2×D412yes—
262C22⋊C4×C31—22no—
263C22⋊C4×C31—24no—
264C22⋊C4×C31—42no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—42no—
268C22⋊C4×C31—42no—
269C22⋊C4×C31—42no—
270C22⋊C4×C31—42no—
271C22⋊C4×C31—81no—
272C22⋊C4×C31D814yescomplemented
273C42×C31—21no—
274C42×C31—21no—
275C42×C31—21no—
276C42×C31—21no—
277C42×C31—42no—
278#25076C3111yesmaximal, characteristic, direct product factor, Sylow
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—22no—
286C23×C31—48no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—84no—
313C23×C31—84no—
314C23×C31—84no—
315C23×C31—84no—
316C23×C31—84no—
317C23×C31—84no—
318C23×C31#12112yes—
319C23×C31C2×D812yes—
320C23×C31AGL(1,ℤ/8)12yes—
321C23×C31C22×D411yescharacteristic
322D4×C31—22no—
323D4×C31—22no—
324D4×C31—22no—
325D4×C31—22no—
326D4×C31—22no—
327D4×C31—22no—
328D4×C31—48no—
329D4×C31—48no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—41no—
333D4×C31—41no—
334D4×C31—41no—
335D4×C31—41no—
336D4×C31—41no—
337D4×C31—41no—
338D4×C31—41no—
339D4×C31—41no—
340D4×C31—84no—
341D4×C31—84no—
342D4×C31—84no—
343D4×C31—84no—
344D4×C31—84no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—21no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—21no—
357C2×C4×C31—22no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—21no—
362C2×C4×C31—21no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—84no—
374C2×C4×C31—84no—
375C2×C4×C31#12112yes—
376C2×C4×C31C2×D812yes—
377C2×C4×C31C2×D812yes—
378C2×C4×C31C22×D411yescharacteristic
379C2×C4×C31C22×D411yescharacteristic
380C2×C4×C31C2×#4111yescharacteristic
381C2×C4×C31C2×#4111yescharacteristic
382C2×C4×C31H(5,𝔽2)11yescharacteristic
383C2×C4×C31H(5,𝔽2)11yescharacteristic
384C8×C31—22no—
385C8×C31—41no—
386C8×C31—41no—
387C8×C31—41no—
388C2×#466C2×C3111yescharacteristic, complemented
389C2×#459C2×C3111yescharacteristic, complemented
390C2×#447C2×C3111yescharacteristic, complemented
391C22×#102C2×C3111yescharacteristic, complemented
392#2433C2×C3111yescharacteristic, complemented
393#2361C2×C3111yescharacteristic, complemented
394#2067C2×C3111yescharacteristic, complemented
395#2054C2×C3111yescharacteristic, complemented
396#2041C2×C3111yescharacteristic, complemented
397#2011C2×C3111yescharacteristic, complemented
398#1982C2×C3111yescharacteristic, complemented
399#1925C2×C3111yescharacteristic, complemented
400#1879C2×C3111yescharacteristic, complemented
401#1874C2×C3111yescharacteristic, complemented
402#1850C2×C3111yescharacteristic, complemented
403C22×C31—22no—
404C22×C31—22no—
405C22×C31—22no—
406C22×C31—22no—
407C22×C31—22no—
408C22×C31—22no—
409C22×C31—42no—
410C22×C31—42no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—42no—
416C22×C31—42no—
417C22×C31—42no—
418C22×C31—816no—
419C22×C31—81no—
420C22×C31—81no—
421C22×C31—81no—
422C22×C31—81no—
423C22×C31—81no—
424C22×C31—81no—
425C22×C31—81no—
426C22×C31—81no—
427C22×C31—81no—
428C22×C31—81no—
429C22×C31—81no—
430C22×C31—81no—
431C22×C31—81no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31—81no—
436C22×C31—81no—
437C22×C31—81no—
438C22×C31#45914yescomplemented
439C22×C31C2×#12111yescharacteristic
440C22×C31D4211yescharacteristic
441C22×C31#54611yescharacteristic
442C22×C31C22×D811yescharacteristic
443C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
444C22×C31#57611yescharacteristic
445C22×C31#57711yescharacteristic
446C4×C31—22no—
447C4×C31—22no—
448C4×C31—22no—
449C4×C31—41no—
450C4×C31—42no—
451C4×C31—42no—
452C4×C31—41no—
453C4×C31—81no—
454C4×C31—81no—
455C4×C31#52511yescharacteristic
456C4×C31#53811yescharacteristic
457C4×C31D4211yescharacteristic
458C4×C31#54611yescharacteristic
459C23×D4C22×C3111yescharacteristic
460C22×D8C22×C3111yescharacteristic
461C22×D8C22×C3111yescharacteristic
