Finite Group Databasebeta

← C31×#24403 #21481162

Subgroups — C31×#24403 #21481162

Order 7936.

1332 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic
2C2×C31×#473C211yesmaximal, characteristic, complemented
3C2×C31×#471C211yesmaximal, characteristic, complemented
4C31×#3007C211yesmaximal, characteristic, complemented
5C2×C31×#452C211yesmaximal, characteristic, complemented
6C31×#2880C211yesmaximal, characteristic, complemented
7C31×#2052C211yesmaximal, characteristic, complemented
8C31×#2051C211yesmaximal, characteristic, complemented
9C31×#2020C211yesmaximal, characteristic, complemented
10C31×#2019C211yesmaximal, characteristic, complemented
11C31×#1908C211yesmaximal, characteristic, complemented
12C31×#1907C211yesmaximal, characteristic, complemented
13C31×#1901C211yesmaximal, characteristic, complemented
14C31×#1855C211yesmaximal, characteristic, complemented
15C31×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C31×#575—24no—
19C31×#575—24no—
20C2×C31×#137—21no—
21C2×C31×#137C2211yescharacteristic
22C2×C31×#137C2211yescharacteristic
23C2×C31×#137C2211yescharacteristic
24C2×C31×#137C2211yescharacteristic
25C2×C31×AGL(1,ℤ/8)—21no—
26C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
28C2×C31×#135—21no—
29C2×C31×#135—21no—
30C22×Q16×C31C2211yescharacteristic, complemented
31C22×SD16×C31C2211yescharacteristic, complemented
32C2×C31×#131C2211yescharacteristic
33C2×C31×#131C2211yescharacteristic
34C22×M16×C31C2211yescharacteristic
35C2×C31×C22⋊Q8C2211yescharacteristic
36C31×#473—24no—
37C31×#471—24no—
38C31×#452—21no—
39C31×#452—21no—
40C31×#452—21no—
41C31×#452—21no—
42C31×#452—21no—
43C31×#452—21no—
44C31×#451—21no—
45C31×#450—21no—
46C2×C31×#108C2211yescharacteristic, complemented
47C2×C31×#108C2211yescharacteristic, complemented
48C31×#417C2211yescharacteristic
49C31×#417C2211yescharacteristic
50C2×C31×#103C2211yescharacteristic, complemented
51C2×C31×#102C2211yescharacteristic, complemented
52C2×C31×#101C2211yescharacteristic, complemented
53C2×C31×#101C2211yescharacteristic, complemented
54C2×C31×#101C2211yescharacteristic, complemented
55C2×C31×#101C2211yescharacteristic, complemented
56C2×C31×#100C2211yescharacteristic, complemented
57C2×C31×#100C2211yescharacteristic, complemented
58C31×#408—21no—
59C31×#408—21no—
60C31×#408C2211yescharacteristic
61C31×#408C2211yescharacteristic
62C31×#407—21no—
63C31×#407C2211yescharacteristic
64C31×#407C2211yescharacteristic
65C2×C31×C22⋊C8—21no—
66C2×C31×C22⋊C8C2211yescharacteristic
67C31×#343C2211yescharacteristic, complemented
68C31×#343C2211yescharacteristic, complemented
69C31×#341C2211yescharacteristic, complemented
70C31×#341C2211yescharacteristic, complemented
71C2×#41×C31—21no—
72C2×#41×C31—21no—
73C2×#41×C31—22no—
74C2×#41×C31—22no—
75C2×#41×C31—22no—
76C2×#41×C31—22no—
77C2×#41×C31—21no—
78C2×#41×C31—21no—
79C2×#41×C31—21no—
80C2×#41×C31—21no—
81C2×#41×C31—41no—
82C2×#41×C31—41no—
83C2×#41×C31—41no—
84C2×#41×C31—41no—
85C2×#41×C31D411yescharacteristic
86C2×#41×C31D411yescharacteristic
