Finite Group Databasebeta

← C31×#24394 #21481153

Subgroups — C31×#24394 #21481153

Order 7936.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#535C211yesmaximal, characteristic
2C2×C31×#468C211yesmaximal, characteristic, complemented
3C2×C31×#465C211yesmaximal, characteristic, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C2×C31×#408C211yesmaximal, characteristic, complemented
6C31×#2616C211yesmaximal, characteristic, complemented
7C31×#2034C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic, complemented
12C31×#1893C211yesmaximal, characteristic, complemented
13C31×#1873C211yesmaximal, characteristic, complemented
14C31×#1854C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic, complemented
21C23×C8×C31C2211yescharacteristic, complemented
22C31×#535—24no—
23C31×#535—24no—
24C2×C31×#127—21no—
25C2×C31×#124—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic, complemented
28C2×C31×C22⋊Q8C2211yescharacteristic, complemented
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C31×#121C2211yescharacteristic
33C2×C31×#120—21no—
34C2×C31×#120—21no—
35C2×C31×#117C2211yescharacteristic
36C31×#468—24no—
37C31×#465—24no—
38C31×#450—24no—
39C2×C31×#107C2211yescharacteristic, complemented
40C2×C31×#106C2211yescharacteristic, complemented
41C2×C31×#103C2211yescharacteristic, complemented
42C2×C31×#103C2211yescharacteristic, complemented
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C31×#408—24no—
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#395—21no—
55C31×#394—21no—
56C31×#394—21no—
57C31×#394—21no—
58C31×#380C2211yescharacteristic
59C31×#380C2211yescharacteristic, complemented
60C31×#380C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C31×#340C2211yescharacteristic, complemented
65C25×C31—21no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—41no—
71C2×#41×C31—41no—
72C22×Q8×C31D411yescharacteristic
73C22×Q8×C31C2311yescharacteristic
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—22no—
79C22×D4×C31—22no—
80C22×D4×C31—21no—
81C22×D4×C31—22no—
82C22×D4×C31—22no—
83C22×D4×C31—41no—
84C22×D4×C31—41no—
85C22×D4×C31D411yescharacteristic
86C22×D4×C31D411yescharacteristic
87C22×D4×C31D411yescharacteristic
88C22×D4×C31C2311yescharacteristic
89C22×D4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—41no—
98C2×SD16×C31—41no—
99C2×M16×C31—22no—
100C2×M16×C31—22no—
101C2×M16×C31—41no—
102C22×C8×C31—22no—
103C22×C8×C31—22no—
104C22×C8×C31—41no—
105C22×C8×C31C2311yescharacteristic
106C22×C8×C31C2311yescharacteristic
107C22×C8×C31C2311yescharacteristic
108C22×C8×C31C2311yescharacteristic
109C31×#127—28no—
110C31×#124—28no—
111C31×C22⋊Q8—22no—
112C31×C22⋊Q8—22no—
113C31×C22⋊Q8—22no—
114C31×C22⋊Q8—22no—
115C31×C22⋊Q8—41no—
116C31×C22⋊Q8—41no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—22no—
123C31×#121D414yes—
124C31×#121D414yes—
125C31×#120—28no—
126C31×#120—28no—
127C31×#117—22no—
128C31×#117—22no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31C2311yescharacteristic
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31—21no—
148C2×C42×C31—21no—
149C31×#107—22no—
150C31×#106—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—41no—
158C31×#102—41no—
