Finite Group Databasebeta

← C31×#24362 #21481121

Subgroups — C31×#24362 #21481121

Order 7936.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#135C211yesmaximal, characteristic, complemented
2C2×C31×#464C211yesmaximal, characteristic, complemented
3C2×C31×#460C211yesmaximal, characteristic, complemented
4C2×C31×#449C211yesmaximal, characteristic, complemented
5C31×#2431C211yesmaximal, characteristic, complemented
6C31×#2341C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2012C211yesmaximal, characteristic, complemented
10C31×#2011C211yesmaximal, characteristic, complemented
11C31×#1893C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1850C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C2×C31×#135—24no—
19C2×C31×#135—24no—
20C2×C31×#135—24no—
21C22×Q16×C31C2211yescharacteristic
22C22×SD16×C31C2211yescharacteristic
23C22×SD16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic
25C22×D8×C31C2211yescharacteristic
26C22×D8×C31C2211yescharacteristic
27C23×C8×C31C2211yescharacteristic
28C2×C31×#127C2211yescharacteristic
29C2×C31×#124C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C4×Q8×C31C2211yescharacteristic
32C2×C4×Q8×C31C2211yescharacteristic
33C31×#464—24no—
34C31×#460—24no—
35C31×#449—24no—
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#392—21no—
48C31×#392—21no—
49C31×#391C2211yescharacteristic
50C31×#390—21no—
51C31×#390—21no—
52C31×#390C2211yescharacteristic
53C31×#390C2211yescharacteristic
54C31×#390C2211yescharacteristic
55C31×#386—21no—
56C31×#386—21no—
57C31×#380—21no—
58C31×#380C2211yescharacteristic
59C4×C22⋊C4×C31—21no—
60C4×C22⋊C4×C31C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—22no—
72C2×#41×C31—41no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C2×#41×C31—41no—
76C2×#41×C31D414yescomplemented
77C22×Q8×C31C2311yescharacteristic
78C22×Q8×C31C2311yescharacteristic
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31C2311yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C23×C4×C31—21no—
88C23×C4×C31—21no—
89C23×C4×C31C2311yescharacteristic
90C31×#135—232no—
91C2×Q16×C31—22no—
92C2×Q16×C31—22no—
93C2×Q16×C31D414yescomplemented
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—22no—
100C2×SD16×C31—22no—
101C2×SD16×C31—22no—
102C2×SD16×C31D414yescomplemented
103C2×D8×C31—22no—
104C2×D8×C31—22no—
105C2×D8×C31—22no—
106C2×D8×C31—22no—
107C2×D8×C31—41no—
108C2×D8×C31—41no—
109C22×C8×C31—22no—
110C22×C8×C31—22no—
111C22×C8×C31—22no—
112C22×C8×C31C2311yescharacteristic
113C22×C8×C31C2311yescharacteristic
114C22×C8×C31C2311yescharacteristic
115C22×C8×C31C2311yescharacteristic
116C31×#127—22no—
117C31×#127—41no—
118C31×#124—22no—
119C31×#124—41no—
120C31×#121—22no—
121C31×#121—22no—
122C4×Q8×C31—22no—
123C4×Q8×C31—22no—
124C4×Q8×C31—41no—
125C4×Q8×C31—41no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C4⋊C4×C31C2311yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31D411yescharacteristic
142C2×C22⋊C4×C31D411yescharacteristic
143C2×C42×C31—21no—
144C2×C42×C31—21no—
145C2×C42×C31C2311yescharacteristic
146C2×C42×C31C2311yescharacteristic
147C31×C4⋊C8—22no—
148C31×C4⋊C8—22no—
149C31×#103—22no—
150C31×#103—22no—
151C31×#103—41no—
152C31×#102—22no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—41no—
157C31×C22⋊C8—22no—
158C31×#95—21no—
159C31×#95—21no—
160C31×#95—21no—
161C31×#95D411yescharacteristic
162C31×#95D411yescharacteristic
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31C2×D411yescharacteristic
167#41×C31—28no—
168#41×C31—28no—
169#41×C31—44no—
170#41×C31—44no—
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174#41×C31—44no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31C2×D412yes—
184C2×Q8×C31C2×D412yes—
185C2×Q8×C31C2×D412yes—
186C2×Q8×C31C2×D412yes—
187C2×D4×C31—24no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—81no—
215C2×D4×C31—81no—
216C2×D4×C31—81no—
