Finite Group Databasebeta

← C31×#34294 #21491053

Subgroups — C31×#34294 #21491053

Order 7936.

3112 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#548C211yesmaximal, characteristic
2C2×C31×#520C211yesmaximal, characteristic, complemented
3C22×C4×Q8×C31C211yesmaximal, characteristic, complemented
4C31×#2367C213yesmaximal, complemented
5C31×#2361C213yesmaximal, complemented
6C31×#2360C213yesmaximal, complemented
7Q8×C4⋊C4×C31C211yesmaximal, characteristic, complemented
8D4×C4⋊C4×C31C213yesmaximal, complemented
9C31×#2341C211yesmaximal, characteristic, complemented
10Q8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
11C31×#2326C213yesmaximal, complemented
12C31×#2323C213yesmaximal, complemented
13C4×C31×#121C213yesmaximal, complemented
14C31×#2290C213yesmaximal, complemented
15C31×#2276C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C31×#548C4116yescomplemented
19C2×C31×#124C2213yes—
20C2×C31×C22⋊Q8C2213yes—
21C2×C31×#121C2213yes—
22C31×#520—28no—
23C2×C4×Q8×C31—28no—
24C2×C4×Q8×C31C2213yes—
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×Q8×C31C2213yes—
29C2×C4×Q8×C31C2211yescharacteristic
30C2×C4×Q8×C31C2211yescharacteristic
31C2×C4×D4×C31C2213yes—
32C2×C4×D4×C31C2213yes—
33C2×C4×D4×C31C2216yes—
34C2×C4×D4×C31C2213yes—
35C2×C31×#117C2213yes—
36C22×C4⋊C4×C31C2213yes—
37C22×C4⋊C4×C31C2213yes—
38C22×C42×C31C2213yes—
39C31×#391C2213yes—
40C31×#391C2213yes—
41C31×#390C2213yes—
42C31×#390C2213yes—
43C31×#389C2216yes—
44C31×#389C2213yes—
45C31×#389C2213yes—
46C31×#388C2216yes—
47C31×#388C2216yes—
48C31×#388C2213yes—
49C31×#388C2213yes—
50C31×#387C2213yes—
51C31×#387C2213yes—
52C31×#386C2213yes—
53C31×#386C2213yes—
54C31×#385C2216yes—
55C31×#385C2216yes—
56C31×#385C2213yes—
57C31×#385C2211yescharacteristic
58C31×#384C2213yes—
59C31×#380C2213yes—
60C31×#380C2213yes—
61C4×C4⋊C4×C31C2213yes—
62C4×C4⋊C4×C31C2213yes—
63C4×C4⋊C4×C31C2213yes—
64C4×C4⋊C4×C31C2213yes—
65C4×C22⋊C4×C31C2213yes—
66C4×C22⋊C4×C31C2213yes—
67C4×C22⋊C4×C31C2216yes—
68C31×#376C2213yes—
69C2×#41×C31—24no—
70C2×#41×C31—24no—
71C2×#41×C31C2×C418yescomplemented
72C22×Q8×C31—24no—
73C22×Q8×C31—24no—
74C22×Q8×C31C2×C418yescomplemented
75C22×Q8×C31C2313yes—
76C22×Q8×C31C2311yescharacteristic
77C22×D4×C31C2313yes—
78C22×D4×C31C2313yes—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2313yes—
81C23×C4×C31C2313yes—
82C23×C4×C31C2313yes—
83C23×C4×C31C2316yes—
84C31×#124C2×C4124yescomplemented
85C31×C22⋊Q8C2×C4124yescomplemented
86C31×#121C2×C4124yescomplemented
87C4×Q8×C31—24no—
88C4×Q8×C31—24no—
89C4×Q8×C31—24no—
90C4×Q8×C31—212no—
91C4×Q8×C31—212no—
92C4×Q8×C31C2×C418yescomplemented
93C4×Q8×C31D418yescomplemented
94C4×D4×C31—212no—
95C4×D4×C31—212no—
96C4×D4×C31—412no—
97C4×D4×C31C2×C4124yescomplemented
98C31×#117—212no—
99C2×C4⋊C4×C31—212no—
100C2×C4⋊C4×C31—212no—
