Finite Group Databasebeta

← #30609320

Subgroups — #30609320

Order 15616.

1266 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C2×#6923)⋊Q8C211yesmaximal, characteristic
2C2×#16840707C211yesmaximal, characteristic
3#21461009C211yesmaximal, characteristic
4#21461006C211yesmaximal, characteristic
5#21461006C211yesmaximal, characteristic
6#21461005C211yesmaximal, characteristic
7#21461005C211yesmaximal, characteristic
8#21461004C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic
11#21460998C211yesmaximal, characteristic
12#21460995C211yesmaximal, characteristic
13#21460994C211yesmaximal, characteristic
14#21460994C211yesmaximal, characteristic
15#391×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4×#6923C2211yescharacteristic
19C22×C4×#6923C2211yescharacteristic
20(C2×#6923)⋊Q8—24no—
21#16840707—24no—
22C2×(C2×#6923)⋊C4C2211yescharacteristic
23C2×(C2×#6923)⋊C4C2211yescharacteristic
24C2×(C2×#6923)⋊C4C2211yescharacteristic
25C2×(C2×#6923)⋊C4C2211yescharacteristic
26C2×(C2×#6923)⋊C4C2211yescharacteristic
27C2×(C2×#6923)⋊C4C2211yescharacteristic
28C2×(C2×#6923)⋊C4C2211yescharacteristic
29C2×(C2×#6923)⋊C4C2211yescharacteristic
30C2×(C2×#6923)⋊C4C2211yescharacteristic
31C2×(C2×#6923)⋊C4C2211yescharacteristic
32C2×(C2×#6923)⋊C4C2211yescharacteristic
33C2×(C2×#6923)⋊C4C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36C2×(C2×#6923)⋊C4C2211yescharacteristic
37C2×(C2×#6923)⋊C4C2211yescharacteristic
38C2×(C2×#6923)⋊C4C2211yescharacteristic
39C2×(C2×#6923)⋊C4C2211yescharacteristic
40C2×(C2×#6923)⋊C4C2211yescharacteristic
41C2×(C2×#6923)⋊C4C2211yescharacteristic
42C2×(C2×#6923)⋊C4C2211yescharacteristic
43C2×(C2×#6923)⋊C4C2211yescharacteristic
44C2×(C2×#6923)⋊C4C2211yescharacteristic
45C2×(C2×#6923)⋊C4C2211yescharacteristic
46C22×Q8×D61C2211yescharacteristic
47C2×C4⋊C4×D61C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839669C411yescharacteristic, complemented
50#16839668C411yescharacteristic, complemented
51#16839667C411yescharacteristic, complemented
52#16839666C411yescharacteristic, complemented
53#16839666C411yescharacteristic, complemented
54#16839666C411yescharacteristic, complemented
55#16839666C411yescharacteristic, complemented
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58#95×D61C2211yescharacteristic
59#95×D61C2211yescharacteristic
60C61×#391C411yescharacteristic, complemented
61C23×#6923C2311yescharacteristic
62C23×#6923C2311yescharacteristic
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C2×C4⋊#6923—22no—
70C2×C4⋊#6923—22no—
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923—41no—
73C2×C4⋊#6923—41no—
74C2×C4⋊#6923—41no—
75C2×C4×#6923—22no—
76C2×C4×#6923—22no—
77C2×C4×#6923—22no—
78C2×C4×#6923—41no—
79C2×C4×#6923—41no—
80C2×C4×#6923—41no—
81(C2×#6923)⋊C4—22no—
82(C2×#6923)⋊C4—22no—
83(C2×#6923)⋊C4—22no—
84(C2×#6923)⋊C4—22no—
85(C2×#6923)⋊C4—22no—
86(C2×#6923)⋊C4—22no—
87(C2×#6923)⋊C4—22no—
88(C2×#6923)⋊C4—22no—
89(C2×#6923)⋊C4—22no—
90(C2×#6923)⋊C4—22no—
91(C2×#6923)⋊C4—22no—
92(C2×#6923)⋊C4—22no—
93(C2×#6923)⋊C4—22no—
94(C2×#6923)⋊C4—22no—
95(C2×#6923)⋊C4—22no—
96(C2×#6923)⋊C4—41no—
97(C2×#6923)⋊C4—41no—
98(C2×#6923)⋊C4—41no—
99(C2×#6923)⋊C4—41no—
100(C2×#6923)⋊C4—41no—
101(C2×#6923)⋊C4—41no—
102(C2×#6923)⋊C4—41no—
103(C2×#6923)⋊C4—41no—
104(C2×#6923)⋊C4D414yes—
105C22×Dic122C2×C411yescharacteristic
106C22×Dic122C2×C411yescharacteristic
107C22×Dic122C2×C411yescharacteristic
108C2×Q8×D61—22no—
109C2×Q8×D61—22no—
110C2×Q8×D61—22no—
111C2×Q8×D61—22no—
112C2×Q8×D61—41no—
113C2×Q8×D61—41no—
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C4⋊C4×D61—41no—
125C4⋊C4×D61—41no—