217C2×D4×C31—81no—
218C2×D4×C31C2×D412yes—
219C2×D4×C31C2×D412yes—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—24no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—42no—
231C22×C4×C31—42no—
232C22×C4×C31—42no—
233C22×C4×C31—42no—
234C22×C4×C31—42no—
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D411yescharacteristic
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D411yescharacteristic
239C22×C4×C31C2×D412yes—
240C22×C4×C31C2×D411yescharacteristic
241C22×C4×C31#4112yes—
242C22×C4×C31C2411yescharacteristic
243Q16×C31—28no—
244SD16×C31—28no—
245SD16×C31—28no—
246SD16×C31—44no—
247D8×C31—28no—
248D8×C31—44no—
249C2×C8×C31—28no—
250C2×C8×C31—21no—
251C2×C8×C31—21no—
252C2×C8×C31—21no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31C2×D412yes—
261C2×C8×C31C2×D412yes—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—42no—
269C4⋊C4×C31—42no—
270C22⋊C4×C31—22no—
271C22⋊C4×C31—41no—
272C22⋊C4×C31—42no—
273C22⋊C4×C31—42no—
274C22⋊C4×C31—42no—
275C22⋊C4×C31—42no—
276C22⋊C4×C31—42no—
277C22⋊C4×C31—81no—
278C22⋊C4×C31—81no—
279C22⋊C4×C31—81no—
280C22⋊C4×C31—81no—
281C22⋊C4×C31—81no—
282C42×C31—21no—
283C42×C31—21no—
284C42×C31—21no—
285C42×C31—21no—
286C42×C31—42no—
287C42×C31—42no—
288#24362C3111yesmaximal, characteristic, direct product factor, Sylow
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—21no—
293C23×C31—21no—
294C23×C31—21no—
295C23×C31—22no—
296C23×C31—22no—
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—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31#12112yes—
317C23×C31C22×D411yescharacteristic
318Q8×C31—22no—
319Q8×C31—22no—
320Q8×C31—22no—
321Q8×C31—22no—
322Q8×C31—22no—
323Q8×C31—41no—
324Q8×C31—41no—
325Q8×C31#12014yes—
326D4×C31—22no—
327D4×C31—22no—
328D4×C31—22no—
329D4×C31—22no—
330D4×C31—48no—
331D4×C31—48no—
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—
343C2×C4×C31—22no—
344C2×C4×C31—21no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—21no—
355C2×C4×C31—21no—
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—21no—
364C2×C4×C31—48no—
365C2×C4×C31—48no—
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—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31#12112yes—
378C2×C4×C31#13512yescomplemented
379C2×C4×C31C22×D411yescharacteristic
380C2×C4×C31C22×D411yescharacteristic
381C2×C4×C31C22×D411yescharacteristic
382C2×C4×C31C2×#4111yescharacteristic
383C2×C4×C31H(5,𝔽2)11yescharacteristic
384C2×C4×C31H(5,𝔽2)11yescharacteristic
385C8×C31—22no—
386C8×C31—22no—
387C8×C31—41no—
388C8×C31—41no—
389C22×#135C2×C3111yescharacteristic, complemented
390C2×#464C2×C3111yescharacteristic, complemented
391C2×#460C2×C3111yescharacteristic, complemented
392C2×#449C2×C3111yescharacteristic, complemented
393#2431C2×C3111yescharacteristic, complemented
394#2341C2×C3111yescharacteristic, complemented
395#2055C2×C3111yescharacteristic, complemented
396#2054C2×C3111yescharacteristic, complemented
397#2012C2×C3111yescharacteristic, complemented
398#2011C2×C3111yescharacteristic, complemented
399#1893C2×C3111yescharacteristic, complemented
400#1880C2×C3111yescharacteristic, complemented
401#1878C2×C3111yescharacteristic, complemented
402#1850C2×C3111yescharacteristic, complemented
403#1788C2×C3111yescharacteristic, complemented
404C22×C31—22no—
405C22×C31—22no—
406C22×C31—22no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—42no—
416C22×C31—42no—
417C22×C31—81no—
418C22×C31—81no—
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×C31C2×#12111yescharacteristic
433C22×C31D4211yescharacteristic
434C22×C31D4211yescharacteristic
435C22×C31C2×#13511yescharacteristic
436C22×C31#57511yescharacteristic
437C22×C31#57611yescharacteristic
438C22×C31#57711yescharacteristic
439C4×C31—22no—
440C4×C31—24no—
441C4×C31—22no—
442C4×C31—42no—
443C4×C31—41no—
444C4×C31—41no—
445C4×C31—41no—
446C4×C31—81no—
