Finite Group Databasebeta

← #30609412

Subgroups — #30609412

Order 15616.

1146 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461008C211yesmaximal, characteristic
2#21461006C211yesmaximal, characteristic
3#21461005C211yesmaximal, characteristic
4#21461005C211yesmaximal, characteristic
5#21461004C211yesmaximal, characteristic
6#21461004C211yesmaximal, characteristic
7#21460999C211yesmaximal, characteristic
8#21460999C211yesmaximal, characteristic
9#21460999C211yesmaximal, characteristic
10#21460999C211yesmaximal, characteristic
11#21460998C211yesmaximal, characteristic
12#21460997C211yesmaximal, characteristic
13#21460997C211yesmaximal, characteristic
14#21460994C211yesmaximal, characteristic
15#387×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
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×C4⋊C4×D61C2211yescharacteristic
45C2×C4⋊C4×D61C2211yescharacteristic
46C2×C42×D61C2211yescharacteristic
47#16839649C411yescharacteristic, complemented
48#16839648C411yescharacteristic, complemented
49#16839647C411yescharacteristic, complemented
50#16839646C411yescharacteristic, complemented
51#16839645C411yescharacteristic, complemented
52#16839644C411yescharacteristic, complemented
53#16839643C411yescharacteristic, complemented
54#95×D61C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#95×D61C2211yescharacteristic
57#95×D61C2211yescharacteristic
58C61×#387C411yescharacteristic, complemented
59C23×#6923C2311yescharacteristic
60C23×#6923C2311yescharacteristic
61C23×#6923C2311yescharacteristic
62C23×#6923C2311yescharacteristic
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C2×C4⋊#6923—22no—
68C2×C4⋊#6923—22no—
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—41no—
76C2×C4⋊#6923—41no—
77C2×C4⋊#6923—41no—
78C2×C4⋊#6923Q814yes—
79C2×C4×#6923—22no—
80C2×C4×#6923—41no—
81C2×C4×#6923—41no—
82C2×C4×#6923—41no—
83C2×C4×#6923—41no—
84C2×C4×#6923—41no—
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—41no—
93(C2×#6923)⋊C4—41no—
94(C2×#6923)⋊C4—41no—
95(C2×#6923)⋊C4—41no—
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)⋊C4—41no—
105(C2×#6923)⋊C4—41no—
106(C2×#6923)⋊C4—41no—
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109C22×C4×D61C2311yescharacteristic
110C22×C4×D61C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×C4⋊Dic61C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C4⋊C4×D61—22no—
121C4⋊C4×D61—22no—
122C4⋊C4×D61—41no—
123C4⋊C4×D61—41no—
124C2×C4×Dic61C2×C411yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C42×D61—41no—
128C42×D61—41no—
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
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
141C2×C4⋊C4×C61C2×C411yescharacteristic
142C2×C4⋊C4×C61C2×C411yescharacteristic
143C2×C42×C61C2×C411yescharacteristic
144#95×C61C2×C411yescharacteristic
145#95×C61C2×C411yescharacteristic
146#95×C61C2×C411yescharacteristic
147#95×C61C2×C411yescharacteristic
148C23×D61C2411yescharacteristic
149C22×#6923—21no—
150C22×#6923—21no—
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×#6923C2×Q812yes—
202C22×#6923C2×Q812yes—
203C22×#6923#4112yes—
204C22×#6923#4112yes—
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C22×C4×C61C22×C411yescharacteristic