462C22×D8C22×C3111yescharacteristic, complemented
463C23×C8C22×C3111yescharacteristic
464C2×#127C22×C3111yescharacteristic
465C2×#127C22×C3111yescharacteristic
466C2×#121C22×C3111yescharacteristic
467C2×#121C22×C3111yescharacteristic
468C2×#120—21no—
469C2×#120—21no—
470C2×C4×D4—21no—
471C2×C4×D4C22×C3111yescharacteristic, complemented
472C22×C4⋊C4C22×C3111yescharacteristic
473#466—24no—
474#459—24no—
475#447—24no—
476C2×#107C22×C3111yescharacteristic, complemented
477C2×C4⋊C8C22×C3111yescharacteristic, complemented
478C2×C4⋊C8C22×C3111yescharacteristic, complemented
479C2×#102—24no—
480C2×#102C22×C3111yescharacteristic
481C2×#102C22×C3111yescharacteristic
482C2×#102C22×C3111yescharacteristic
483C2×#102C22×C3111yescharacteristic
484C2×#102C22×C3111yescharacteristic
485C2×#102C22×C3111yescharacteristic
486C2×#102C22×C3111yescharacteristic, complemented
487C2×#102C22×C3111yescharacteristic, complemented
488C2×#102C22×C3111yescharacteristic, complemented
489C2×#102C22×C3111yescharacteristic, complemented
490C2×C22⋊C8C22×C3111yescharacteristic
491#392—21no—
492#392—21no—
493#390C22×C3111yescharacteristic
494#390C22×C3111yescharacteristic
495#390C22×C3111yescharacteristic, complemented
496#389C22×C3111yescharacteristic, complemented
497#388—21no—
498#386—21no—
499#385—21no—
500C4×C4⋊C4C22×C3111yescharacteristic, complemented
501C4×C22⋊C4C22×C3111yescharacteristic
502#340C22×C3111yescharacteristic, complemented
503#340C22×C3111yescharacteristic, complemented
504#336C22×C3111yescharacteristic, complemented
505#336C22×C3111yescharacteristic, complemented
506C2×C31—24no—
507C2×C31—82no—
508C2×C31—82no—
509C2×C31—82no—
510C2×C31—161no—
511C2×C31#242411yescharacteristic
512C2×C31C2×#45911yescharacteristic
513C2×C31#304511yescharacteristic
514C2×C31#326511yescharacteristic
515C2×C31D4×D811yescharacteristic
516C2×C31#329411yescharacteristic
517C2×C31#331811yescharacteristic
518C25—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C23×C3111yescharacteristic
533C22×D4C23×C3111yescharacteristic
534C22×D4C23×C3111yescharacteristic
535C22×D4C23×C3111yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C23×C3111yescharacteristic
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C22×C8—22no—
549C22×C8—22no—
550C22×C8—41no—
551C22×C8C23×C3111yescharacteristic
552C22×C8C23×C3111yescharacteristic
553C22×C8C23×C3111yescharacteristic
554C22×C8C23×C3111yescharacteristic
555#127—22no—
556#127—22no—
557#127—41no—
558#127—41no—
559#121—22no—
560#121—22no—
561#121—22no—
562#121D4×C3114yescomplemented
563#120—44no—
564#120—44no—
565C4×D4—22no—
566C4×D4—41no—
567C4×D4—44no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4C23×C3111yescharacteristic
573C2×C4⋊C4C23×C3111yescharacteristic
574C2×C4⋊C4C23×C3111yescharacteristic
575C2×C4⋊C4C23×C3111yescharacteristic
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4D4×C3111yescharacteristic
586C2×C22⋊C4D4×C3111yescharacteristic
587C2×C42—21no—
588C2×C42C23×C3111yescharacteristic
589C2×C42C23×C3111yescharacteristic
590#107—22no—
591C4⋊C8—22no—
592C4⋊C8—41no—
593#102—22no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—41no—
602#102D4×C3114yescomplemented
603C22⋊C8—22no—
604#95—21no—
605#95—21no—
606#95D4×C3111yescharacteristic
607#95D4×C3111yescharacteristic
608C31#2507611yescharacteristic, direct product factor, Sylow
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C3111yescharacteristic
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C3112yes—
668C2×D4C2×D4×C3112yes—
669C2×D4#41×C3112yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C3111yescharacteristic
685C22×C4C2×D4×C3111yescharacteristic
686C22×C4C2×D4×C3111yescharacteristic
687C22×C4C2×D4×C3112yes—
688C22×C4C2×D4×C3111yescharacteristic