159C31×C22⋊C8—22no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8D414yescomplemented
163C31×#95—21no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—24no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—42no—
170C24×C31—42no—
171C24×C31—81no—
172C24×C31—81no—
173C24×C31—81no—
174C24×C31—81no—
175C24×C31C2×D411yescharacteristic
176C24×C31C2×D411yescharacteristic
177C24×C31C2×D411yescharacteristic
178#41×C31—44no—
179#41×C31—44no—
180#41×C31—44no—
181#41×C31—44no—
182C2×Q8×C31—22no—
183C2×Q8×C31—22no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31—21no—
189C2×Q8×C31—21no—
190C2×Q8×C31—41no—
191C2×D4×C31—24no—
192C2×D4×C31—22no—
193C2×D4×C31—22no—
194C2×D4×C31—22no—
195C2×D4×C31—22no—
196C2×D4×C31—24no—
197C2×D4×C31—24no—
198C2×D4×C31—24no—
199C2×D4×C31—24no—
200C2×D4×C31—22no—
201C2×D4×C31—22no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—21no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—44no—
213C2×D4×C31—44no—
214C2×D4×C31—44no—
215C2×D4×C31—44no—
216C2×D4×C31—41no—
217C2×D4×C31—41no—
218C2×D4×C31—41no—
219C2×D4×C31—42no—
220C2×D4×C31—42no—
221C2×D4×C31—81no—
222C2×D4×C31—81no—
223C2×D4×C31—81no—
224C2×D4×C31—81no—
225C2×D4×C31—81no—
226C2×D4×C31—81no—
227C2×D4×C31—81no—
228C2×D4×C31—81no—
229C2×D4×C31C2×D412yes—
230C2×D4×C31C2×D412yes—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
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×C31C2×D411yescharacteristic
252C22×C4×C31C2×D411yescharacteristic
253C22×C4×C31C2×D412yes—
254C22×C4×C31C2×D412yes—
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D412yes—
257C22×C4×C31#4112yes—
258C22×C4×C31C2411yescharacteristic
259SD16×C31—44no—
260SD16×C31—44no—
261M16×C31—44no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31—21no—
268C2×C8×C31—21no—
269C2×C8×C31—21no—
270C2×C8×C31—21no—
271C2×C8×C31—21no—
272C2×C8×C31—44no—
273C2×C8×C31C2×D412yes—
274C2×C8×C31C2×D412yes—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—21no—
280C4⋊C4×C31—21no—
281C4⋊C4×C31—21no—
282C4⋊C4×C31—21no—
283C4⋊C4×C31—42no—
284C4⋊C4×C31—42no—
285C4⋊C4×C31—42no—
286C4⋊C4×C31C2×D412yes—
287C4⋊C4×C31C2×D412yes—
288C22⋊C4×C31—24no—
289C22⋊C4×C31—24no—
290C22⋊C4×C31—24no—
291C22⋊C4×C31—24no—
292C22⋊C4×C31—24no—
293C22⋊C4×C31—42no—
294C22⋊C4×C31—42no—
295C22⋊C4×C31—42no—
296C22⋊C4×C31—81no—
297C22⋊C4×C31—81no—
298C22⋊C4×C31—81no—
299C42×C31—24no—
300#24394C3111yesmaximal, characteristic, direct product factor, Sylow
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—21no—
313C23×C31—22no—
314C23×C31—22no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—21no—
321C23×C31—21no—
322C23×C31—48no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—84no—
336C23×C31—84no—
337C23×C31—84no—
338C23×C31—84no—
339C23×C31—84no—
340C23×C31—84no—
341C23×C31#12012yes—
342C23×C31#12112yes—
343C23×C31C22×D411yescharacteristic
344Q8×C31—44no—
345Q8×C31—41no—
346Q8×C31—41no—
347Q8×C31—41no—
348Q8×C31—41no—
349D4×C31—22no—
350D4×C31—22no—
351D4×C31—22no—
352D4×C31—22no—
353D4×C31—44no—
354D4×C31—44no—
355D4×C31—48no—
356D4×C31—44no—
357D4×C31—41no—
358D4×C31—41no—
359D4×C31—41no—
360D4×C31—41no—
361D4×C31—84no—
362D4×C31—84no—
363D4×C31—84no—
364D4×C31—84no—
365C2×C4×C31—21no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—22no—