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×Dic61C22×C411yescharacteristic
213C22×Dic61C22×C411yescharacteristic
214C22×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216C22×Dic61C22×C411yescharacteristic
217C22×Dic61C22×C411yescharacteristic
218C22×Dic61C22×C411yescharacteristic
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
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×D61C2×Q812yes—
258C2×C4×D61#4112yes—
259C2×C4×D61#4112yes—
260C2×C4×D61#4112yes—
261C4⋊#6923—44no—
262C4⋊#6923—44no—
263C4⋊#6923—44no—
264C4⋊#6923—44no—
265C4×#6923—44no—
266C4×#6923—44no—
267C4⋊C4×C61—22no—
268C4⋊C4×C61—41no—
269C42×C61—41no—
270C4⋊Dic61—22no—
271C4⋊Dic61—41no—
272#11758196—22no—
273#11758196—22no—
274#11758196—41no—
275#11758196—41no—
276C4×Dic61—41no—
277C4×Dic61—41no—
278C4×Dic61—41no—
279C23×C61C23×C411yescharacteristic
280C22×D61C22×Q811yescharacteristic
281C22×D61C2×#4111yescharacteristic
282C22×D61C2×#4111yescharacteristic
283C22×D61C2×#4111yescharacteristic
284C22×D61C2×#4111yescharacteristic
285C22×D61C2×#4111yescharacteristic
286C22×D61H(5,𝔽2)11yescharacteristic
287C22×D61H(5,𝔽2)11yescharacteristic
288C22×D61H(5,𝔽2)11yescharacteristic
289C22×D61H(5,𝔽2)11yescharacteristic
290C22×D61H(5,𝔽2)11yescharacteristic
291C22×D612−1+411yescharacteristic
292C22×D612−1+411yescharacteristic
293C22×D612−1+411yescharacteristic
294C2×#6923—22no—
295C2×#6923—22no—
296C2×#6923—22no—
297C2×#6923—22no—
298C2×#6923—22no—
299C2×#6923—22no—
300C2×#6923—22no—
301C2×#6923—22no—
302C2×#6923—22no—
303C2×#6923—22no—
304C2×#6923—22no—
305C2×#6923—22no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
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×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
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#11712yes—
370C2×C4×C61C4×Q812yes—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61#11712yes—
391C2×Dic61C4×Q812yes—
392C4×D61—22no—
393C4×D61—22no—
394C4×D61—22no—
395C4×D61—22no—
396C4×D61—22no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—22no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420#14472—611nomaximal, Sylow
421C22×C61C2×#11711yescharacteristic
422C22×C61C2×C4×Q811yescharacteristic
423C22×C61C4×#4111yescharacteristic
424C22×C61#51811yescharacteristic
425C22×C61#52011yescharacteristic
426C22×C61#52011yescharacteristic
427C22×C61#52011yescharacteristic
428C2×D61#53811yescharacteristic
429C2×D61#53811yescharacteristic
430C2×D61#53911yescharacteristic
431C2×D61#53911yescharacteristic
432C2×D61#54011yescharacteristic
433C2×D61#54111yescharacteristic
434C2×D61#54111yescharacteristic
435C2×D61#54211yescharacteristic
436C2×D61#54211yescharacteristic
437C2×D61#54211yescharacteristic
438C2×D61#54311yescharacteristic
439C2×D61#54411yescharacteristic
440C2×D61#55111yescharacteristic
441C2×D61#55111yescharacteristic
442C2×D61#55211yescharacteristic
443C2×D61#55311yescharacteristic
444C2×D61#55311yescharacteristic
445C2×D61#55311yescharacteristic
446C2×D61#55411yescharacteristic
447C2×D61#55411yescharacteristic
448C2×D61#55611yescharacteristic
449C2×D61#55711yescharacteristic
450C2×D61#55711yescharacteristic
451C2×D61#55911yescharacteristic
452C2×D61#56011yescharacteristic
453C2×D61#56211yescharacteristic
