Finite Group Databasebeta

← C31×#22858 #21479617

Subgroups — C31×#22858 #21479617

Order 7936.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#447C211yesmaximal, characteristic
2C2×C31×#442C211yesmaximal, characteristic, complemented
3C22×C31×#102C211yesmaximal, characteristic, complemented
4C31×#2361C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#1972C211yesmaximal, characteristic, complemented
7C31×#1936C211yesmaximal, characteristic, complemented
8C31×#1926C211yesmaximal, characteristic, complemented
9C31×#1893C211yesmaximal, characteristic, complemented
10C31×#1879C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1864C211yesmaximal, characteristic, complemented
13C31×#1853C211yesmaximal, characteristic, complemented
14C31×#1762C211yesmaximal, characteristic, complemented
15C31×#1752C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C2×C31×#121C2211yescharacteristic
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic, complemented
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31—21no—
27C31×#447C418yescomplemented
28C31×#442—24no—
29C2×C31×#106C2211yescharacteristic, complemented
30C2×C31×#106C2211yescharacteristic, complemented
31C2×C31×#102—24no—
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic, complemented
39C2×C31×#102C2211yescharacteristic, complemented
40C2×C31×C22⋊C8C2211yescharacteristic
41C2×C31×#97C2211yescharacteristic, complemented
42C2×C31×#97C2211yescharacteristic, complemented
43C31×#390C2211yescharacteristic
44C31×#390C2211yescharacteristic
45C31×#390C2211yescharacteristic, complemented
46C31×#389C2211yescharacteristic, complemented
47C31×#388—21no—
48C31×#386—21no—
49C31×#386—21no—
50C31×#386—21no—
51C31×#385—21no—
52C31×#380C2211yescharacteristic
53C31×#379—21no—
54C4×C4⋊C4×C31C2211yescharacteristic, complemented
55C4×C22⋊C4×C31C2211yescharacteristic
56C31×#340C2211yescharacteristic, complemented
57C31×#340C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#336C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C25×C31—21no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31C2×C414yescomplemented
71C22×D4×C31C2311yescharacteristic
72C22×D4×C31C2311yescharacteristic
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31—21no—
78C23×C4×C31C2311yescharacteristic
79C2×D8×C31—22no—
80C2×D8×C31—22no—
81C2×D8×C31—41no—
82C2×D8×C31—41no—
83C2×D8×C31C2×C414yescomplemented
84C2×D8×C31C2×C414yescomplemented
85C22×C8×C31—22no—
86C22×C8×C31—22no—
87C22×C8×C31—41no—
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C31×#121—22no—
93C31×#121C2×C414yescomplemented
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—41no—
98C4×D4×C31—41no—
99C4×D4×C31—41no—
100C4×D4×C31—44no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—41no—
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—44no—
122C2×C22⋊C4×C31D411yescharacteristic
123C2×C22⋊C4×C31D411yescharacteristic
124C2×C42×C31—21no—
125C2×C42×C31C2311yescharacteristic
126C2×C42×C31C2311yescharacteristic
127C31×#106—22no—
128C31×#106—41no—
129C31×#102—22no—
130C31×#102—22no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—41no—
134C31×#102C2×C414yescomplemented
135C31×#102C2×C414yescomplemented
136C31×#102D414yescomplemented
137C31×C22⋊C8C2×C414yescomplemented
138C31×#97—22no—