376C2×C4×C31—22no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—21no—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31#12012yes—
403C2×C4×C31#12112yes—
404C2×C4×C31C22×D411yescharacteristic
405C2×C4×C31C22×D411yescharacteristic
406C2×C4×C31C22×D411yescharacteristic
407C2×C4×C31C2×#4111yescharacteristic
408C2×C4×C31H(5,𝔽2)11yescharacteristic
409C2×C4×C31H(5,𝔽2)11yescharacteristic
410C8×C31—22no—
411C8×C31—22no—
412C8×C31—41no—
413C8×C31—41no—
414C2×#535C2×C3111yescharacteristic
415C2×#468C2×C3111yescharacteristic, complemented
416C2×#465C2×C3111yescharacteristic, complemented
417C2×#450C2×C3111yescharacteristic, complemented
418C2×#408C2×C3111yescharacteristic, complemented
419#2616C2×C3111yescharacteristic, complemented
420#2034C2×C3111yescharacteristic, complemented
421#2033C2×C3111yescharacteristic, complemented
422#2000C2×C3111yescharacteristic, complemented
423#2000C2×C3111yescharacteristic, complemented
424#1895C2×C3111yescharacteristic, complemented
425#1893C2×C3111yescharacteristic, complemented
426#1873C2×C3111yescharacteristic, complemented
427#1854C2×C3111yescharacteristic, complemented
428#1786C2×C3111yescharacteristic, complemented
429C22×C31—22no—
430C22×C31—22no—
431C22×C31—22no—
432C22×C31—22no—
433C22×C31—22no—
434C22×C31—22no—
435C22×C31—41no—
436C22×C31—41no—
437C22×C31—41no—
438C22×C31—41no—
439C22×C31—41no—
440C22×C31—41no—
441C22×C31—41no—
442C22×C31—41no—
443C22×C31—41no—
444C22×C31—42no—
445C22×C31—42no—
446C22×C31—41no—
447C22×C31—41no—
448C22×C31—41no—
449C22×C31—42no—
450C22×C31—42no—
451C22×C31—41no—
452C22×C31—42no—
453C22×C31—42no—
454C22×C31—41no—
455C22×C31—41no—
456C22×C31—816no—
457C22×C31—81no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31—81no—
463C22×C31—81no—
464C22×C31—81no—
465C22×C31C2×#12011yescharacteristic
466C22×C31C2×#12111yescharacteristic
467C22×C31#53411yescharacteristic
468C22×C31#57611yescharacteristic
469C22×C31#57711yescharacteristic
470C22×C31#57711yescharacteristic
471C22×C31#57711yescharacteristic
472C4×C31—22no—
473C4×C31—22no—
474C4×C31—41no—
475C4×C31—42no—
476C4×C31—42no—
477C4×C31—81no—
478C4×C31—81no—
479C4×C31—81no—
480C4×C31—81no—
481C4×C31D4211yescharacteristic
482C4×C31D4211yescharacteristic
483C4×C31#54611yescharacteristic
484C4×C31#54611yescharacteristic
485C22×#41C22×C3111yescharacteristic
486C23×D4C22×C3111yescharacteristic
487C22×SD16C22×C3111yescharacteristic
488C22×SD16C22×C3111yescharacteristic
489C22×M16C22×C3111yescharacteristic, complemented
490C23×C8C22×C3111yescharacteristic, complemented
491#535—24no—
492#535—24no—
493C2×#127—21no—
494C2×#124—21no—
495C2×C22⋊Q8C22×C3111yescharacteristic
496C2×C22⋊Q8C22×C3111yescharacteristic, complemented
497C2×C22⋊Q8C22×C3111yescharacteristic, complemented
498C2×#121C22×C3111yescharacteristic
499C2×#121C22×C3111yescharacteristic
500C2×#121C22×C3111yescharacteristic
501C2×#121C22×C3111yescharacteristic
502C2×#120—21no—
503C2×#120—21no—
504C2×#117C22×C3111yescharacteristic
505#468—24no—
506#465—24no—
507#450—24no—
508C2×#107C22×C3111yescharacteristic, complemented
509C2×#106C22×C3111yescharacteristic, complemented
510C2×#103C22×C3111yescharacteristic, complemented
511C2×#103C22×C3111yescharacteristic, complemented