454C2×D61#56211yescharacteristic
455C2×D61#56311yescharacteristic
456#6923—42no—
457#6923—42no—
458#6923—42no—
459#6923—42no—
460#6923—81no—
461#6923—81no—
462#6923—81no—
463#6923—81no—
464C4×C61—22no—
465C4×C61—22no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—41no—
470C4×C61—41no—
471Dic61—22no—
472Dic61—22no—
473Dic61—41no—
474Dic61—41no—
475Dic61—41no—
476Dic61—41no—
477Dic61—41no—
478C2×#387—611no—
479#1445—611no—
480#1443—611no—
481#1442—611no—
482#1442—611no—
483#1441—611no—
484#1441—611no—
485#1436—611no—
486#1436—611no—
487#1436—611no—
488#1436—611no—
489#1436—611no—
490C4⋊#95—611no—
491C4⋊#95—611no—
492#1434—611no—
493C2×C61#231411yescharacteristic
494C2×C61#232911yescharacteristic
495C2×C61#233411yescharacteristic
496C2×C61#235311yescharacteristic
497C2×C61#235511yescharacteristic
498C2×C61#237011yescharacteristic
499C2×C61#237611yescharacteristic
500D61#275111yescharacteristic
501D61#275511yescharacteristic
502D61#277611yescharacteristic
503D61#278011yescharacteristic
504D61#279611yescharacteristic
505D61#279911yescharacteristic
506D61#280011yescharacteristic
507D61#280211yescharacteristic
508C22×C4⋊C4—611no—
509C22×C4⋊C4—611no—
510C22×C4⋊C4—611no—
511C22×C4⋊C4—611no—
512C22×C4⋊C4—611no—
513C22×C4⋊C4—611no—
514C22×C42—611no—
515C22×C42—611no—
516C22×C42—611no—
517#387—611no—
518#387—611no—
519#387—611no—
520#387—611no—
521#387—611no—
522#387—611no—
523#387—611no—
524#387#692311yescharacteristic, complemented
525C2×#95—611no—
526C2×#95—611no—
527C2×#95—611no—
528C2×#95—611no—
529C2×#95—611no—
530C2×#95—611no—
531C2×#95—611no—
532C2×#95—611no—
533C2×#95—611no—
534C2×#95—611no—
535C2×#95—611no—
536C2×#95—611no—
537C2×#95—611no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
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—
551C61#1447211yescharacteristic, complemented, Sylow
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4—611no—
556C23×C4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—614no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—1222no—
575C2×C4⋊C4—1222no—
576C2×C4⋊C4—1222no—
577C2×C4⋊C4—1222no—
578C2×C4⋊C4—1222no—
579C2×C4⋊C4—1222no—
580C2×C4⋊C4—1222no—
581C2×C4⋊C4—2441no—
582C2×C4⋊C4—2441no—
583C2×C4⋊C4—2441no—
584C2×C4⋊C4—2441no—
585C2×C4⋊C4—2441no—
586C2×C4⋊C4—2441no—
587C2×C4⋊C4—2441no—
588C2×C4⋊C4—2441no—
589C2×C4⋊C4C2×#692311yescharacteristic
590C2×C4⋊C4C2×#692311yescharacteristic
591C2×C42—611no—
592C2×C42—611no—
593C2×C42—611no—
594C2×C42—1222no—
595C2×C42—2441no—
596C2×C42—2441no—
597C2×C42—2441no—
598C2×C42—2441no—
599C2×C42—2441no—
600C2×C42—2441no—
601C2×C42—2441no—
602C2×C42C2×#692311yescharacteristic
603#95—611no—
604#95—611no—
605#95—611no—
606#95—611no—
607#95—611no—
608#95—611no—
609#95—611no—
610#95—611no—
611#95—611no—
612#95—611no—
613#95—611no—
614#95—611no—
615#95—1222no—
616#95—1222no—
617#95—1222no—
618#95—1222no—
619#95—1222no—
620#95—1222no—
621#95—1222no—
622#95—2441no—
623#95—2441no—
624#95—2441no—
625#95—2441no—
626#95—2441no—
627#95—2441no—
628#95—2441no—
629#95—2441no—
630#95—2441no—
631#95—2441no—
632#95—2441no—
633#95—2441no—
634#95—2441no—
635#95—2441no—
636#95—2441no—
637#95C2×#692311yescharacteristic
638#95C2×#692311yescharacteristic
639#95C2×#692311yescharacteristic