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2×C411yescharacteristic
129C42×D61—22no—
130C42×D61—22no—
131#14519684C2×C411yescharacteristic
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137#14519684C2×C411yescharacteristic
138#14519684C2×C411yescharacteristic
139#14519684C2×C411yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143C22×Q8×C61C2×C411yescharacteristic
144C2×C4⋊C4×C61C2×C411yescharacteristic
145C2×C42×C61C2×C411yescharacteristic
146#95×C61C2×C411yescharacteristic
147#95×C61C2×C411yescharacteristic
148#95×C61C2×C411yescharacteristic
149#95×C61C2×C411yescharacteristic
150C23×D61C2411yescharacteristic
151C22×#6923—21no—
152C22×#6923—21no—
153C22×#6923—21no—
154C22×#6923—21no—
155C22×#6923—21no—
156C22×#6923—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—21no—
182C22×#6923—21no—
183C22×#6923—21no—
184C22×#6923—21no—
185C22×#6923—21no—
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—21no—
194C22×#6923—21no—
195C22×#6923—21no—
196C22×#6923—21no—
197C22×#6923—21no—
198C22×#6923—21no—
199C22×#6923—21no—
200C22×#6923—21no—
201C22×#6923—21no—
202C22×#6923—21no—
203C22×#6923C2×D412yes—
204C22×#6923C2×D412yes—
205C22×#6923#4112yes—
206C22×#6923#4112yes—
207C2×Q8×C61—22no—
208C2×Q8×C61—22no—
209C2×Q8×C61—41no—
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C22×Dic61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224Q8×D61—44no—
225Q8×D61—44no—
226Q8×D61—44no—
227Q8×D61—44no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61C2×D412yes—
267C2×C4×D61#4112yes—
268C2×C4×D61#4112yes—
269C2×C4×D61#4112yes—
270C2×Dic122—22no—
271C2×Dic122—22no—
272C2×Dic122—22no—
273C2×Dic122—22no—
274C2×Dic122—22no—
275C2×Dic122—22no—
276C2×Dic122—41no—
277C2×Dic122—41no—
278C2×Dic122—41no—
279C4⋊#6923—44no—
280C4⋊#6923—44no—
281C4×#6923—44no—
282C4×#6923—44no—
283C4⋊C4×C61—41no—
284C42×C61—22no—
285C4⋊Dic61—41no—
286#11758196—41no—
287#11758196—41no—
288C4×Dic61—22no—
289C4×Dic61—22no—
290C4×Dic61—22no—
291C23×C61C23×C411yescharacteristic
292C22×D61C22×D411yescharacteristic
293C22×D61C2×#4111yescharacteristic
294C22×D61C2×#4111yescharacteristic
295C22×D61C2×#4111yescharacteristic
296C22×D61C2×#4111yescharacteristic
297C22×D61C2×#4111yescharacteristic
298C22×D61H(5,𝔽2)11yescharacteristic
299C22×D61H(5,𝔽2)11yescharacteristic
300C22×D61H(5,𝔽2)11yescharacteristic
301C22×D612−1+411yescharacteristic
302C22×D612−1+411yescharacteristic
303C22×D612−1+411yescharacteristic
304C22×D612−1+411yescharacteristic
305C22×D612−1+411yescharacteristic
306C2×#6923—22no—
307C2×#6923—22no—
308C2×#6923—22no—
309C2×#6923—22no—
310C2×#6923—22no—
311C2×#6923—22no—
312C2×#6923—22no—
313C2×#6923—22no—
314C2×#6923—22no—
315C2×#6923—22no—
316C2×#6923—22no—
317C2×#6923—22no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—41no—
361C2×#6923—41no—
362Q8×C61—44no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61#11712yes—
383C2×C4×C61C4×D412yes—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—21no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61#11712yes—
404C2×Dic61C4×D412yes—
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433Dic122—44no—
434Dic122—44no—
435Dic122—44no—
436#14380—611nomaximal, Sylow
437C22×C61C2×#11711yescharacteristic
438C22×C61C2×C4×D411yescharacteristic
439C22×C61C4×#4111yescharacteristic
440C22×C61#51811yescharacteristic
441C22×C61#51911yescharacteristic
442C22×C61#51911yescharacteristic
443C22×C61#52011yescharacteristic
444C2×D61#53611yescharacteristic
445C2×D61#53711yescharacteristic
446C2×D61#53811yescharacteristic
447C2×D61#53811yescharacteristic
448C2×D61#54111yescharacteristic
