Finite Group Databasebeta

← C31×#25079 #21481838

Subgroups — C31×#25079 #21481838

Order 7936.

1078 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#467C211yesmaximal, characteristic, complemented
2C2×C31×#462C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic
4C2×C31×#416C211yesmaximal, characteristic
5C31×#2432C211yesmaximal, characteristic
6C31×#2362C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2056C211yesmaximal, characteristic, complemented
9C31×#2043C211yesmaximal, characteristic, complemented
10C31×#2015C211yesmaximal, characteristic, complemented
11C31×#1983C211yesmaximal, characteristic, complemented
12C31×#1928C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1873C211yesmaximal, characteristic, complemented
15C31×#1850C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C23×C8×C31C2211yescharacteristic
21C2×C31×C4⋊Q8C2211yescharacteristic
22C2×C31×#124C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C31×#117C2211yescharacteristic
27C31×#467—24no—
28C31×#462—24no—
29C31×#452—24no—
30C2×C31×#107C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C31×#416—24no—
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C31×#394—21no—
46C31×#394—21no—
47C31×#391C2211yescharacteristic
48C31×#391C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#389C2211yescharacteristic
51C31×#388—21no—
52C31×#388—21no—
53C31×#387—21no—
54C31×#385—21no—
55C31×#385—21no—
56C4×C4⋊C4×C31—21no—
57C4×C4⋊C4×C31C2211yescharacteristic
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C22×Q8×C31C2311yescharacteristic
70C22×Q8×C31C2311yescharacteristic
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—21no—
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31C2311yescharacteristic
76C2×Q16×C31—22no—
77C2×Q16×C31—22no—
78C2×Q16×C31—22no—
79C2×Q16×C31—22no—
80C2×Q16×C31—41no—
81C2×Q16×C31—41no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—41no—
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×C4⋊Q8—22no—
93C31×C4⋊Q8—41no—
94C31×#124—22no—
95C31×#124—41no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8D414yes—
100C4×Q8×C31—22no—
101C4×Q8×C31—41no—
102C31×#117—22no—
103C31×#117—41no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
122C2×C22⋊C4×C31D411yescharacteristic
123C2×C42×C31—21no—
124C2×C42×C31—21no—
125C2×C42×C31—21no—
126C2×C42×C31C2311yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C31×#107—22no—
129C31×C4⋊C8—22no—
130C31×C4⋊C8—41no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—41no—
137C31×#103D414yes—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×C22⋊C8—22no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95D411yescharacteristic
149C31×#95D411yescharacteristic
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152#41×C31—28no—
153#41×C31—44no—
154#41×C31—44no—
155#41×C31—44no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31C2×D412yes—
173C2×Q8×C31C2×D412yes—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—42no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
182C2×D4×C31#4112yes—
183C22×C4×C31—21no—
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—21no—
194C22×C4×C31—42no—
195C22×C4×C31—42no—
196C22×C4×C31—42no—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31#4112yes—
204C22×C4×C31C2411yescharacteristic
205Q16×C31—44no—
206Q16×C31—44no—
207SD16×C31—44no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—44no—
220C2×C8×C31C2×D412yes—
221C4⋊C4×C31—24no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—42no—
229C4⋊C4×C31—42no—
230C4⋊C4×C31—42no—
231C4⋊C4×C31—42no—
232C4⋊C4×C31—42no—
233C4⋊C4×C31C2×D412yes—
234C4⋊C4×C31C2×D412yes—
235C22⋊C4×C31—24no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—41no—
238C22⋊C4×C31—42no—
239C22⋊C4×C31—42no—
240C22⋊C4×C31—42no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C42×C31—21no—
245C42×C31—21no—
246C42×C31—21no—
247C42×C31—21no—
248C42×C31—42no—
249C42×C31—42no—
250C42×C31—42no—
251#25079C3111yesmaximal, characteristic, direct product factor, Sylow
252C23×C31—21no—
253C23×C31—21no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—22no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31#12112yes—
266C23×C31C22×D411yescharacteristic
267Q8×C31—22no—
268Q8×C31—22no—
269Q8×C31—22no—
270Q8×C31—22no—
271Q8×C31—41no—
272Q8×C31—41no—
273Q8×C31—41no—