447C4×C31—81no—
448C4×C31—81no—
449C4×C31C2×#12011yescharacteristic
450C4×C31#53411yescharacteristic
451C4×C31#54611yescharacteristic
452C4×C31#54611yescharacteristic
453C22×#41C22×C3111yescharacteristic
454C22×#41C22×C3111yescharacteristic
455C2×#135—24no—
456C2×#135—24no—
457C2×#135—24no—
458C22×Q16C22×C3111yescharacteristic
459C22×SD16C22×C3111yescharacteristic
460C22×SD16C22×C3111yescharacteristic
461C22×SD16C22×C3111yescharacteristic
462C22×D8C22×C3111yescharacteristic
463C22×D8C22×C3111yescharacteristic
464C23×C8C22×C3111yescharacteristic
465C2×#127C22×C3111yescharacteristic
466C2×#124C22×C3111yescharacteristic
467C2×#121C22×C3111yescharacteristic
468C2×C4×Q8C22×C3111yescharacteristic
469C2×C4×Q8C22×C3111yescharacteristic
470#464—24no—
471#460—24no—
472#449—24no—
473C2×C4⋊C8C22×C3111yescharacteristic
474C2×C4⋊C8C22×C3111yescharacteristic
475C2×#103C22×C3111yescharacteristic
476C2×#103C22×C3111yescharacteristic
477C2×#103C22×C3111yescharacteristic
478C2×#102C22×C3111yescharacteristic
479C2×#102C22×C3111yescharacteristic
480C2×#102C22×C3111yescharacteristic
481C2×#102C22×C3111yescharacteristic
482C2×#102C22×C3111yescharacteristic
483C2×C22⋊C8C22×C3111yescharacteristic
484#392—21no—
485#392—21no—
486#391C22×C3111yescharacteristic
487#390—21no—
488#390—21no—
489#390C22×C3111yescharacteristic
490#390C22×C3111yescharacteristic
491#390C22×C3111yescharacteristic
492#386—21no—
493#386—21no—
494#380—21no—
495#380C22×C3111yescharacteristic
496C4×C22⋊C4—21no—
497C4×C22⋊C4C22×C3111yescharacteristic
498#340C22×C3111yescharacteristic
499#340C22×C3111yescharacteristic
500#336C22×C3111yescharacteristic
501#336C22×C3111yescharacteristic
502C2×C31—42no—
503C2×C31—82no—
504C2×C31—82no—
505C2×C31—161no—
506C2×C31#241011yescharacteristic
507C2×C31#303511yescharacteristic
508C2×C31#304511yescharacteristic
509C2×C31#326811yescharacteristic
510C2×C31#327111yescharacteristic
511C2×C31#328211yescharacteristic
512C2×C31#328711yescharacteristic
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41D4×C3114yescomplemented
525C22×Q8C23×C3111yescharacteristic
526C22×Q8C23×C3111yescharacteristic
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C23×C3111yescharacteristic
533C22×D4C23×C3111yescharacteristic
534C22×D4C23×C3111yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C23×C3111yescharacteristic
538#135—232no—
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16D4×C3114yescomplemented
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16D4×C3114yescomplemented
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8C23×C3111yescharacteristic
561C22×C8C23×C3111yescharacteristic
562C22×C8C23×C3111yescharacteristic
563C22×C8C23×C3111yescharacteristic
564#127—22no—
565#127—41no—
566#124—22no—
567#124—41no—
568#121—22no—
569#121—22no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—41no—
573C4×Q8—41no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4C23×C3111yescharacteristic
577C2×C4⋊C4C23×C3111yescharacteristic
578C2×C4⋊C4C23×C3111yescharacteristic
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⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C3111yescharacteristic
590C2×C22⋊C4D4×C3111yescharacteristic
591C2×C42—21no—
592C2×C42—21no—
593C2×C42C23×C3111yescharacteristic
594C2×C42C23×C3111yescharacteristic
595C4⋊C8—22no—
596C4⋊C8—22no—
597#103—22no—
598#103—22no—
599#103—41no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—41no—
605C22⋊C8—22no—
606#95—21no—
607#95—21no—
608#95—21no—
609#95D4×C3111yescharacteristic
610#95D4×C3111yescharacteristic
611C31#2436211yescharacteristic, direct product factor, Sylow
612C24—21no—
613C24—21no—
614C24—21no—
615C24C2×D4×C3111yescharacteristic
616#41—28no—
617#41—28no—
618#41—44no—
619#41—44no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×D4×C3112yes—
633C2×Q8C2×D4×C3112yes—
634C2×Q8C2×D4×C3112yes—