87C2×#41×C31C2311yescharacteristic
88C2×#41×C31C2311yescharacteristic
89C22×Q8×C31D411yescharacteristic
90C22×Q8×C31C2311yescharacteristic
91C22×Q8×C31C2311yescharacteristic
92C22×D4×C31—21no—
93C22×D4×C31—21no—
94C22×D4×C31D411yescharacteristic
95C22×D4×C31C2311yescharacteristic
96C23×C4×C31—21no—
97C23×C4×C31—21no—
98C23×C4×C31C2311yescharacteristic
99C31×#137—28no—
100C31×#137—22no—
101C31×#137—22no—
102C31×#137—22no—
103C31×#137—22no—
104C31×#137—22no—
105C31×#137—41no—
106C31×#137—41no—
107C31×#137D414yes—
108C31×AGL(1,ℤ/8)—28no—
109C31×AGL(1,ℤ/8)—22no—
110C31×AGL(1,ℤ/8)—22no—
111C31×AGL(1,ℤ/8)—22no—
112C31×AGL(1,ℤ/8)D414yes—
113C31×#135—28no—
114C31×#135—28no—
115C2×Q16×C31—21no—
116C2×Q16×C31—21no—
117C2×Q16×C31—21no—
118C2×Q16×C31—21no—
119C2×Q16×C31—22no—
120C2×Q16×C31—21no—
121C2×Q16×C31—21no—
122C2×Q16×C31—41no—
123C2×SD16×C31—21no—
124C2×SD16×C31—21no—
125C2×SD16×C31—21no—
126C2×SD16×C31—21no—
127C2×SD16×C31—21no—
128C2×SD16×C31—21no—
129C2×SD16×C31—22no—
130C2×SD16×C31—21no—
131C2×SD16×C31—21no—
132C2×SD16×C31—41no—
133C2×D8×C31—21no—
134C2×D8×C31—21no—
135C31×#131—22no—
136C31×#131—22no—
137C31×#131—41no—
138C31×#131—41no—
139C2×M16×C31—21no—
140C2×M16×C31—22no—
141C2×M16×C31—22no—
142C2×M16×C31—21no—
143C2×M16×C31—21no—
144C2×M16×C31C2311yescharacteristic
145C2×M16×C31C2311yescharacteristic
146C2×M16×C31C2311yescharacteristic
147C2×M16×C31C2311yescharacteristic
148C2×M16×C31C2311yescharacteristic
149C2×M16×C31C2311yescharacteristic
150C22×C8×C31—21no—
151C22×C8×C31—21no—
152C22×C8×C31—21no—
153C22×C8×C31C2311yescharacteristic
154C22×C8×C31C2311yescharacteristic
155C31×C22⋊Q8—21no—
156C31×C22⋊Q8—21no—
157C31×C22⋊Q8—21no—
158C31×C22⋊Q8—21no—
159C2×C4⋊C4×C31—21no—
160C2×C4⋊C4×C31C2311yescharacteristic
161C2×C22⋊C4×C31—21no—
162C31×#108—22no—
163C31×#108—22no—
164C31×#103—21no—
165C31×#103—21no—
166C31×#103—21no—
167C31×#103—21no—
168C31×#102—21no—
169C31×#102—21no—
170C31×#102—21no—
171C31×#102—21no—
172C31×#101—22no—
173C31×#101—22no—
174C31×#101—22no—
175C31×#101—41no—
176C31×#100—22no—
177C31×#100—41no—
178C31×C22⋊C8—21no—
179C31×C22⋊C8—21no—
180C31×C22⋊C8—21no—
181C31×C22⋊C8—21no—
182C31×C22⋊C8—21no—
183C31×C22⋊C8—21no—
184C31×C22⋊C8—21no—
185C31×C22⋊C8—21no—
186C31×C22⋊C8D411yescharacteristic
187C31×C22⋊C8D411yescharacteristic
188C31×C22⋊C8D411yescharacteristic
189C31×C22⋊C8D411yescharacteristic
190C24×C31—21no—
191C24×C31—21no—
192C24×C31#4111yescharacteristic
193#41×C31—21no—
194#41×C31—21no—
195#41×C31—24no—
196#41×C31—24no—
197#41×C31—22no—
198#41×C31—22no—
199#41×C31—21no—
200#41×C31—21no—
201#41×C31—21no—
202#41×C31—21no—
203#41×C31—42no—
204#41×C31—42no—
205#41×C31—41no—
206#41×C31—41no—
207#41×C31—42no—
208#41×C31—42no—
209#41×C31—42no—
210#41×C31—42no—
211#41×C31—42no—
212#41×C31—42no—
213#41×C31—42no—
214#41×C31—42no—
215#41×C31C2×D412yes—
216#41×C31C2×D412yes—
217C2×Q8×C31—21no—
218C2×Q8×C31—21no—
219C2×Q8×C31—22no—
220C2×Q8×C31—21no—
221C2×Q8×C31—21no—
222C2×Q8×C31—21no—
223C2×Q8×C31—21no—
224C2×Q8×C31—21no—
225C2×Q8×C31—21no—
226C2×Q8×C31—21no—