449C2×D61#54111yescharacteristic
450C2×D61#54111yescharacteristic
451C2×D61#54211yescharacteristic
452C2×D61#54211yescharacteristic
453C2×D61#54211yescharacteristic
454C2×D61#54211yescharacteristic
455C2×D61#54211yescharacteristic
456C2×D61#54611yescharacteristic
457C2×D61#54611yescharacteristic
458C2×D61#54711yescharacteristic
459C2×D61#54811yescharacteristic
460C2×D61#55111yescharacteristic
461C2×D61#55111yescharacteristic
462C2×D61#55211yescharacteristic
463C2×D61#55211yescharacteristic
464C2×D61#55211yescharacteristic
465C2×D61#55611yescharacteristic
466C2×D61#55611yescharacteristic
467C2×D61#55611yescharacteristic
468C2×D61#56311yescharacteristic
469C2×D61#56311yescharacteristic
470C2×D61#56311yescharacteristic
471C2×D61#56311yescharacteristic
472#6923—42no—
473#6923—42no—
474#6923—42no—
475#6923—42no—
476#6923—81no—
477#6923—81no—
478#6923—81no—
479#6923—81no—
480C4×C61—22no—
481C4×C61—22no—
482C4×C61—41no—
483C4×C61—41no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61—41no—
487Dic61—22no—
488Dic61—22no—
489Dic61—41no—
490Dic61—41no—
491Dic61—41no—
492Dic61—41no—
493Dic61—41no—
494C2×#391—611no—
495C2×#391—611no—
496C2×#383—611no—
497#1446—611no—
498#1443—611no—
499#1443—611no—
500#1442—611no—
501#1442—611no—
502#1441—611no—
503#1436—611no—
504#1436—611no—
505#1436—611no—
506#1434—611no—
507#1434—611no—
508#1434—611no—
509C2×C61#232011yescharacteristic
510C2×C61#232311yescharacteristic
511C2×C61#233711yescharacteristic
512C2×C61#234211yescharacteristic
513C2×C61#235611yescharacteristic
514C2×C61#236211yescharacteristic
515C2×C61#238111yescharacteristic
516D61#269811yescharacteristic
517D61#270211yescharacteristic
518D61#271511yescharacteristic
519D61#271611yescharacteristic
520D61#275811yescharacteristic
521D61#275911yescharacteristic
522D61#276211yescharacteristic
523D61#276411yescharacteristic
524C23×Q8—611no—
525C22×C4⋊C4—611no—
526C22×C4⋊C4—611no—
527C22×C4⋊C4—611no—
528C22×C42—611no—
529C22×C42—611no—
530C22×C42—611no—
531#391—611no—
532#391—611no—
533#391—611no—
534#391—611no—
535#391—611no—
536#391—611no—
537#391—611no—
538#391—1224no—
539#391#692311yescharacteristic, complemented
540#383—1224no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95—611no—
555C2×#95—611no—
556C2×#95—611no—
557C2×#95—611no—
558C2×#95—611no—
559C2×#95—611no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C2×#95—611no—
568C2×#95—611no—
569C61#1438011yescharacteristic, complemented, Sylow
570C22×Q8—611no—
571C22×Q8—611no—
572C22×Q8—611no—
573C22×Q8—1222no—
574C22×Q8—1222no—
575C22×Q8—1222no—
576C22×Q8—1222no—
577C22×Q8—2441no—
578C22×Q8—2441no—
579C22×Q8C2×#692311yescharacteristic
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—611no—
587C23×C4—611no—
588C23×C4—611no—
589C23×C4—611no—
590C23×C4—611no—
591C23×C4—611no—
592C23×C4—611no—
593C23×C4—611no—
594C23×C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1222no—
601C2×C4⋊C4—2441no—
602C2×C4⋊C4—2441no—
603C2×C4⋊C4—2441no—
604C2×C4⋊C4—2441no—
605C2×C4⋊C4—2441no—
606C2×C4⋊C4C2×#692311yescharacteristic
607C2×C42—611no—
608C2×C42—611no—
609C2×C42—611no—
610C2×C42—1222no—
611C2×C42—1222no—
612C2×C42—1222no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42—2441no—
616C2×C42—2441no—
617C2×C42—2441no—
618C2×C42C2×#692311yescharacteristic
619#95—614no—
620#95—611no—
621#95—611no—
622#95—611no—
623#95—611no—
624#95—611no—
625#95—611no—
626#95—611no—
627#95—611no—
628#95—611no—
629#95—611no—
630#95—611no—
631#95—611no—
632#95—1222no—
633#95—1222no—
634#95—1222no—
635#95—1222no—
636#95—1222no—
637#95—1222no—
638#95—1222no—
639#95—1222no—
640#95—1222no—
641#95—1222no—
642#95—1222no—