512C2×#102C22×C3111yescharacteristic
513C2×#102C22×C3111yescharacteristic
514C2×#102C22×C3111yescharacteristic
515C2×#102C22×C3111yescharacteristic
516C2×#102C22×C3111yescharacteristic
517C2×#102C22×C3111yescharacteristic
518#408—24no—
519C2×C22⋊C8C22×C3111yescharacteristic
520C2×C22⋊C8C22×C3111yescharacteristic
521C2×C22⋊C8C22×C3111yescharacteristic, complemented
522C2×C22⋊C8C22×C3111yescharacteristic, complemented
523#395—21no—
524#394—21no—
525#394—21no—
526#394—21no—
527#380C22×C3111yescharacteristic
528#380C22×C3111yescharacteristic, complemented
529#380C22×C3111yescharacteristic, complemented
530#340C22×C3111yescharacteristic, complemented
531#340C22×C3111yescharacteristic, complemented
532#340C22×C3111yescharacteristic, complemented
533#340C22×C3111yescharacteristic, complemented
534C2×C31—42no—
535C2×C31—42no—
536C2×C31—81no—
537C2×C31—82no—
538C2×C31—82no—
539C2×C31#241011yescharacteristic
540C2×C31#300911yescharacteristic
541C2×C31#301211yescharacteristic
542C2×C31#305711yescharacteristic
543C2×C31#306211yescharacteristic
544C2×C31#319811yescharacteristic
545C2×C31#320011yescharacteristic
546C25—21no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C22×Q8D4×C3111yescharacteristic
554C22×Q8C23×C3111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—21no—
562C22×D4—22no—
563C22×D4—22no—
564C22×D4—41no—
565C22×D4—41no—
566C22×D4D4×C3111yescharacteristic
567C22×D4D4×C3111yescharacteristic
568C22×D4D4×C3111yescharacteristic
569C22×D4C23×C3111yescharacteristic
570C22×D4C23×C3111yescharacteristic
571C23×C4C23×C3111yescharacteristic
572C23×C4C23×C3111yescharacteristic
573C23×C4C23×C3111yescharacteristic
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16—41no—
583C22×C8—22no—
584C22×C8—22no—
585C22×C8—41no—
586C22×C8C23×C3111yescharacteristic
587C22×C8C23×C3111yescharacteristic
588C22×C8C23×C3111yescharacteristic
589C22×C8C23×C3111yescharacteristic
590#127—28no—
591#124—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121D4×C3114yes—
605#121D4×C3114yes—
606#120—28no—
607#120—28no—
608#117—22no—
609#117—22no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4C23×C3111yescharacteristic
614C2×C4⋊C4C23×C3111yescharacteristic
615C2×C4⋊C4C23×C3111yescharacteristic
616C2×C4⋊C4C23×C3111yescharacteristic
617C2×C4⋊C4C23×C3111yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C42—21no—
630#107—22no—
631#106—22no—
632#103—22no—
633#103—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—41no—
639#102—41no—
640C22⋊C8—22no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8D4×C3114yescomplemented
644#95—21no—
645#95—21no—
646#95—21no—
647C31#2439411yescharacteristic, direct product factor, Sylow
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C3111yescharacteristic
658C24C2×D4×C3111yescharacteristic
659C24C2×D4×C3111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C3112yes—
712C2×D4C2×D4×C3112yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C3111yescharacteristic
734C22×C4C2×D4×C3111yescharacteristic
735C22×C4C2×D4×C3112yes—
736C22×C4C2×D4×C3112yes—
737C22×C4C2×D4×C3111yescharacteristic
738C22×C4C2×D4×C3112yes—
739C22×C4#41×C3112yes—
740C22×C4C24×C3111yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C3112yes—