139C31×#97—41no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95D411yescharacteristic
144C31×#95D411yescharacteristic
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—21no—
148C24×C31—24no—
149C24×C31—42no—
150C24×C31—42no—
151C24×C31—42no—
152C24×C31—42no—
153C24×C31—81no—
154C24×C31—81no—
155C24×C31C2×D411yescharacteristic
156C2×D4×C31—28no—
157C2×D4×C31—24no—
158C2×D4×C31—24no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—44no—
173C2×D4×C31—44no—
174C2×D4×C31—44no—
175C2×D4×C31—42no—
176C2×D4×C31—42no—
177C2×D4×C31—42no—
178C2×D4×C31—42no—
179C2×D4×C31C22×C412yes—
180C2×D4×C31C22×C412yes—
181C2×D4×C31C22×C412yes—
182C2×D4×C31C2×D412yes—
183C2×D4×C31#4112yes—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—42no—
194C22×C4×C31—42no—
195C22×C4×C31—42no—
196C22×C4×C31—42no—
197C22×C4×C31—42no—
198C22×C4×C31—42no—
199C22×C4×C31—42no—
200C22×C4×C31—42no—
201C22×C4×C31—81no—
202C22×C4×C31—81no—
203C22×C4×C31—81no—
204C22×C4×C31—81no—
205C22×C4×C31C22×C412yes—
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31#4112yes—
212C22×C4×C31C2411yescharacteristic
213D8×C31—28no—
214D8×C31—44no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—44no—
225C2×C8×C31C22×C412yes—
226C2×C8×C31C22×C412yes—
227C2×C8×C31C2×D412yes—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—42no—
237C4⋊C4×C31—42no—
238C4⋊C4×C31C22×C412yes—
239C4⋊C4×C31C2×D412yes—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—24no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—81no—
251C22⋊C4×C31—81no—
252C22⋊C4×C31—81no—
253C42×C31—21no—
254C42×C31—21no—
255C42×C31—21no—
256C42×C31—21no—
257C42×C31—42no—
258#22858C3111yesmaximal, characteristic, direct product factor, Sylow
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—22no—
268C23×C31—48no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—48no—
286C23×C31—84no—
287C23×C31—84no—
288C23×C31—84no—
289C23×C31—84no—
290C23×C31—84no—
291C23×C31C4×D412yes—
292C23×C31AGL(1,ℤ/8)12yes—
293C23×C31AGL(1,ℤ/8)12yes—
294C23×C31C22×D411yescharacteristic
295D4×C31—22no—
296D4×C31—22no—
297D4×C31—22no—
298D4×C31—22no—
299D4×C31—22no—
300D4×C31—22no—
301D4×C31—22no—
302D4×C31—48no—
303D4×C31—48no—
304D4×C31—41no—
305D4×C31—41no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31C4×D414yescomplemented
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—22no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—84no—
343C2×C4×C31—84no—
344C2×C4×C31—84no—
345C2×C4×C31—84no—
346C2×C4×C31C4×D412yes—
347C2×C4×C31C23×C411yescharacteristic
348C2×C4×C31C22×D411yescharacteristic
349C2×C4×C31C2×#4111yescharacteristic
350C2×C4×C31C2×#4111yescharacteristic
351C2×C4×C31H(5,𝔽2)11yescharacteristic
352C2×C4×C31H(5,𝔽2)11yescharacteristic
353C8×C31—22no—
354C8×C31—22no—
355C8×C31—22no—
356C8×C31—41no—
357C2×#447C2×C3111yescharacteristic
358C2×#442C2×C3111yescharacteristic, complemented
359C22×#102C2×C3111yescharacteristic, complemented
360#2361C2×C3111yescharacteristic, complemented
361D4×C22⋊C4C2×C3111yescharacteristic, complemented
362#1972C2×C3111yescharacteristic, complemented
363#1936C2×C3111yescharacteristic, complemented
364#1926C2×C3111yescharacteristic, complemented
365#1893C2×C3111yescharacteristic, complemented
366#1879C2×C3111yescharacteristic, complemented
367#1879C2×C3111yescharacteristic, complemented
368#1864C2×C3111yescharacteristic, complemented