689C22×C4C2×D4×C3111yescharacteristic
690C22×C4#41×C3112yes—
691C22×C4C24×C3111yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—44no—
707C2×C8C2×D4×C3112yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C3112yes—
717C4⋊C4C2×D4×C3112yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C3114yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23C31×#12112yes—
774C23C2×D8×C3112yes—
775C23C31×AGL(1,ℤ/8)12yes—
776C23C22×D4×C3111yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4C31×#12112yes—
831C2×C4C2×D8×C3112yes—
832C2×C4C2×D8×C3112yes—
833C2×C4C22×D4×C3111yescharacteristic
834C2×C4C22×D4×C3111yescharacteristic
835C2×C4C2×#41×C3111yescharacteristic
836C2×C4C2×#41×C3111yescharacteristic
837C2×C4C31×H(5,𝔽2)11yescharacteristic
838C2×C4C31×H(5,𝔽2)11yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22C31×#45914yescomplemented
879C22C2×C31×#12111yescharacteristic
880C22D42×C3111yescharacteristic
881C22C31×#54611yescharacteristic
882C22C22×D8×C3111yescharacteristic
883C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
884C22C31×#57611yescharacteristic
885C22C31×#57711yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—81no—
894C4—81no—
895C4C31×#52511yescharacteristic
896C4C31×#53811yescharacteristic
897C4D42×C3111yescharacteristic
898C4C31×#54611yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2C31×#242411yescharacteristic
905C2C2×C31×#45911yescharacteristic
906C2C31×#304511yescharacteristic
907C2C31×#326511yescharacteristic
908C2D4×D8×C3111yescharacteristic
909C2C31×#329411yescharacteristic
910C2C31×#331811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#466C2semidirect
2. C2×C31×#459C2semidirect
3. C2×C31×#447C2semidirect
4. C22×C31×#102C2semidirect
5. C31×#2433C2semidirect
6. C31×#2361C2semidirect
7. C31×#2067C2semidirect
8. C31×#2054C2semidirect
9. C31×#2041C2semidirect
10. C31×#2011C2semidirect
11. C31×#1982C2semidirect
12. C31×#1925C2semidirect
13. C31×#1879C2semidirect
14. C31×#1874C2semidirect
15. C31×#1850C2semidirect
19. C22×D8×C31C22semidirect
28. C2×C4×D4×C31C22semidirect
33. C2×C31×#107C22semidirect
34. C2×C31×C4⋊C8C22semidirect
35. C2×C31×C4⋊C8C22semidirect
43. C2×C31×#102C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
52. C31×#390C22semidirect
53. C31×#389C22semidirect
57. C4×C4⋊C4×C31C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
107. C31×#121D4semidirect
147. C31×#102D4semidirect
272. C22⋊C4×C31D8semidirect
278. #25076C31direct (N × H)
388. C2×#466C2×C31semidirect
389. C2×#459C2×C31semidirect
390. C2×#447C2×C31semidirect
391. C22×#102C2×C31semidirect
392. #2433C2×C31semidirect
393. #2361C2×C31semidirect
394. #2067C2×C31semidirect
395. #2054C2×C31semidirect
396. #2041C2×C31semidirect
397. #2011C2×C31semidirect
398. #1982C2×C31semidirect
399. #1925C2×C31semidirect
400. #1879C2×C31semidirect
401. #1874C2×C31semidirect
402. #1850C2×C31semidirect
438. C22×C31#459semidirect
462. C22×D8C22×C31semidirect
471. C2×C4×D4C22×C31semidirect
476. C2×#107C22×C31semidirect
477. C2×C4⋊C8C22×C31semidirect
478. C2×C4⋊C8C22×C31semidirect
486. C2×#102C22×C31semidirect
487. C2×#102C22×C31semidirect
488. C2×#102C22×C31semidirect
489. C2×#102C22×C31semidirect
495. #390C22×C31semidirect
496. #389C22×C31semidirect
500. C4×C4⋊C4C22×C31semidirect
502. #340C22×C31semidirect
503. #340C22×C31semidirect
504. #336C22×C31semidirect
505. #336C22×C31semidirect
562. #121D4×C31semidirect
602. #102D4×C31semidirect
608. C31#25076direct (N × H)
728. C22⋊C4D8×C31semidirect
878. C22C31×#459semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4662
C2×C31×#4592
C2×C31×#4472
C22×C31×#1022
C31×#24332
C31×#23612
C31×#20672
C31×#20542
C31×#20412
C31×#20112
C31×#19822
C31×#19252
C31×#18792
C31×#18742
C31×#18502
#2507631