Finite Group Databasebeta

← #30609325

Subgroups — #30609325

Order 15616.

1302 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×#16840713C211yesmaximal, characteristic
2C2×#16840711C211yesmaximal, characteristic
3C2×#16840711C211yesmaximal, characteristic
4C2×#16840706C211yesmaximal, characteristic
5#21461008C211yesmaximal, characteristic
6#21461006C211yesmaximal, characteristic
7#21461005C211yesmaximal, characteristic
8#21461004C211yesmaximal, characteristic
9#21461004C211yesmaximal, characteristic
10#21461004C211yesmaximal, characteristic
11#21460999C211yesmaximal, characteristic
12#21460998C211yesmaximal, characteristic
13#21460995C211yesmaximal, characteristic
14#21460994C211yesmaximal, characteristic
15#389×D61C211yesmaximal, characteristic
16C22×C4⋊#6923C2211yescharacteristic
17C22×C4⋊#6923C2211yescharacteristic
18C22×C4⋊#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21C22×C4×#6923C2211yescharacteristic
22#16840713—24no—
23#16840711—24no—
24#16840711—24no—
25#16840706—24no—
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
46C2×(C2×#6923)⋊C4C2211yescharacteristic
47C2×(C2×#6923)⋊C4C2211yescharacteristic
48C2×C4⋊C4×D61C2211yescharacteristic
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×C4⋊C4×D61C2211yescharacteristic
51C2×C4⋊C4×D61C2211yescharacteristic
52C2×C42×D61C2211yescharacteristic
53#16839661C411yescharacteristic, complemented
54#16839660C411yescharacteristic, complemented
55#16839659C411yescharacteristic, complemented
56#16839659C411yescharacteristic, complemented
57#16839658C411yescharacteristic, complemented
58#16839657C411yescharacteristic, complemented
59#16839657C411yescharacteristic, complemented
60#95×D61C2211yescharacteristic
61#95×D61C2211yescharacteristic
62C61×#389C411yescharacteristic, complemented
63C23×#6923C2311yescharacteristic
64C23×#6923C2311yescharacteristic
65C23×#6923C2311yescharacteristic
66C23×#6923C2311yescharacteristic
67C23×#6923C2311yescharacteristic
68C23×#6923C2311yescharacteristic
69C23×#6923C2311yescharacteristic
70C23×#6923C2311yescharacteristic
71C2×C4⋊#6923—22no—
72C2×C4⋊#6923—22no—
73C2×C4⋊#6923—22no—
74C2×C4⋊#6923—22no—
75C2×C4⋊#6923—22no—
76C2×C4⋊#6923—22no—
77C2×C4⋊#6923—22no—
78C2×C4⋊#6923—22no—
79C2×C4⋊#6923—41no—
80C2×C4⋊#6923—41no—
81C2×C4⋊#6923—41no—
82C2×C4⋊#6923—41no—
83C2×C4×#6923—22no—
84C2×C4×#6923—22no—
85C2×C4×#6923—22no—
86C2×C4×#6923—22no—
87C2×C4×#6923—41no—
88C2×C4×#6923—41no—
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—22no—
97(C2×#6923)⋊C4—22no—
98(C2×#6923)⋊C4—22no—
99(C2×#6923)⋊C4—22no—
100(C2×#6923)⋊C4—22no—
101(C2×#6923)⋊C4—22no—
102(C2×#6923)⋊C4—22no—
103(C2×#6923)⋊C4—41no—
104(C2×#6923)⋊C4—41no—
105(C2×#6923)⋊C4—41no—
106(C2×#6923)⋊C4—41no—
107(C2×#6923)⋊C4—41no—
108(C2×#6923)⋊C4—41no—
109(C2×#6923)⋊C4D414yes—
110(C2×#6923)⋊C4D414yes—
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114C22×C4×D61C2311yescharacteristic
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C2×C4⋊Dic61C2×C411yescharacteristic
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×C4⋊Dic61C2×C411yescharacteristic
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C4⋊C4×D61—22no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61—22no—
134C4⋊C4×D61—22no—
135C4⋊C4×D61—22no—
136C4⋊C4×D61—22no—
137C4⋊C4×D61—22no—
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61C2×C411yescharacteristic
141C42×D61—22no—
142C42×D61—22no—
143#14519684C2×C411yescharacteristic
144#14519684C2×C411yescharacteristic
145#14519684C2×C411yescharacteristic
146#14519684C2×C411yescharacteristic