227C2×Q8×C31—21no—
228C2×Q8×C31—21no—
229C2×Q8×C31—21no—
230C2×Q8×C31—41no—
231C2×Q8×C31C2×D412yes—
232C2×Q8×C31C2×D411yescharacteristic
233C2×Q8×C31C2×D411yescharacteristic
234C2×D4×C31—21no—
235C2×D4×C31—22no—
236C2×D4×C31—21no—
237C2×D4×C31—21no—
238C2×D4×C31—21no—
239C2×D4×C31—21no—
240C2×D4×C31—21no—
241C2×D4×C31—21no—
242C2×D4×C31—21no—
243C2×D4×C31—21no—
244C2×D4×C31—21no—
245C2×D4×C31—41no—
246C2×D4×C31—42no—
247C2×D4×C31—42no—
248C2×D4×C31—42no—
249C2×D4×C31—42no—
250C2×D4×C31—41no—
251C2×D4×C31—41no—
252C2×D4×C31C2×D412yes—
253C2×D4×C31C2×D411yescharacteristic
254C2×D4×C31C2×D411yescharacteristic
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—42no—
268C22×C4×C31—42no—
269C22×C4×C31—42no—
270C22×C4×C31—42no—
271C22×C4×C31—41no—
272C22×C4×C31—41no—
273C22×C4×C31C2×D411yescharacteristic
274C22×C4×C31C2×D411yescharacteristic
275C22×C4×C31C2×D411yescharacteristic
276C22×C4×C31C2×D411yescharacteristic
277C22×C4×C31#4111yescharacteristic
278C22×C4×C31C2411yescharacteristic
279Q16×C31—24no—
280Q16×C31—24no—
281Q16×C31—42no—
282Q16×C31—42no—
283Q16×C31—42no—
284Q16×C31—42no—
285SD16×C31—24no—
286SD16×C31—24no—
287SD16×C31—24no—
288SD16×C31—24no—
289SD16×C31—42no—
290SD16×C31—42no—
291SD16×C31—42no—
292SD16×C31—42no—
293D8×C31—24no—
294D8×C31—24no—
295M16×C31—24no—
296M16×C31—21no—
297M16×C31—21no—
298M16×C31—21no—
299M16×C31—21no—
300M16×C31—21no—
301M16×C31—21no—
302M16×C31—21no—
303M16×C31—21no—
304M16×C31—21no—
305M16×C31—21no—
306M16×C31—42no—
307M16×C31—42no—
308M16×C31C2×D412yes—
309M16×C31C2×D412yes—
310C2×C8×C31—24no—
311C2×C8×C31—21no—
312C2×C8×C31—21no—
313C2×C8×C31—21no—
314C2×C8×C31—21no—
315C2×C8×C31—21no—
316C2×C8×C31—21no—
317C2×C8×C31—21no—
318C2×C8×C31—21no—
319C2×C8×C31—21no—
320C2×C8×C31—21no—
321C2×C8×C31—42no—
322C2×C8×C31—42no—
323C2×C8×C31C2×D411yescharacteristic
324C2×C8×C31C2×D411yescharacteristic
325C2×C8×C31C2×D411yescharacteristic
326C2×C8×C31C2×D411yescharacteristic
327C4⋊C4×C31—21no—
328C4⋊C4×C31—21no—
329C4⋊C4×C31—41no—
330C4⋊C4×C31—41no—
331C22⋊C4×C31—41no—
332C22⋊C4×C31—41no—
333#24403C3111yesmaximal, characteristic, direct product factor, Sylow
334C23×C31—21no—
335C23×C31—21no—
336C23×C31—21no—
337C23×C31—21no—
338C23×C31—22no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—42no—
342C23×C31—42no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—81no—
346C23×C31—81no—
347C23×C31—81no—
348C23×C31#12111yescharacteristic
349C23×C31#12111yescharacteristic
350C23×C31C2×#4111yescharacteristic
351Q8×C31—21no—
352Q8×C31—21no—
353Q8×C31—22no—
354Q8×C31—21no—
355Q8×C31—22no—
356Q8×C31—42no—
357Q8×C31—41no—
358Q8×C31—41no—
359Q8×C31—41no—
360Q8×C31—41no—
361Q8×C31—41no—
362Q8×C31—41no—
363Q8×C31#12012yes—
364D4×C31—22no—
365D4×C31—22no—
366D4×C31—21no—
367D4×C31—22no—
368D4×C31—21no—
369D4×C31—21no—
370D4×C31—22no—
371D4×C31—42no—
372D4×C31—42no—
373D4×C31—42no—
374D4×C31—44no—
375D4×C31—44no—
376D4×C31—41no—
377D4×C31—41no—
378D4×C31—41no—
379D4×C31—41no—
380D4×C31#12012yes—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—21no—