640#95C2×#692311yescharacteristic
641C24—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—612no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—612no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
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×C4C22×#692311yescharacteristic
748C22×C4C22×#692311yescharacteristic
749C22×C4C22×#692311yescharacteristic
750C22×C4C22×#692311yescharacteristic
751C22×C4C22×#692311yescharacteristic
752C22×C4C22×#692311yescharacteristic
753C22×C4C22×#692311yescharacteristic
754C4⋊C4—22no—
755C4⋊C4—41no—
756C4⋊C4—1222no—
757C4⋊C4—1222no—
758C4⋊C4—1222no—
759C4⋊C4—2441no—
760C4⋊C4—2441no—
761C4⋊C4—2441no—
762C4⋊C4—2444no—
763C4⋊C4—2444no—
764C4⋊C4—2444no—
765C4⋊C4—2444no—
766C42—41no—
767C42—2441no—
768C42—2441no—
769C42—2441no—
770C42—2444no—
771C42—2444no—
772C23—611no—
773C23—611no—
774C23—611no—
775C23—611no—
776C23—611no—
777C23—611no—
778C23—611no—
779C23—611no—
780C23—611no—
781C23—611no—
782C23—611no—
783C23—611no—
784C23—611no—
785C23—611no—
786C23C23×#692311yescharacteristic
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—612no—
807C2×C4—612no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1222no—
814C2×C4—1222no—
815C2×C4—1222no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
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#1451985612yes—
912C2×C4Q8×#692312yes—
913C22—611no—
914C22—611no—
915C22—611no—
916C22—611no—
917C22—611no—
918C22—611no—
919C22—611no—
920C22—611no—
921C22—611no—
922C22—611no—
923C22—611no—
924C22—611no—
925C22—611no—
926C22—611no—
927C22—611no—
928C22—611no—
929C22—611no—
930C22—611no—
931C22—611no—
932C22—611no—
933C22—611no—
934C22—611no—
935C22—611no—
936C22—611no—
937C22—611no—
938C22—611no—
939C22—611no—
940C22—611no—
941C22C2×#1451985611yescharacteristic
942C22C2×Q8×#692311yescharacteristic
943C22#41×#692311yescharacteristic
944C22#1684082911yescharacteristic
945C22#1684083111yescharacteristic
946C22#1684083111yescharacteristic
947C22#1684083111yescharacteristic
948C4—22no—
949C4—22no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—1222no—
956C4—1222no—
957C4—4881no—
958C4—4881no—
959C4—4881no—
960C4—4881no—
961C4—2442no—
962C4—2442no—
963C4—2442no—
964C4—2442no—
965C4—2441no—
966C4—2441no—
967C4—2441no—
968C4—2441no—
969C4—2441no—
970C2—611no—
971C2—611no—
972C2—611no—
973C2—611no—
974C2—611no—
975C2—611no—
976C2—611no—
977C2—611no—
978C2#2146229711yescharacteristic
979C2#2146231211yescharacteristic
980C2#2146231711yescharacteristic
981C2#2146233611yescharacteristic
982C2#2146233811yescharacteristic
983C2#2146235311yescharacteristic
984C2#2146235911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radical, cosocleC23×D61C24
hypercenter#387#6923
hypocenterC61#14472
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
47. #16839649C4semidirect
48. #16839648C4semidirect
49. #16839647C4semidirect
50. #16839646C4semidirect
51. #16839645C4semidirect
52. #16839644C4semidirect
53. #16839643C4semidirect
58. C61×#387C4semidirect
524. #387#6923semidirect
551. C61#14472semidirect

Maximal subgroups

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

subgroupindex
#214610082
#214610062
#214610052
#214610042
#214609992
#214609982
#214609972
#214609942
#387×D612
#1447261