147#14519684C2×C411yescharacteristic
148#14519684C2×C411yescharacteristic
149C2×C4⋊C4×C61C2×C411yescharacteristic
150C2×C4⋊C4×C61C2×C411yescharacteristic
151C2×C4⋊C4×C61C2×C411yescharacteristic
152C2×C4⋊C4×C61C2×C411yescharacteristic
153C2×C42×C61C2×C411yescharacteristic
154#95×C61C2×C411yescharacteristic
155#95×C61C2×C411yescharacteristic
156C23×D61C2411yescharacteristic
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×#6923—21no—
204C22×#6923—21no—
205C22×#6923—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923C2×D412yes—
210C22×#6923C2×D412yes—
211C22×#6923C2×D412yes—
212C22×#6923C2×D412yes—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C22×C411yescharacteristic
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×Dic61C22×C411yescharacteristic
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
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×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2×D412yes—
265C2×C4×D61#4112yes—
266C2×C4×D61#4112yes—
267C2×C4×D61#4112yes—
268C2×C4×D61#4112yes—
269C4⋊#6923—44no—
270C4⋊#6923—44no—
271C4⋊#6923—44no—
272C4⋊#6923—44no—
273C4×#6923—44no—
274C4×#6923—44no—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—22no—
278C4⋊C4×C61—22no—
279C42×C61—22no—
280C4⋊Dic61—22no—
281C4⋊Dic61—22no—
282C4⋊Dic61—22no—
283C4⋊Dic61—22no—
284#11758196—22no—
285#11758196—22no—
286#11758196—22no—
287#11758196—22no—
288#11758196—22no—
289#11758196—22no—
290#11758196—22no—
291#11758196—22no—
292C4×Dic61—22no—
293C4×Dic61—22no—
294C4×Dic61—22no—
295C23×C61C23×C411yescharacteristic
296C22×D61C22×D411yescharacteristic
297C22×D61C22×D411yescharacteristic
298C22×D61C2×#4111yescharacteristic
299C22×D61C2×#4111yescharacteristic
300C22×D61C2×#4111yescharacteristic
301C22×D61C2×#4111yescharacteristic
302C22×D61H(5,𝔽2)11yescharacteristic
303C22×D61H(5,𝔽2)11yescharacteristic
304C22×D612−1+411yescharacteristic
305C22×D612−1+411yescharacteristic
306C22×D612−1+411yescharacteristic
307C22×D612−1+411yescharacteristic
308C22×D612−1+411yescharacteristic
309C22×D612−1+411yescharacteristic
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—22no—
319C2×#6923—22no—
320C2×#6923—22no—
321C2×#6923—22no—
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—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
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—21no—
383C2×C4×C61—21no—
384C2×C4×C61#11712yes—
385C2×C4×C61C4×D412yes—
386C2×C4×C61C4×D412yes—
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—21no—
404C2×Dic61—21no—
405C2×Dic61#11712yes—
406C2×Dic61C4×D412yes—
407C2×Dic61C4×D412yes—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—22no—
411C4×D61—22no—
412C4×D61—22no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
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—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436#14385—611nomaximal, Sylow
437C22×C61C2×#11711yescharacteristic
438C22×C61C2×C4×D411yescharacteristic
439C22×C61C2×C4×D411yescharacteristic
440C22×C61#51911yescharacteristic
441C22×C61#51911yescharacteristic
442C22×C61#52011yescharacteristic
443C22×C61#52011yescharacteristic
444C2×D61#53611yescharacteristic
445C2×D61#53611yescharacteristic
446C2×D61#53611yescharacteristic
447C2×D61#53711yescharacteristic
448C2×D61#54111yescharacteristic
449C2×D61#54111yescharacteristic
450C2×D61#54111yescharacteristic
451C2×D61#54111yescharacteristic
452C2×D61#54111yescharacteristic
453C2×D61#54211yescharacteristic
454C2×D61#54211yescharacteristic
455C2×D61#54211yescharacteristic
456C2×D61D4211yescharacteristic