101C2×C4⋊C4×C31C2313yes—
102C2×C4⋊C4×C31C2313yes—
103C2×C4⋊C4×C31C2313yes—
104C2×C4⋊C4×C31C2316yes—
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2313yes—
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2316yes—
109C2×C4⋊C4×C31C2313yes—
110C2×C4⋊C4×C31C2313yes—
111C2×C4⋊C4×C31C2313yes—
112C2×C4⋊C4×C31C2313yes—
113C2×C22⋊C4×C31C2313yes—
114C2×C22⋊C4×C31C2313yes—
115C2×C22⋊C4×C31C2313yes—
116C2×C22⋊C4×C31C2311yescharacteristic
117C2×C22⋊C4×C31C2313yes—
118C2×C22⋊C4×C31C2316yes—
119C2×C22⋊C4×C31C2313yes—
120C2×C22⋊C4×C31C2311yescharacteristic
121C2×C22⋊C4×C31C2313yes—
122C2×C22⋊C4×C31C2316yes—
123C2×C42×C31—212no—
124C2×C42×C31C2313yes—
125C2×C42×C31C2313yes—
126C2×C42×C31C2313yes—
127C2×C42×C31C2313yes—
128C2×C42×C31C2313yes—
129C2×C42×C31C2316yes—
130C2×C42×C31C2313yes—
131C2×C42×C31C2313yes—
132C31×#95C2311yescharacteristic
133C31×#95C2313yes—
134C31×#95C2313yes—
135C31×#95C2313yes—
136C31×#95C2311yescharacteristic
137C31×#95C2313yes—
138C31×#95C2313yes—
139C31×#95C2316yes—
140C31×#95C2313yes—
141C31×#95C2313yes—
142C31×#95C2313yes—
143C24×C31C2413yes—
144C24×C31C2411yescharacteristic
145#41×C31—232no—
146C2×Q8×C31—232no—
147C2×Q8×C31—26no—
148C2×Q8×C31—26no—
149C2×Q8×C31C22×C4112yes—
150C2×Q8×C31C22×C414yes—
151C2×Q8×C31C2×D414yes—
152C2×Q8×C31#4114yes—
153C2×D4×C31—26no—
154C2×D4×C31—26no—
155C2×D4×C31—26no—
156C2×D4×C31—26no—
157C2×D4×C31C22×C4112yes—
158C2×D4×C31C22×C4112yes—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—26no—
162C22×C4×C31—26no—
163C22×C4×C31—26no—
164C22×C4×C31—26no—
165C22×C4×C31—22no—
166C22×C4×C31—26no—
167C22×C4×C31—26no—
168C22×C4×C31—212no—
169C22×C4×C31—43no—
170C22×C4×C31—46no—
171C22×C4×C31—46no—
172C22×C4×C31C22×C4112yes—
173C22×C4×C31C22×C4112yes—
174C22×C4×C31C2411yescharacteristic
175C22×C4×C31C2411yescharacteristic
176C22×C4×C31C2413yes—
177C22×C4×C31C2413yes—
178C22×C4×C31C2413yes—
179C22×C4×C31C2411yescharacteristic
180C22×C4×C31C2413yes—
181C22×C4×C31C2413yes—
182C22×C4×C31C2411yescharacteristic
183C22×C4×C31C2411yescharacteristic
184C22×C4×C31C2413yes—
185C22×C4×C31C2411yescharacteristic
186C22×C4×C31C2413yes—
187C4⋊C4×C31—26no—
188C4⋊C4×C31—26no—
189C4⋊C4×C31—212no—
190C4⋊C4×C31—26no—
191C4⋊C4×C31—22no—
192C4⋊C4×C31—26no—
193C4⋊C4×C31—22no—
194C4⋊C4×C31—43no—
195C4⋊C4×C31—46no—
196C4⋊C4×C31C22×C4112yes—
197C4⋊C4×C31C22×C4112yes—
198C4⋊C4×C31C2×D4112yes—
199C22⋊C4×C31—26no—
200C22⋊C4×C31—22no—
201C22⋊C4×C31—26no—
202C22⋊C4×C31—26no—
203C22⋊C4×C31—26no—
204C22⋊C4×C31—43no—
205C22⋊C4×C31—46no—
206C22⋊C4×C31C22×C414yes—
207C22⋊C4×C31C22×C4112yes—
208C22⋊C4×C31C22×C4124yes—
209C42×C31—26no—
210C42×C31—26no—
211C42×C31—26no—
212C42×C31—26no—
213C42×C31—26no—
214C42×C31—46no—
215C42×C31C22×C4112yes—
216C42×C31C2×D4112yes—
217#34294C3111yesmaximal, characteristic, direct product factor, Sylow