643#95—1222no—
644#95—1222no—
645#95—1222no—
646#95—1222no—
647#95—2441no—
648#95—2441no—
649#95—2441no—
650#95—2441no—
651#95—2441no—
652#95—2441no—
653#95—2441no—
654#95—2441no—
655#95C2×#692311yescharacteristic
656#95C2×#692311yescharacteristic
657#95C2×#692311yescharacteristic
658#95C2×#692311yescharacteristic
659C24—611no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8—41no—
663C2×Q8—1222no—
664C2×Q8—1222no—
665C2×Q8—1222no—
666C2×Q8—1222no—
667C2×Q8—1222no—
668C2×Q8—1222no—
669C2×Q8—2441no—
670C2×Q8—2441no—
671C2×Q8—2441no—
672C2×Q8—2444no—
673C2×Q8—2444no—
674C2×Q8—2444no—
675C2×Q8—2444no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—612no—
679C22×C4—612no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4C22×#692311yescharacteristic
782C22×C4C22×#692311yescharacteristic
783C22×C4C22×#692311yescharacteristic
784C22×C4C22×#692311yescharacteristic
785C22×C4C22×#692311yescharacteristic
786C22×C4C22×#692311yescharacteristic
787C22×C4C22×#692311yescharacteristic
788C4⋊C4—41no—
789C4⋊C4—2441no—
790C4⋊C4—2441no—
791C4⋊C4—2441no—
792C4⋊C4—2444no—
793C4⋊C4—2444no—
794C42—22no—
795C42—1222no—
796C42—1222no—
797C42—1222no—
798C42—2444no—
799C42—2444no—
800C23—611no—
801C23—611no—
802C23—611no—
803C23—611no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—611no—
808C23—611no—
809C23—611no—
810C23—611no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23C23×#692311yescharacteristic
815Q8—44no—
816Q8—2444no—
817Q8—2444no—
818Q8—2444no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—612no—
839C2×C4—612no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4#1451985612yes—
944C2×C4D4×#692312yes—
945C22—611no—
946C22—611no—
947C22—611no—
948C22—611no—
949C22—611no—
950C22—611no—
951C22—611no—
952C22—611no—
953C22—611no—
954C22—611no—
955C22—611no—
956C22—611no—
957C22—611no—
958C22—611no—
959C22—611no—
960C22—611no—
961C22—611no—
962C22—611no—
963C22—611no—
964C22—611no—
965C22—611no—
966C22—611no—
967C22—611no—
968C22—611no—
969C22—611no—
970C22—611no—
971C22—611no—
972C22—611no—
973C22C2×#1451985611yescharacteristic
974C22C2×D4×#692311yescharacteristic
975C22#41×#692311yescharacteristic
976C22#1684082911yescharacteristic
977C22#1684083011yescharacteristic
978C22#1684083011yescharacteristic
979C22#1684083111yescharacteristic
980C4—22no—
981C4—22no—
982C4—41no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—1222no—
988C4—1222no—
989C4—4881no—
990C4—4881no—
991C4—4881no—
992C4—4881no—
993C4—2442no—
994C4—2442no—
995C4—2442no—
996C4—2442no—
997C4—2441no—
998C4—2441no—
999C4—2441no—
1000C4—2441no—
1001C4—2441no—
1002C2—611no—
1003C2—611no—
1004C2—611no—
1005C2—611no—
1006C2—611no—
1007C2—611no—
1008C2—611no—
1009C2—611no—
1010C2#2146230311yescharacteristic
1011C2#2146230611yescharacteristic
1012C2#2146232011yescharacteristic
1013C2#2146232511yescharacteristic
1014C2#2146233911yescharacteristic
1015C2#2146234511yescharacteristic
1016C2#2146236411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#391C4
prime radical, cosocleC23×D61C24
hypercenter#391#6923
hypocenterC61#14380
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
49. #16839669C4semidirect
50. #16839668C4semidirect
51. #16839667C4semidirect
52. #16839666C4semidirect
53. #16839666C4semidirect
54. #16839666C4semidirect
55. #16839666C4semidirect
60. C61×#391C4semidirect
539. #391#6923semidirect
569. C61#14380semidirect

Maximal subgroups

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

subgroupindex
C2×(C2×#6923)⋊Q82
C2×#168407072
#214610092
#214610062
#214610052
#214610042
#214609992
#214609982
#214609952
#214609942
#391×D612
#1438061