385C2×C4×C31—21no—
386C2×C4×C31—21no—
387C2×C4×C31—21no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—21no—
391C2×C4×C31—21no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
395C2×C4×C31—22no—
396C2×C4×C31—42no—
397C2×C4×C31—42no—
398C2×C4×C31—42no—
399C2×C4×C31—44no—
400C2×C4×C31—44no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—81no—
410C2×C4×C31#12111yescharacteristic
411C2×C4×C31#12111yescharacteristic
412C2×C4×C31C22×D411yescharacteristic
413C2×C4×C31C22×D411yescharacteristic
414C2×C4×C31C22×D411yescharacteristic
415C2×C4×C31C22×D411yescharacteristic
416C2×C4×C31H(5,𝔽2)11yescharacteristic
417C2×C4×C31H(5,𝔽2)11yescharacteristic
418C8×C31—22no—
419C8×C31—22no—
420C8×C31—21no—
421C8×C31—21no—
422C8×C31—21no—
423C8×C31—21no—
424C8×C31—41no—
425C8×C31—41no—
426C8×C31—41no—
427C8×C31—41no—
428C2×#575C2×C3111yescharacteristic
429C2×#473C2×C3111yescharacteristic, complemented
430C2×#471C2×C3111yescharacteristic, complemented
431#3007C2×C3111yescharacteristic, complemented
432C2×#452C2×C3111yescharacteristic, complemented
433#2880C2×C3111yescharacteristic, complemented
434#2052C2×C3111yescharacteristic, complemented
435#2051C2×C3111yescharacteristic, complemented
436#2020C2×C3111yescharacteristic, complemented
437#2019C2×C3111yescharacteristic, complemented
438#1908C2×C3111yescharacteristic, complemented
439#1907C2×C3111yescharacteristic, complemented
440#1901C2×C3111yescharacteristic, complemented
441#1855C2×C3111yescharacteristic, complemented
442#1785C2×C3111yescharacteristic, complemented
443C22×C31—21no—
444C22×C31—21no—
445C22×C31—21no—
446C22×C31—21no—
447C22×C31—22no—
448C22×C31—21no—
449C22×C31—21no—
450C22×C31—21no—
451C22×C31—21no—
452C22×C31—41no—
453C22×C31—41no—
454C22×C31—41no—
455C22×C31—42no—
456C22×C31—41no—
457C22×C31—41no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—82no—
461C22×C31—82no—
462C22×C31—84no—
463C22×C31—81no—
464C22×C31—81no—
465C22×C31C2×#12111yescharacteristic
466C22×C31#54611yescharacteristic
467C22×C31#54611yescharacteristic
468C4×C31—21no—
469C4×C31—21no—
470C4×C31—22no—
471C4×C31—41no—
472C4×C31—42no—
473C4×C31—81no—
474C4×C31—81no—
475C4×C31C2×#12011yescharacteristic
476C4×C31#53411yescharacteristic
477C4×C31D4211yescharacteristic
478C4×C31D4211yescharacteristic
479C22×#41C22×C3111yescharacteristic
480C22×#41C22×C3111yescharacteristic
481#575—24no—
482#575—24no—
483C2×#137—21no—
484C2×#137C22×C3111yescharacteristic
485C2×#137C22×C3111yescharacteristic
486C2×#137C22×C3111yescharacteristic
487C2×#137C22×C3111yescharacteristic
488C2×AGL(1,ℤ/8)—21no—
489C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
490C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
491C2×#135—21no—
492C2×#135—21no—
493C22×Q16C22×C3111yescharacteristic, complemented
494C22×SD16C22×C3111yescharacteristic, complemented
495C2×#131C22×C3111yescharacteristic
496C2×#131C22×C3111yescharacteristic
497C22×M16C22×C3111yescharacteristic
498C2×C22⋊Q8C22×C3111yescharacteristic
499#473—24no—
500#471—24no—
501#452—21no—