274Q8×C31—41no—
275Q8×C31—41no—
276Q8×C31—41no—
277Q8×C31—41no—
278Q8×C31—41no—
279D4×C31—22no—
280D4×C31—22no—
281D4×C31—48no—
282D4×C31—41no—
283D4×C31—41no—
284C2×C4×C31—21no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—21no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—21no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—48no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31#12112yes—
324C2×C4×C31#13512yes—
325C2×C4×C31C22×D411yescharacteristic
326C2×C4×C31C22×D411yescharacteristic
327C2×C4×C31C2×#4111yescharacteristic
328C2×C4×C31C2×#4111yescharacteristic
329C2×C4×C31H(5,𝔽2)11yescharacteristic
330C2×C4×C31H(5,𝔽2)11yescharacteristic
331C8×C31—22no—
332C8×C31—41no—
333C8×C31—41no—
334C8×C31—41no—
335C2×#467C2×C3111yescharacteristic, complemented
336C2×#462C2×C3111yescharacteristic, complemented
337C2×#452C2×C3111yescharacteristic
338C2×#416C2×C3111yescharacteristic
339#2432C2×C3111yescharacteristic
340#2362C2×C3111yescharacteristic, complemented
341#2067C2×C3111yescharacteristic, complemented
342#2056C2×C3111yescharacteristic, complemented
343#2043C2×C3111yescharacteristic, complemented
344#2015C2×C3111yescharacteristic, complemented
345#1983C2×C3111yescharacteristic, complemented
346#1928C2×C3111yescharacteristic, complemented
347#1880C2×C3111yescharacteristic, complemented
348#1873C2×C3111yescharacteristic, complemented
349#1850C2×C3111yescharacteristic, complemented
350C22×C31—22no—
351C22×C31—22no—
352C22×C31—22no—
353C22×C31—41no—
354C22×C31—41no—
355C22×C31—41no—
356C22×C31—41no—
357C22×C31—42no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—81no—
361C22×C31—81no—
362C22×C31—81no—
363C22×C31—81no—
364C22×C31C2×#12111yescharacteristic
365C22×C31D4211yescharacteristic
366C22×C31#54611yescharacteristic
367C22×C31C2×#13511yescharacteristic
368C22×C31#57511yescharacteristic
369C22×C31#57811yescharacteristic
370C22×C31#57811yescharacteristic
371C4×C31—22no—
372C4×C31—22no—
373C4×C31—42no—
374C4×C31—42no—
375C4×C31—41no—
376C4×C31—42no—
377C4×C31—42no—
378C4×C31—41no—
379C4×C31—41no—
380C4×C31—81no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31#52511yescharacteristic
384C4×C31#53811yescharacteristic
385C4×C31D4211yescharacteristic
386C4×C31#54611yescharacteristic
387C22×#41C22×C3111yescharacteristic
388C22×Q16C22×C3111yescharacteristic
389C22×Q16C22×C3111yescharacteristic
390C22×SD16C22×C3111yescharacteristic
391C23×C8C22×C3111yescharacteristic
392C2×C4⋊Q8C22×C3111yescharacteristic
393C2×#124C22×C3111yescharacteristic
394C2×C22⋊Q8C22×C3111yescharacteristic
395C2×C22⋊Q8C22×C3111yescharacteristic
396C2×C4×Q8C22×C3111yescharacteristic
397C2×#117C22×C3111yescharacteristic
398#467—24no—
399#462—24no—
400#452—24no—
401C2×#107C22×C3111yescharacteristic
402C2×C4⋊C8C22×C3111yescharacteristic
403C2×C4⋊C8C22×C3111yescharacteristic
404#416—24no—
405C2×#103C22×C3111yescharacteristic
406C2×#103C22×C3111yescharacteristic
407C2×#103C22×C3111yescharacteristic
408C2×#103C22×C3111yescharacteristic
409C2×#103C22×C3111yescharacteristic
410C2×#103C22×C3111yescharacteristic
411C2×#103C22×C3111yescharacteristic
412C2×#102C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×C22⋊C8C22×C3111yescharacteristic
416#394—21no—
417#394—21no—
418#391C22×C3111yescharacteristic
419#391C22×C3111yescharacteristic
420#390C22×C3111yescharacteristic
421#389C22×C3111yescharacteristic
422#388—21no—
423#388—21no—
424#387—21no—
425#385—21no—
426#385—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4C22×C3111yescharacteristic
429C4×C22⋊C4C22×C3111yescharacteristic
430#340C22×C3111yescharacteristic
431#340C22×C3111yescharacteristic
432#336C22×C3111yescharacteristic
433#336C22×C3111yescharacteristic
434C2×C31—42no—
435C2×C31—82no—
436C2×C31#242411yescharacteristic
437C2×C31#303511yescharacteristic
438C2×C31#304411yescharacteristic
439C2×C31#326911yescharacteristic
440C2×C31#328511yescharacteristic
441C2×C31#330211yescharacteristic
442C2×C31#331511yescharacteristic
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C23×C3111yescharacteristic
450C22×Q8C23×C3111yescharacteristic
451C22×Q8C23×C3111yescharacteristic
452C22×D4—21no—
453C22×D4C23×C3111yescharacteristic
454C23×C4—21no—
455C23×C4C23×C3111yescharacteristic
456C2×Q16—22no—
457C2×Q16—22no—
458C2×Q16—22no—
459C2×Q16—22no—
460C2×Q16—41no—
461C2×Q16—41no—