369#1853C2×C3111yescharacteristic, complemented
370#1762C2×C3111yescharacteristic, complemented
371#1752C2×C3111yescharacteristic, complemented
372C22×C31—22no—
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—22no—
376C22×C31—22no—
377C22×C31—22no—
378C22×C31—24no—
379C22×C31—42no—
380C22×C31—42no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—42no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31—42no—
389C22×C31—42no—
390C22×C31—42no—
391C22×C31—816no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31—81no—
396C22×C31—81no—
397C22×C31—81no—
398C22×C31—81no—
399C22×C31—81no—
400C22×C31#44214yescomplemented
401C22×C31C2×C4×D411yescharacteristic
402C22×C31D4211yescharacteristic
403C22×C31#54611yescharacteristic
404C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
406C22×C31#57611yescharacteristic
407C22×C31#57711yescharacteristic
408C4×C31—22no—
409C4×C31—42no—
410C4×C31—41no—
411C4×C31—42no—
412C4×C31—41no—
413C4×C31—41no—
414C4×C31—41no—
415C4×C31—81no—
416C4×C31—81no—
417C4×C31—81no—
418C4×C31C2×C4×D411yescharacteristic
419C4×C31#51811yescharacteristic
420C4×C31#54611yescharacteristic
421C4×C31#55111yescharacteristic
422C23×D4C22×C3111yescharacteristic
423C22×D8C22×C3111yescharacteristic
424C22×D8C22×C3111yescharacteristic
425C23×C8C22×C3111yescharacteristic
426C2×#121C22×C3111yescharacteristic
427C2×C4×D4—21no—
428C2×C4×D4C22×C3111yescharacteristic
429C2×C4×D4C22×C3111yescharacteristic
430C2×C4×D4C22×C3111yescharacteristic, complemented
431C22×C4⋊C4C22×C3111yescharacteristic
432C22×C22⋊C4—21no—
433#447C4×C3118yescomplemented
434#442—24no—
435C2×#106C22×C3111yescharacteristic, complemented
436C2×#106C22×C3111yescharacteristic, complemented
437C2×#102—24no—
438C2×#102C22×C3111yescharacteristic
439C2×#102C22×C3111yescharacteristic
440C2×#102C22×C3111yescharacteristic
441C2×#102C22×C3111yescharacteristic
442C2×#102C22×C3111yescharacteristic
443C2×#102C22×C3111yescharacteristic
444C2×#102C22×C3111yescharacteristic, complemented
445C2×#102C22×C3111yescharacteristic, complemented
446C2×C22⋊C8C22×C3111yescharacteristic
447C2×#97C22×C3111yescharacteristic, complemented
448C2×#97C22×C3111yescharacteristic, complemented
449#390C22×C3111yescharacteristic
450#390C22×C3111yescharacteristic
451#390C22×C3111yescharacteristic, complemented
452#389C22×C3111yescharacteristic, complemented
453#388—21no—
454#386—21no—
455#386—21no—
456#386—21no—
457#385—21no—
458#380C22×C3111yescharacteristic
459#379—21no—
460C4×C4⋊C4C22×C3111yescharacteristic, complemented
461C4×C22⋊C4C22×C3111yescharacteristic
462#340C22×C3111yescharacteristic, complemented
463#340C22×C3111yescharacteristic, complemented
464#340C22×C3111yescharacteristic, complemented
465#340C22×C3111yescharacteristic, complemented
466#336C22×C3111yescharacteristic, complemented
467#336C22×C3111yescharacteristic, complemented
468C2×C31—24no—
469C2×C31—44no—
470C2×C31—82no—
471C2×C31—82no—
472C2×C31#235811yescharacteristic
473C2×C31C2×#44211yescharacteristic
474C2×C31#294611yescharacteristic
475C2×C31#326411yescharacteristic
476C2×C31#326511yescharacteristic
477C2×C31#330611yescharacteristic
478C2×C31#331811yescharacteristic
479C25—21no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—22no—
485C22×D4—41no—
486C22×D4—41no—
487C22×D4C2×C4×C3114yescomplemented