635C2×Q8C2×D4×C3112yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
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—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4C2×D4×C3111yescharacteristic
685C22×C4C2×D4×C3111yescharacteristic
686C22×C4C2×D4×C3111yescharacteristic
687C22×C4C2×D4×C3111yescharacteristic
688C22×C4C2×D4×C3112yes—
689C22×C4C2×D4×C3111yescharacteristic
690C22×C4#41×C3112yes—
691C22×C4C24×C3111yescharacteristic
692Q16—28no—
693SD16—28no—
694SD16—28no—
695SD16—44no—
696D8—28no—
697D8—44no—
698C2×C8—28no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8C2×D4×C3112yes—
710C2×C8C2×D4×C3112yes—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C22⋊C4—22no—
720C22⋊C4—41no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—81no—
727C22⋊C4—81no—
728C22⋊C4—81no—
729C22⋊C4—81no—
730C22⋊C4—81no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—42no—
736C42—42no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
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—
764C23C31×#12112yes—
765C23C22×D4×C3111yescharacteristic
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—41no—
772Q8—41no—
773Q8C31×#12014yes—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—48no—
779D4—48no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4—84no—
790D4—84no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4C31×#12112yes—
826C2×C4C31×#13512yescomplemented
827C2×C4C22×D4×C3111yescharacteristic
828C2×C4C22×D4×C3111yescharacteristic
829C2×C4C22×D4×C3111yescharacteristic
830C2×C4C2×#41×C3111yescharacteristic
831C2×C4C31×H(5,𝔽2)11yescharacteristic
832C2×C4C31×H(5,𝔽2)11yescharacteristic
833C8—22no—
834C8—22no—
835C8—41no—
836C8—41no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22C2×C31×#12111yescharacteristic
866C22D42×C3111yescharacteristic
867C22D42×C3111yescharacteristic
868C22C2×C31×#13511yescharacteristic
869C22C31×#57511yescharacteristic
870C22C31×#57611yescharacteristic
871C22C31×#57711yescharacteristic
872C4—22no—
873C4—24no—
874C4—22no—
875C4—42no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4C2×C31×#12011yescharacteristic
883C4C31×#53411yescharacteristic
884C4C31×#54611yescharacteristic
885C4C31×#54611yescharacteristic
886C2—42no—
887C2—82no—
888C2—82no—
889C2—161no—
890C2C31×#241011yescharacteristic
891C2C31×#303511yescharacteristic
892C2C31×#304511yescharacteristic
893C2C31×#326811yescharacteristic
894C2C31×#327111yescharacteristic
895C2C31×#328211yescharacteristic
896C2C31×#328711yescharacteristic
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. C22×C31×#135C2semidirect
2. C2×C31×#464C2semidirect
3. C2×C31×#460C2semidirect
4. C2×C31×#449C2semidirect
5. C31×#2431C2semidirect
6. C31×#2341C2semidirect
7. C31×#2055C2semidirect
8. C31×#2054C2semidirect
9. C31×#2012C2semidirect
10. C31×#2011C2semidirect
11. C31×#1893C2semidirect
12. C31×#1880C2semidirect
13. C31×#1878C2semidirect
14. C31×#1850C2semidirect
15. C31×#1788C2semidirect
76. C2×#41×C31D4semidirect
93. C2×Q16×C31D4semidirect
102. C2×SD16×C31D4semidirect
288. #24362C31direct (N × H)
378. C2×C4×C31#135semidirect
389. C22×#135C2×C31semidirect
390. C2×#464C2×C31semidirect
391. C2×#460C2×C31semidirect
392. C2×#449C2×C31semidirect
393. #2431C2×C31semidirect
394. #2341C2×C31semidirect
395. #2055C2×C31semidirect
396. #2054C2×C31semidirect
397. #2012C2×C31semidirect
398. #2011C2×C31semidirect
399. #1893C2×C31semidirect
400. #1880C2×C31semidirect
401. #1878C2×C31semidirect
402. #1850C2×C31semidirect
403. #1788C2×C31semidirect
524. C2×#41D4×C31semidirect
541. C2×Q16D4×C31semidirect
550. C2×SD16D4×C31semidirect
611. C31#24362direct (N × H)
826. C2×C4C31×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1352
C2×C31×#4642
C2×C31×#4602
C2×C31×#4492
C31×#24312
C31×#23412
C31×#20552
C31×#20542
C31×#20122
C31×#20112
C31×#18932
C31×#18802
C31×#18782
C31×#18502
C31×#17882
#2436231