502#452—21no—
503#452—21no—
504#452—21no—
505#452—21no—
506#452—21no—
507#451—21no—
508#450—21no—
509C2×#108C22×C3111yescharacteristic, complemented
510C2×#108C22×C3111yescharacteristic, complemented
511#417C22×C3111yescharacteristic
512#417C22×C3111yescharacteristic
513C2×#103C22×C3111yescharacteristic, complemented
514C2×#102C22×C3111yescharacteristic, complemented
515C2×#101C22×C3111yescharacteristic, complemented
516C2×#101C22×C3111yescharacteristic, complemented
517C2×#101C22×C3111yescharacteristic, complemented
518C2×#101C22×C3111yescharacteristic, complemented
519C2×#100C22×C3111yescharacteristic, complemented
520C2×#100C22×C3111yescharacteristic, complemented
521#408—21no—
522#408—21no—
523#408C22×C3111yescharacteristic
524#408C22×C3111yescharacteristic
525#407—21no—
526#407C22×C3111yescharacteristic
527#407C22×C3111yescharacteristic
528C2×C22⋊C8—21no—
529C2×C22⋊C8C22×C3111yescharacteristic
530#343C22×C3111yescharacteristic, complemented
531#343C22×C3111yescharacteristic, complemented
532#341C22×C3111yescharacteristic, complemented
533#341C22×C3111yescharacteristic, complemented
534C2×C31—21no—
535C2×C31—21no—
536C2×C31—41no—
537C2×C31—41no—
538C2×C31—42no—
539C2×C31—81no—
540C2×C31—82no—
541C2×C31#241011yescharacteristic
542C2×C31#306711yescharacteristic
543C2×C31#306911yescharacteristic
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—41no—
555C2×#41—41no—
556C2×#41—41no—
557C2×#41—41no—
558C2×#41D4×C3111yescharacteristic
559C2×#41D4×C3111yescharacteristic
560C2×#41C23×C3111yescharacteristic
561C2×#41C23×C3111yescharacteristic
562C22×Q8D4×C3111yescharacteristic
563C22×Q8C23×C3111yescharacteristic
564C22×Q8C23×C3111yescharacteristic
565C22×D4—21no—
566C22×D4—21no—
567C22×D4D4×C3111yescharacteristic
568C22×D4C23×C3111yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C3111yescharacteristic
572#137—28no—
573#137—22no—
574#137—22no—
575#137—22no—
576#137—22no—
577#137—22no—
578#137—41no—
579#137—41no—
580#137D4×C3114yes—
581AGL(1,ℤ/8)—28no—
582AGL(1,ℤ/8)—22no—
583AGL(1,ℤ/8)—22no—
584AGL(1,ℤ/8)—22no—
585AGL(1,ℤ/8)D4×C3114yes—
586#135—28no—
587#135—28no—
588C2×Q16—21no—
589C2×Q16—21no—
590C2×Q16—22no—
591C2×Q16—21no—
592C2×Q16—21no—
593C2×Q16—21no—
594C2×Q16—21no—
595C2×Q16—41no—
596C2×SD16—21no—
597C2×SD16—21no—
598C2×SD16—21no—
599C2×SD16—21no—
600C2×SD16—22no—
601C2×SD16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—41no—
606C2×D8—21no—
607C2×D8—21no—
608#131—22no—
609#131—22no—
610#131—41no—
611#131—41no—
612C2×M16—21no—
613C2×M16—22no—
614C2×M16—22no—
615C2×M16—21no—
616C2×M16—21no—
617C2×M16C23×C3111yescharacteristic
618C2×M16C23×C3111yescharacteristic
619C2×M16C23×C3111yescharacteristic
620C2×M16C23×C3111yescharacteristic
621C2×M16C23×C3111yescharacteristic
622C2×M16C23×C3111yescharacteristic
623C22×C8—21no—
624C22×C8—21no—
625C22×C8—21no—
626C22×C8C23×C3111yescharacteristic
627C22×C8C23×C3111yescharacteristic
628C22⋊Q8—21no—
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4C23×C3111yescharacteristic
634C2×C22⋊C4—21no—
635#108—22no—