218C23×C31—21no—
219C23×C31—21no—
220C23×C31—21no—
221C23×C31—21no—
222C23×C31—23no—
223C23×C31—23no—
224C23×C31—23no—
225C23×C31—23no—
226C23×C31—23no—
227C23×C31—23no—
228C23×C31C23×C416yes—
229C23×C31C23×C412yes—
230C23×C31H(5,𝔽2)12yes—
231C23×C312−1+412yes—
232C23×C31C2511yescharacteristic
233Q8×C31—224no—
234Q8×C31C4×D4116yescomplemented
235D4×C31—224no—
236D4×C31—224no—
237C2×C4×C31—28no—
238C2×C4×C31—21no—
239C2×C4×C31—23no—
240C2×C4×C31—21no—
241C2×C4×C31—21no—
242C2×C4×C31—23no—
243C2×C4×C31—23no—
244C2×C4×C31—23no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—23no—
250C2×C4×C31—21no—
251C2×C4×C31—23no—
252C2×C4×C31—224no—
253C2×C4×C31—224no—
254C2×C4×C31—21no—
255C2×C4×C31—23no—
256C2×C4×C31—23no—
257C2×C4×C31—21no—
258C2×C4×C31—23no—
259C2×C4×C31—23no—
260C2×C4×C31—23no—
261C2×C4×C31—23no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—23no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—23no—
268C2×C4×C31—23no—
269C2×C4×C31—412no—
270C2×C4×C31—812no—
271C2×C4×C31C23×C412yes—
272C2×C4×C31C23×C416yes—
273C2×C4×C31C23×C416yes—
274C2×C4×C31C23×C412yes—
275C2×C4×C31C23×C416yes—
276C2×C4×C31C22×D412yes—
277C2×C4×C31C22×D416yes—
278C2×C4×C31C22×D416yes—
279C2×C4×C31C2×#4116yes—
280C2×C4×C312−1+412yes—
281C2×#548C2×C3111yescharacteristic
282C2×#520C2×C3111yescharacteristic, complemented
283C22×C4×Q8C2×C3111yescharacteristic, complemented
284#2367C2×C3113yescomplemented
285#2361C2×C3113yescomplemented
286#2360C2×C3113yescomplemented
287Q8×C4⋊C4C2×C3111yescharacteristic, complemented
288D4×C4⋊C4C2×C3113yescomplemented
289#2341C2×C3111yescharacteristic, complemented
290Q8×C22⋊C4C2×C3111yescharacteristic, complemented
291#2326C2×C3113yescomplemented
292#2323C2×C3113yescomplemented
293C4×#121C2×C3113yescomplemented
294#2290C2×C3113yescomplemented
295#2276C2×C3111yescharacteristic, complemented
296C22×C31—22no—
297C22×C31—22no—
298C22×C31—22no—
299C22×C31—22no—
300C22×C31—22no—
301C22×C31—22no—
302C22×C31—26no—
303C22×C31—26no—
304C22×C31—26no—
305C22×C31—43no—
306C22×C31—43no—
307C22×C31—43no—
308C22×C31—43no—
309C22×C31#52014yescomplemented
310C22×C31C24×C411yescharacteristic
311C22×C31C23×D411yescharacteristic
312C22×C31C22×#4111yescharacteristic
313C22×C31C2×H(5,𝔽2)11yescharacteristic
314C22×C31C2×2−1+411yescharacteristic
315C22×C31C2×2−1+411yescharacteristic
316C22×C31#58511yescharacteristic
317C4×C31—22no—
318C4×C31—26no—
319C4×C31—26no—
320C4×C31—22no—
321C4×C31—22no—
322C4×C31—22no—
323C4×C31—26no—
324C4×C31—41no—
325C4×C31—43no—
326C4×C31—43no—
327C4×C31—41no—
328C4×C31—43no—
329C4×C31C2×C4×D4112yes—
330C22×#41C22×C3111yescharacteristic
331C23×Q8C22×C3111yescharacteristic
332#548C4×C31116yescomplemented
333C2×#124C22×C3113yes—
334C2×C22⋊Q8C22×C3113yes—
335C2×#121C22×C3113yes—
336#520—28no—
337C2×C4×Q8—28no—
338C2×C4×Q8C22×C3113yes—