756C2×C8C2×D4×C3112yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C3112yes—
769C4⋊C4C2×D4×C3112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23C31×#12012yes—
823C23C31×#12112yes—
824C23C22×D4×C3111yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4C31×#12012yes—
884C2×C4C31×#12112yes—
885C2×C4C22×D4×C3111yescharacteristic
886C2×C4C22×D4×C3111yescharacteristic
887C2×C4C22×D4×C3111yescharacteristic
888C2×C4C2×#41×C3111yescharacteristic
889C2×C4C31×H(5,𝔽2)11yescharacteristic
890C2×C4C31×H(5,𝔽2)11yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×C31×#12011yescharacteristic
932C22C2×C31×#12111yescharacteristic
933C22C31×#53411yescharacteristic
934C22C31×#57611yescharacteristic
935C22C31×#57711yescharacteristic
936C22C31×#57711yescharacteristic
937C22C31×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C3111yescharacteristic
948C4D42×C3111yescharacteristic
949C4C31×#54611yescharacteristic
950C4C31×#54611yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C31×#241011yescharacteristic
957C2C31×#300911yescharacteristic
958C2C31×#301211yescharacteristic
959C2C31×#305711yescharacteristic
960C2C31×#306211yescharacteristic
961C2C31×#319811yescharacteristic
962C2C31×#320011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#468C2semidirect
3. C2×C31×#465C2semidirect
4. C2×C31×#450C2semidirect
5. C2×C31×#408C2semidirect
6. C31×#2616C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#2000C2semidirect
10. C31×#2000C2semidirect
11. C31×#1895C2semidirect
12. C31×#1893C2semidirect
13. C31×#1873C2semidirect
14. C31×#1854C2semidirect
15. C31×#1786C2semidirect
20. C22×M16×C31C22semidirect
21. C23×C8×C31C22semidirect
27. C2×C31×C22⋊Q8C22semidirect
28. C2×C31×C22⋊Q8C22semidirect
39. C2×C31×#107C22semidirect
40. C2×C31×#106C22semidirect
41. C2×C31×#103C22semidirect
42. C2×C31×#103C22semidirect
52. C2×C31×C22⋊C8C22semidirect
53. C2×C31×C22⋊C8C22semidirect
59. C31×#380C22semidirect
60. C31×#380C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#340C22semidirect
64. C31×#340C22semidirect
162. C31×C22⋊C8D4semidirect
300. #24394C31direct (N × H)
415. C2×#468C2×C31semidirect
416. C2×#465C2×C31semidirect
417. C2×#450C2×C31semidirect
418. C2×#408C2×C31semidirect
419. #2616C2×C31semidirect
420. #2034C2×C31semidirect
421. #2033C2×C31semidirect
422. #2000C2×C31semidirect
423. #2000C2×C31semidirect
424. #1895C2×C31semidirect
425. #1893C2×C31semidirect
426. #1873C2×C31semidirect
427. #1854C2×C31semidirect
428. #1786C2×C31semidirect
489. C22×M16C22×C31semidirect
490. C23×C8C22×C31semidirect
496. C2×C22⋊Q8C22×C31semidirect
497. C2×C22⋊Q8C22×C31semidirect
508. C2×#107C22×C31semidirect
509. C2×#106C22×C31semidirect
510. C2×#103C22×C31semidirect
511. C2×#103C22×C31semidirect
521. C2×C22⋊C8C22×C31semidirect
522. C2×C22⋊C8C22×C31semidirect
528. #380C22×C31semidirect
529. #380C22×C31semidirect
530. #340C22×C31semidirect
531. #340C22×C31semidirect
532. #340C22×C31semidirect
533. #340C22×C31semidirect
643. C22⋊C8D4×C31semidirect
647. C31#24394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5352
C2×C31×#4682
C2×C31×#4652
C2×C31×#4502
C2×C31×#4082
C31×#26162
C31×#20342
C31×#20332
C31×#20002
C31×#18952
C31×#18932
C31×#18732
C31×#18542
C31×#17862
#2439431