636#108—22no—
637#103—21no—
638#103—21no—
639#103—21no—
640#103—21no—
641#102—21no—
642#102—21no—
643#102—21no—
644#102—21no—
645#101—22no—
646#101—22no—
647#101—22no—
648#101—41no—
649#100—22no—
650#100—41no—
651C22⋊C8—21no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—21no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—21no—
658C22⋊C8—21no—
659C22⋊C8D4×C3111yescharacteristic
660C22⋊C8D4×C3111yescharacteristic
661C22⋊C8D4×C3111yescharacteristic
662C22⋊C8D4×C3111yescharacteristic
663C31#2440311yescharacteristic, direct product factor, Sylow
664C24—21no—
665C24—21no—
666C24#41×C3111yescharacteristic
667#41—21no—
668#41—21no—
669#41—24no—
670#41—24no—
671#41—22no—
672#41—22no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—21no—
677#41—42no—
678#41—42no—
679#41—41no—
680#41—41no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41—42no—
687#41—42no—
688#41—42no—
689#41C2×D4×C3112yes—
690#41C2×D4×C3112yes—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—41no—
705C2×Q8C2×D4×C3112yes—
706C2×Q8C2×D4×C3111yescharacteristic
707C2×Q8C2×D4×C3111yescharacteristic
708C2×D4—21no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—41no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4C2×D4×C3112yes—
727C2×D4C2×D4×C3111yescharacteristic
728C2×D4C2×D4×C3111yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4C2×D4×C3111yescharacteristic
748C22×C4C2×D4×C3111yescharacteristic
749C22×C4C2×D4×C3111yescharacteristic
750C22×C4C2×D4×C3111yescharacteristic
751C22×C4#41×C3111yescharacteristic
752C22×C4C24×C3111yescharacteristic
753Q16—24no—
754Q16—24no—
755Q16—42no—
756Q16—42no—
757Q16—42no—
758Q16—42no—
759SD16—24no—
760SD16—24no—
761SD16—24no—
762SD16—24no—
763SD16—42no—
764SD16—42no—
765SD16—42no—
766SD16—42no—
767D8—24no—
768D8—24no—
769M16—24no—
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—21no—
779M16—21no—
780M16—42no—
781M16—42no—
782M16C2×D4×C3112yes—
783M16C2×D4×C3112yes—
784C2×C8—24no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—42no—
796C2×C8—42no—
797C2×C8C2×D4×C3111yescharacteristic
798C2×C8C2×D4×C3111yescharacteristic
799C2×C8C2×D4×C3111yescharacteristic
800C2×C8C2×D4×C3111yescharacteristic
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—41no—
804C4⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—41no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23C31×#12111yescharacteristic
822C23C31×#12111yescharacteristic
823C23C2×#41×C3111yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—22no—
827Q8—21no—
828Q8—22no—
829Q8—42no—
830Q8—41no—
831Q8—41no—
832Q8—41no—
833Q8—41no—
834Q8—41no—
835Q8—41no—
836Q8C31×#12012yes—
837D4—22no—
838D4—22no—
839D4—21no—
840D4—22no—
841D4—21no—
842D4—21no—
843D4—22no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4C31×#12012yes—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—44no—
873C2×C4—44no—
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—81no—
883C2×C4C31×#12111yescharacteristic
884C2×C4C31×#12111yescharacteristic
885C2×C4C22×D4×C3111yescharacteristic