339C2×C4×Q8C22×C3111yescharacteristic
340C2×C4×Q8C22×C3111yescharacteristic
341C2×C4×Q8C22×C3111yescharacteristic
342C2×C4×Q8C22×C3113yes—
343C2×C4×Q8C22×C3111yescharacteristic
344C2×C4×Q8C22×C3111yescharacteristic
345C2×C4×D4C22×C3113yes—
346C2×C4×D4C22×C3113yes—
347C2×C4×D4C22×C3116yes—
348C2×C4×D4C22×C3113yes—
349C2×#117C22×C3113yes—
350C22×C4⋊C4C22×C3113yes—
351C22×C4⋊C4C22×C3113yes—
352C22×C42C22×C3113yes—
353#391C22×C3113yes—
354#391C22×C3113yes—
355#390C22×C3113yes—
356#390C22×C3113yes—
357#389C22×C3116yes—
358#389C22×C3113yes—
359#389C22×C3113yes—
360#388C22×C3116yes—
361#388C22×C3116yes—
362#388C22×C3113yes—
363#388C22×C3113yes—
364#387C22×C3113yes—
365#387C22×C3113yes—
366#386C22×C3113yes—
367#386C22×C3113yes—
368#385C22×C3116yes—
369#385C22×C3116yes—
370#385C22×C3113yes—
371#385C22×C3111yescharacteristic
372#384C22×C3113yes—
373#380C22×C3113yes—
374#380C22×C3113yes—
375C4×C4⋊C4C22×C3113yes—
376C4×C4⋊C4C22×C3113yes—
377C4×C4⋊C4C22×C3113yes—
378C4×C4⋊C4C22×C3113yes—
379C4×C22⋊C4C22×C3113yes—
380C4×C22⋊C4C22×C3113yes—
381C4×C22⋊C4C22×C3116yes—
382#376C22×C3113yes—
383C2×C31—24no—
384C2×C31—46no—
385C2×C31C22×C4×D411yescharacteristic
386C2×C31C2×#52011yescharacteristic
387C2×C31C4×2−1+411yescharacteristic
388C2×C31#348611yescharacteristic
389C2×C31#348811yescharacteristic
390C2×C31#351611yescharacteristic
391C2×C31#352211yescharacteristic
392C2×#41—24no—
393C2×#41—24no—
394C2×#41C2×C4×C3118yescomplemented
395C22×Q8—24no—
396C22×Q8—24no—
397C22×Q8C2×C4×C3118yescomplemented
398C22×Q8C23×C3113yes—
399C22×Q8C23×C3111yescharacteristic
400C22×D4C23×C3113yes—
401C22×D4C23×C3113yes—
402C23×C4C23×C3111yescharacteristic
403C23×C4C23×C3113yes—
404C23×C4C23×C3113yes—
405C23×C4C23×C3113yes—
406C23×C4C23×C3116yes—
407#124C2×C4×C31124yescomplemented
408C22⋊Q8C2×C4×C31124yescomplemented
409#121C2×C4×C31124yescomplemented
410C4×Q8—24no—
411C4×Q8—24no—
412C4×Q8—24no—
413C4×Q8—212no—
414C4×Q8—212no—
415C4×Q8C2×C4×C3118yescomplemented
416C4×Q8D4×C3118yescomplemented
417C4×D4—212no—
418C4×D4—212no—
419C4×D4—412no—
420C4×D4C2×C4×C31124yescomplemented
421#117—212no—
422C2×C4⋊C4—212no—
423C2×C4⋊C4—212no—
424C2×C4⋊C4C23×C3113yes—
425C2×C4⋊C4C23×C3113yes—
426C2×C4⋊C4C23×C3113yes—
427C2×C4⋊C4C23×C3116yes—
428C2×C4⋊C4C23×C3111yescharacteristic
429C2×C4⋊C4C23×C3113yes—
430C2×C4⋊C4C23×C3111yescharacteristic
431C2×C4⋊C4C23×C3116yes—
432C2×C4⋊C4C23×C3113yes—
433C2×C4⋊C4C23×C3113yes—
434C2×C4⋊C4C23×C3113yes—
435C2×C4⋊C4C23×C3113yes—
436C2×C22⋊C4C23×C3113yes—
437C2×C22⋊C4C23×C3113yes—
438C2×C22⋊C4C23×C3113yes—
439C2×C22⋊C4C23×C3111yescharacteristic
440C2×C22⋊C4C23×C3113yes—
441C2×C22⋊C4C23×C3116yes—
442C2×C22⋊C4C23×C3113yes—
443C2×C22⋊C4C23×C3111yescharacteristic
444C2×C22⋊C4C23×C3113yes—
445C2×C22⋊C4C23×C3116yes—
446C2×C42—212no—
447C2×C42C23×C3113yes—
448C2×C42C23×C3113yes—