462C2×SD16—22no—
463C2×SD16—22no—
464C2×SD16—41no—
465C22×C8—22no—
466C22×C8—22no—
467C22×C8—41no—
468C22×C8C23×C3111yescharacteristic
469C22×C8C23×C3111yescharacteristic
470C22×C8C23×C3111yescharacteristic
471C22×C8C23×C3111yescharacteristic
472C4⋊Q8—22no—
473C4⋊Q8—41no—
474#124—22no—
475#124—41no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8D4×C3114yes—
480C4×Q8—22no—
481C4×Q8—41no—
482#117—22no—
483#117—41no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C4⋊C4C23×C3111yescharacteristic
492C2×C4⋊C4C23×C3111yescharacteristic
493C2×C4⋊C4C23×C3111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4D4×C3111yescharacteristic
502C2×C22⋊C4D4×C3111yescharacteristic
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42C23×C3111yescharacteristic
507C2×C42C23×C3111yescharacteristic
508#107—22no—
509C4⋊C8—22no—
510C4⋊C8—41no—
511#103—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—22no—
516#103—41no—
517#103D4×C3114yes—
518#102—22no—
519#102—22no—
520#102—22no—
521C22⋊C8—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95D4×C3111yescharacteristic
529#95D4×C3111yescharacteristic
530C31#2507911yescharacteristic, direct product factor, Sylow
531C24—21no—
532C24C2×D4×C3111yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C2×D4×C3112yes—
554C2×Q8C2×D4×C3112yes—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4#41×C3112yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4C2×D4×C3111yescharacteristic
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3112yes—
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4#41×C3112yes—
585C22×C4C24×C3111yescharacteristic
586Q16—44no—
587Q16—44no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—44no—
601C2×C8C2×D4×C3112yes—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4C2×D4×C3112yes—
615C4⋊C4C2×D4×C3112yes—
616C22⋊C4—24no—
617C22⋊C4—22no—
618C22⋊C4—41no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—42no—
630C42—42no—
631C42—42no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C31×#12112yes—
646C23C22×D4×C3111yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659D4—22no—
660D4—22no—
661D4—48no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—48no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4C31×#12112yes—
704C2×C4C31×#13512yes—
705C2×C4C22×D4×C3111yescharacteristic
706C2×C4C22×D4×C3111yescharacteristic
707C2×C4C2×#41×C3111yescharacteristic
708C2×C4C2×#41×C3111yescharacteristic
709C2×C4C31×H(5,𝔽2)11yescharacteristic
710C2×C4C31×H(5,𝔽2)11yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22C2×C31×#12111yescharacteristic
730C22D42×C3111yescharacteristic
731C22C31×#54611yescharacteristic
732C22C2×C31×#13511yescharacteristic
733C22C31×#57511yescharacteristic
734C22C31×#57811yescharacteristic
735C22C31×#57811yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—41no—
741C4—42no—
742C4—42no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4C31×#52511yescharacteristic
749C4C31×#53811yescharacteristic
750C4D42×C3111yescharacteristic
751C4C31×#54611yescharacteristic
752C2—42no—
753C2—82no—
754C2C31×#242411yescharacteristic
755C2C31×#303511yescharacteristic
756C2C31×#304411yescharacteristic
757C2C31×#326911yescharacteristic
758C2C31×#328511yescharacteristic
759C2C31×#330211yescharacteristic
760C2C31×#331511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
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. C2×C31×#467C2semidirect
2. C2×C31×#462C2semidirect
6. C31×#2362C2semidirect
7. C31×#2067C2semidirect
8. C31×#2056C2semidirect
9. C31×#2043C2semidirect
10. C31×#2015C2semidirect
11. C31×#1983C2semidirect
12. C31×#1928C2semidirect
13. C31×#1880C2semidirect
14. C31×#1873C2semidirect
15. C31×#1850C2semidirect
251. #25079C31direct (N × H)
335. C2×#467C2×C31semidirect
336. C2×#462C2×C31semidirect
340. #2362C2×C31semidirect
341. #2067C2×C31semidirect
342. #2056C2×C31semidirect
343. #2043C2×C31semidirect
344. #2015C2×C31semidirect
345. #1983C2×C31semidirect
346. #1928C2×C31semidirect
347. #1880C2×C31semidirect
348. #1873C2×C31semidirect
349. #1850C2×C31semidirect
530. C31#25079direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4672
C2×C31×#4622
C2×C31×#4522
C2×C31×#4162
C31×#24322
C31×#23622
C31×#20672
C31×#20562
C31×#20432
C31×#20152
C31×#19832
C31×#19282
C31×#18802
C31×#18732
C31×#18502
#2507931