886C2×C4C22×D4×C3111yescharacteristic
887C2×C4C22×D4×C3111yescharacteristic
888C2×C4C22×D4×C3111yescharacteristic
889C2×C4C31×H(5,𝔽2)11yescharacteristic
890C2×C4C31×H(5,𝔽2)11yescharacteristic
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—41no—
898C8—41no—
899C8—41no—
900C8—41no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—22no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—81no—
917C22—81no—
918C22—82no—
919C22—82no—
920C22—84no—
921C22—81no—
922C22—81no—
923C22C2×C31×#12111yescharacteristic
924C22C31×#54611yescharacteristic
925C22C31×#54611yescharacteristic
926C4—21no—
927C4—21no—
928C4—22no—
929C4—41no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×C31×#12011yescharacteristic
934C4C31×#53411yescharacteristic
935C4D42×C3111yescharacteristic
936C4D42×C3111yescharacteristic
937C2—21no—
938C2—21no—
939C2—41no—
940C2—41no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C31×#241011yescharacteristic
945C2C31×#306711yescharacteristic
946C2C31×#306911yescharacteristic
subgroupG/H
center, socleC22×C31C2×#121
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#473C2semidirect
3. C2×C31×#471C2semidirect
4. C31×#3007C2semidirect
5. C2×C31×#452C2semidirect
6. C31×#2880C2semidirect
7. C31×#2052C2semidirect
8. C31×#2051C2semidirect
9. C31×#2020C2semidirect
10. C31×#2019C2semidirect
11. C31×#1908C2semidirect
12. C31×#1907C2semidirect
13. C31×#1901C2semidirect
14. C31×#1855C2semidirect
15. C31×#1785C2semidirect
30. C22×Q16×C31C22semidirect
31. C22×SD16×C31C22semidirect
46. C2×C31×#108C22semidirect
47. C2×C31×#108C22semidirect
50. C2×C31×#103C22semidirect
51. C2×C31×#102C22semidirect
52. C2×C31×#101C22semidirect
53. C2×C31×#101C22semidirect
54. C2×C31×#101C22semidirect
55. C2×C31×#101C22semidirect
56. C2×C31×#100C22semidirect
57. C2×C31×#100C22semidirect
67. C31×#343C22semidirect
68. C31×#343C22semidirect
69. C31×#341C22semidirect
70. C31×#341C22semidirect
333. #24403C31direct (N × H)
429. C2×#473C2×C31semidirect
430. C2×#471C2×C31semidirect
431. #3007C2×C31semidirect
432. C2×#452C2×C31semidirect
433. #2880C2×C31semidirect
434. #2052C2×C31semidirect
435. #2051C2×C31semidirect
436. #2020C2×C31semidirect
437. #2019C2×C31semidirect
438. #1908C2×C31semidirect
439. #1907C2×C31semidirect
440. #1901C2×C31semidirect
441. #1855C2×C31semidirect
442. #1785C2×C31semidirect
493. C22×Q16C22×C31semidirect
494. C22×SD16C22×C31semidirect
509. C2×#108C22×C31semidirect
510. C2×#108C22×C31semidirect
513. C2×#103C22×C31semidirect
514. C2×#102C22×C31semidirect
515. C2×#101C22×C31semidirect
516. C2×#101C22×C31semidirect
517. C2×#101C22×C31semidirect
518. C2×#101C22×C31semidirect
519. C2×#100C22×C31semidirect
520. C2×#100C22×C31semidirect
530. #343C22×C31semidirect
531. #343C22×C31semidirect
532. #341C22×C31semidirect
533. #341C22×C31semidirect
663. C31#24403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5752
C2×C31×#4732
C2×C31×#4712
C31×#30072
C2×C31×#4522
C31×#28802
C31×#20522
C31×#20512
C31×#20202
C31×#20192
C31×#19082
C31×#19072
C31×#19012
C31×#18552
C31×#17852
#2440331