449C2×C42C23×C3113yes—
450C2×C42C23×C3113yes—
451C2×C42C23×C3113yes—
452C2×C42C23×C3116yes—
453C2×C42C23×C3113yes—
454C2×C42C23×C3113yes—
455#95C23×C3111yescharacteristic
456#95C23×C3113yes—
457#95C23×C3113yes—
458#95C23×C3113yes—
459#95C23×C3111yescharacteristic
460#95C23×C3113yes—
461#95C23×C3113yes—
462#95C23×C3116yes—
463#95C23×C3113yes—
464#95C23×C3113yes—
465#95C23×C3113yes—
466C31#3429411yescharacteristic, direct product factor, Sylow
467C24C24×C3113yes—
468C24C24×C3111yescharacteristic
469#41—232no—
470C2×Q8—232no—
471C2×Q8—26no—
472C2×Q8—26no—
473C2×Q8C22×C4×C31112yes—
474C2×Q8C22×C4×C3114yes—
475C2×Q8C2×D4×C3114yes—
476C2×Q8#41×C3114yes—
477C2×D4—26no—
478C2×D4—26no—
479C2×D4—26no—
480C2×D4—26no—
481C2×D4C22×C4×C31112yes—
482C2×D4C22×C4×C31112yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—26no—
486C22×C4—26no—
487C22×C4—26no—
488C22×C4—26no—
489C22×C4—22no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—212no—
493C22×C4—43no—
494C22×C4—46no—
495C22×C4—46no—
496C22×C4C22×C4×C31112yes—
497C22×C4C22×C4×C31112yes—
498C22×C4C24×C3111yescharacteristic
499C22×C4C24×C3111yescharacteristic
500C22×C4C24×C3113yes—
501C22×C4C24×C3113yes—
502C22×C4C24×C3113yes—
503C22×C4C24×C3111yescharacteristic
504C22×C4C24×C3113yes—
505C22×C4C24×C3113yes—
506C22×C4C24×C3111yescharacteristic
507C22×C4C24×C3111yescharacteristic
508C22×C4C24×C3113yes—
509C22×C4C24×C3111yescharacteristic
510C22×C4C24×C3113yes—
511C4⋊C4—26no—
512C4⋊C4—26no—
513C4⋊C4—212no—
514C4⋊C4—26no—
515C4⋊C4—22no—
516C4⋊C4—26no—
517C4⋊C4—22no—
518C4⋊C4—43no—
519C4⋊C4—46no—
520C4⋊C4C22×C4×C31112yes—
521C4⋊C4C22×C4×C31112yes—
522C4⋊C4C2×D4×C31112yes—
523C22⋊C4—26no—
524C22⋊C4—22no—
525C22⋊C4—26no—
526C22⋊C4—26no—
527C22⋊C4—26no—
528C22⋊C4—43no—
529C22⋊C4—46no—
530C22⋊C4C22×C4×C3114yes—
531C22⋊C4C22×C4×C31112yes—
532C22⋊C4C22×C4×C31124yes—
533C42—26no—
534C42—26no—
535C42—26no—
536C42—26no—
537C42—26no—
538C42—46no—
539C42C22×C4×C31112yes—
540C42C2×D4×C31112yes—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—23no—
546C23—23no—
547C23—23no—
548C23—23no—
549C23—23no—
550C23—23no—
551C23C23×C4×C3116yes—
552C23C23×C4×C3112yes—
553C23C31×H(5,𝔽2)12yes—
554C23C31×2−1+412yes—
555C23C25×C3111yescharacteristic
556Q8—224no—
557Q8C4×D4×C31116yescomplemented
558D4—224no—
559D4—224no—
560C2×C4—28no—
561C2×C4—21no—
562C2×C4—23no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—23no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—21no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—21no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—23no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—412no—
593C2×C4—812no—
594C2×C4C23×C4×C3112yes—
595C2×C4C23×C4×C3116yes—
596C2×C4C23×C4×C3116yes—
597C2×C4C23×C4×C3112yes—
598C2×C4C23×C4×C3116yes—
599C2×C4C22×D4×C3112yes—