488C22×D4C23×C3111yescharacteristic
489C22×D4C23×C3111yescharacteristic
490C22×D4C23×C3111yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4C23×C3111yescharacteristic
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—41no—
499C2×D8—41no—
500C2×D8C2×C4×C3114yescomplemented
501C2×D8C2×C4×C3114yescomplemented
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—41no—
505C22×C8C23×C3111yescharacteristic
506C22×C8C23×C3111yescharacteristic
507C22×C8C23×C3111yescharacteristic
508C22×C8C23×C3111yescharacteristic
509#121—22no—
510#121C2×C4×C3114yescomplemented
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—41no—
515C4×D4—41no—
516C4×D4—41no—
517C4×D4—44no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4C23×C3111yescharacteristic
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C4⋊C4C23×C3111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—44no—
539C2×C22⋊C4D4×C3111yescharacteristic
540C2×C22⋊C4D4×C3111yescharacteristic
541C2×C42—21no—
542C2×C42C23×C3111yescharacteristic
543C2×C42C23×C3111yescharacteristic
544#106—22no—
545#106—41no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—41no—
551#102C2×C4×C3114yescomplemented
552#102C2×C4×C3114yescomplemented
553#102D4×C3114yescomplemented
554C22⋊C8C2×C4×C3114yescomplemented
555#97—22no—
556#97—41no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95D4×C3111yescharacteristic
561#95D4×C3111yescharacteristic
562C31#2285811yescharacteristic, direct product factor, Sylow
563C24—21no—
564C24—21no—
565C24—21no—
566C24—24no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—81no—
572C24—81no—
573C24C2×D4×C3111yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4C22×C4×C3112yes—
598C2×D4C22×C4×C3112yes—
599C2×D4C22×C4×C3112yes—
600C2×D4C2×D4×C3112yes—
601C2×D4#41×C3112yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4C22×C4×C3112yes—
624C22×C4C2×D4×C3111yescharacteristic
625C22×C4C2×D4×C3111yescharacteristic
626C22×C4C2×D4×C3111yescharacteristic
627C22×C4C2×D4×C3111yescharacteristic
628C22×C4C2×D4×C3111yescharacteristic
629C22×C4#41×C3112yes—
630C22×C4C24×C3111yescharacteristic
631D8—28no—
632D8—44no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—44no—
643C2×C8C22×C4×C3112yes—
644C2×C8C22×C4×C3112yes—
645C2×C8C2×D4×C3112yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4C22×C4×C3112yes—
657C4⋊C4C2×D4×C3112yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C22⋊C4—81no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—48no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23C4×D4×C3112yes—
709C23C31×AGL(1,ℤ/8)12yes—
710C23C31×AGL(1,ℤ/8)12yes—
711C23C22×D4×C3111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4C4×D4×C3114yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4C4×D4×C3112yes—
764C2×C4C23×C4×C3111yescharacteristic
765C2×C4C22×D4×C3111yescharacteristic
766C2×C4C2×#41×C3111yescharacteristic
767C2×C4C2×#41×C3111yescharacteristic
768C2×C4C31×H(5,𝔽2)11yescharacteristic
769C2×C4C31×H(5,𝔽2)11yescharacteristic
770C8—22no—
771C8—22no—
772C8—22no—
773C8—41no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—816no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22C31×#44214yescomplemented
803C22C2×C4×D4×C3111yescharacteristic
804C22D42×C3111yescharacteristic
805C22C31×#54611yescharacteristic
806C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