600C2×C4C22×D4×C3116yes—
601C2×C4C22×D4×C3116yes—
602C2×C4C2×#41×C3116yes—
603C2×C4C31×2−1+412yes—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—26no—
611C22—26no—
612C22—26no—
613C22—43no—
614C22—43no—
615C22—43no—
616C22—43no—
617C22C31×#52014yescomplemented
618C22C24×C4×C3111yescharacteristic
619C22C23×D4×C3111yescharacteristic
620C22C22×#41×C3111yescharacteristic
621C22C2×C31×H(5,𝔽2)11yescharacteristic
622C22C2×C31×2−1+411yescharacteristic
623C22C2×C31×2−1+411yescharacteristic
624C22C31×#58511yescharacteristic
625C4—22no—
626C4—26no—
627C4—26no—
628C4—22no—
629C4—22no—
630C4—22no—
631C4—26no—
632C4—41no—
633C4—43no—
634C4—43no—
635C4—41no—
636C4—43no—
637C4C2×C4×D4×C31112yes—
638C2—24no—
639C2—46no—
640C2C22×C4×D4×C3111yescharacteristic
641C2C2×C31×#52011yescharacteristic
642C2C4×C31×2−1+411yescharacteristic
643C2C31×#348611yescharacteristic
644C2C31×#348811yescharacteristic
645C2C31×#351611yescharacteristic
646C2C31×#352211yescharacteristic
subgroupG/H
center, socleC23×C31C25
commutatorC22C24×C4×C31
Frattini, cosocleC23C25×C31
prime radicalC2×C31×#548C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#520C2semidirect
3. C22×C4×Q8×C31C2semidirect
4. C31×#2367C2semidirect
5. C31×#2361C2semidirect
6. C31×#2360C2semidirect
7. Q8×C4⋊C4×C31C2semidirect
8. D4×C4⋊C4×C31C2semidirect
9. C31×#2341C2semidirect
10. Q8×C22⋊C4×C31C2semidirect
11. C31×#2326C2semidirect
12. C31×#2323C2semidirect
13. C4×C31×#121C2semidirect
14. C31×#2290C2semidirect
15. C31×#2276C2semidirect
18. C31×#548C4semidirect
71. C2×#41×C31C2×C4semidirect
74. C22×Q8×C31C2×C4semidirect
84. C31×#124C2×C4semidirect
85. C31×C22⋊Q8C2×C4semidirect
86. C31×#121C2×C4semidirect
92. C4×Q8×C31C2×C4semidirect
93. C4×Q8×C31D4semidirect
97. C4×D4×C31C2×C4semidirect
217. #34294C31direct (N × H)
234. Q8×C31C4×D4semidirect
282. C2×#520C2×C31semidirect
283. C22×C4×Q8C2×C31semidirect
284. #2367C2×C31semidirect
285. #2361C2×C31semidirect
286. #2360C2×C31semidirect
287. Q8×C4⋊C4C2×C31semidirect
288. D4×C4⋊C4C2×C31semidirect
289. #2341C2×C31semidirect
290. Q8×C22⋊C4C2×C31semidirect
291. #2326C2×C31semidirect
292. #2323C2×C31semidirect
293. C4×#121C2×C31semidirect
294. #2290C2×C31semidirect
295. #2276C2×C31semidirect
309. C22×C31#520semidirect
332. #548C4×C31semidirect
394. C2×#41C2×C4×C31semidirect
397. C22×Q8C2×C4×C31semidirect
407. #124C2×C4×C31semidirect
408. C22⋊Q8C2×C4×C31semidirect
409. #121C2×C4×C31semidirect
415. C4×Q8C2×C4×C31semidirect
416. C4×Q8D4×C31semidirect
420. C4×D4C2×C4×C31semidirect
466. C31#34294direct (N × H)
557. Q8C4×D4×C31semidirect
617. C22C31×#520semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5482
C2×C31×#5202
C22×C4×Q8×C312
C31×#23672
C31×#23612
C31×#23602
Q8×C4⋊C4×C312
D4×C4⋊C4×C312
C31×#23412
Q8×C22⋊C4×C312
C31×#23262
C31×#23232
C4×C31×#1212
C31×#22902
C31×#22762
#3429431