807C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
808C22C31×#57611yescharacteristic
809C22C31×#57711yescharacteristic
810C4—22no—
811C4—42no—
812C4—41no—
813C4—42no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C2×C4×D4×C3111yescharacteristic
821C4C31×#51811yescharacteristic
822C4C31×#54611yescharacteristic
823C4C31×#55111yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—82no—
828C2C31×#235811yescharacteristic
829C2C2×C31×#44211yescharacteristic
830C2C31×#294611yescharacteristic
831C2C31×#326411yescharacteristic
832C2C31×#326511yescharacteristic
833C2C31×#330611yescharacteristic
834C2C31×#331811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
LCSG ▷ C2×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
2. C2×C31×#442C2semidirect
3. C22×C31×#102C2semidirect
4. C31×#2361C2semidirect
5. D4×C22⋊C4×C31C2semidirect
6. C31×#1972C2semidirect
7. C31×#1936C2semidirect
8. C31×#1926C2semidirect
9. C31×#1893C2semidirect
10. C31×#1879C2semidirect
11. C31×#1879C2semidirect
12. C31×#1864C2semidirect
13. C31×#1853C2semidirect
14. C31×#1762C2semidirect
15. C31×#1752C2semidirect
24. C2×C4×D4×C31C22semidirect
27. C31×#447C4semidirect
29. C2×C31×#106C22semidirect
30. C2×C31×#106C22semidirect
38. C2×C31×#102C22semidirect
39. C2×C31×#102C22semidirect
41. C2×C31×#97C22semidirect
42. C2×C31×#97C22semidirect
45. C31×#390C22semidirect
46. C31×#389C22semidirect
54. C4×C4⋊C4×C31C22semidirect
56. C31×#340C22semidirect
57. C31×#340C22semidirect
58. C31×#340C22semidirect
59. C31×#340C22semidirect
60. C31×#336C22semidirect
61. C31×#336C22semidirect
70. C22×D4×C31C2×C4semidirect
83. C2×D8×C31C2×C4semidirect
84. C2×D8×C31C2×C4semidirect
93. C31×#121C2×C4semidirect
134. C31×#102C2×C4semidirect
135. C31×#102C2×C4semidirect
136. C31×#102D4semidirect
137. C31×C22⋊C8C2×C4semidirect
258. #22858C31direct (N × H)
308. D4×C31C4×D4semidirect
358. C2×#442C2×C31semidirect
359. C22×#102C2×C31semidirect
360. #2361C2×C31semidirect
361. D4×C22⋊C4C2×C31semidirect
362. #1972C2×C31semidirect
363. #1936C2×C31semidirect
364. #1926C2×C31semidirect
365. #1893C2×C31semidirect
366. #1879C2×C31semidirect
367. #1879C2×C31semidirect
368. #1864C2×C31semidirect
369. #1853C2×C31semidirect
370. #1762C2×C31semidirect
371. #1752C2×C31semidirect
400. C22×C31#442semidirect
430. C2×C4×D4C22×C31semidirect
433. #447C4×C31semidirect
435. C2×#106C22×C31semidirect
436. C2×#106C22×C31semidirect
444. C2×#102C22×C31semidirect
445. C2×#102C22×C31semidirect
447. C2×#97C22×C31semidirect
448. C2×#97C22×C31semidirect
451. #390C22×C31semidirect
452. #389C22×C31semidirect
460. C4×C4⋊C4C22×C31semidirect
462. #340C22×C31semidirect
463. #340C22×C31semidirect
464. #340C22×C31semidirect
465. #340C22×C31semidirect
466. #336C22×C31semidirect
467. #336C22×C31semidirect
487. C22×D4C2×C4×C31semidirect
500. C2×D8C2×C4×C31semidirect
501. C2×D8C2×C4×C31semidirect
510. #121C2×C4×C31semidirect
551. #102C2×C4×C31semidirect
552. #102C2×C4×C31semidirect
553. #102D4×C31semidirect
554. C22⋊C8C2×C4×C31semidirect
562. C31#22858direct (N × H)
725. D4C4×D4×C31semidirect
802. C22C31×#442semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4472
C2×C31×#4422
C22×C31×#1022
C31×#23612
D4×C22⋊C4×C312
C31×#19722
C31×#19362
C31×#19262
C31×#18932
C31×#18792
C31×#18642
C31×#18532
C31×#17622
C31×#17522
#2285831