457C2×D61#54611yescharacteristic
458C2×D61#54711yescharacteristic
459C2×D61#54711yescharacteristic
460C2×D61#54711yescharacteristic
461C2×D61#54811yescharacteristic
462C2×D61#54811yescharacteristic
463C2×D61#55211yescharacteristic
464C2×D61#55211yescharacteristic
465C2×D61#55211yescharacteristic
466C2×D61#55311yescharacteristic
467C2×D61#55311yescharacteristic
468C2×D61#56211yescharacteristic
469C2×D61#56311yescharacteristic
470C2×D61#56311yescharacteristic
471C2×D61#56411yescharacteristic
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—22no—
483C4×C61—41no—
484C4×C61—41no—
485C4×C61—41no—
486C4×C61—41no—
487Dic61—22no—
488Dic61—22no—
489Dic61—22no—
490Dic61—41no—
491Dic61—41no—
492Dic61—41no—
493Dic61—41no—
494C2×#389—611no—
495C2×#389—611no—
496C2×#387—611no—
497C2×#387—611no—
498C2×#382—611no—
499#1445—611no—
500#1443—611no—
501#1442—611no—
502#1441—611no—
503#1441—611no—
504#1441—611no—
505#1436—611no—
506#1436—611no—
507#1434—611no—
508#1434—611no—
509C2×C61#232011yescharacteristic
510C2×C61#232311yescharacteristic
511C2×C61#232711yescharacteristic
512C2×C61#234411yescharacteristic
513C2×C61#235211yescharacteristic
514C2×C61#236111yescharacteristic
515C2×C61#238211yescharacteristic
516D61#267211yescharacteristic
517D61#267411yescharacteristic
518D61#269811yescharacteristic
519D61#271911yescharacteristic
520D61#271911yescharacteristic
521D61#272511yescharacteristic
522D61#276611yescharacteristic
523D61#277211yescharacteristic
524C22×C4⋊C4—611no—
525C22×C4⋊C4—611no—
526C22×C4⋊C4—611no—
527C22×C4⋊C4—611no—
528C22×C4⋊C4—611no—
529C22×C4⋊C4—611no—
530C22×C4⋊C4—611no—
531C22×C4⋊C4—611no—
532C22×C42—611no—
533C22×C42—611no—
534C22×C42—611no—
535#389—611no—
536#389—611no—
537#389—611no—
538#389—611no—
539#389—611no—
540#389—611no—
541#389—611no—
542#389—1224no—
543#389#692311yescharacteristic, complemented
544#387—1224no—
545#387—1224no—
546#382—1224no—
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—
569C2×#95—611no—
570C2×#95—611no—
571C61#1438511yescharacteristic, complemented, Sylow
572C23×C4—611no—
573C23×C4—611no—
574C23×C4—611no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—611no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1222no—
601C2×C4⋊C4—1222no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4—2441no—
616C2×C4⋊C4—2441no—
617C2×C4⋊C4—2441no—
618C2×C4⋊C4—2441no—
619C2×C4⋊C4C2×#692311yescharacteristic
620C2×C4⋊C4C2×#692311yescharacteristic
621C2×C4⋊C4C2×#692311yescharacteristic
622C2×C4⋊C4C2×#692311yescharacteristic
623C2×C42—611no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1222no—
627C2×C42—1222no—
628C2×C42—1222no—
629C2×C42—1222no—
630C2×C42—1222no—
631C2×C42—1222no—
632C2×C42—2441no—
633C2×C42—2441no—
634C2×C42C2×#692311yescharacteristic
635#95—614no—
636#95—614no—
637#95—611no—
638#95—611no—
639#95—611no—
640#95—611no—
641#95—611no—
642#95—611no—
643#95—1222no—
644#95—1222no—
645#95—1222no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650#95—1222no—
651#95—1222no—
652#95—1222no—
653#95—1222no—
654#95—1222no—
655#95—1222no—
656#95—1222no—
657#95—2441no—
658#95—2441no—
659#95—2441no—
660#95—2441no—
661#95—2441no—
662#95—2441no—
663#95C2×#692311yescharacteristic
664#95C2×#692311yescharacteristic
665C24—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—612no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—612no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
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×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×C4C22×#692311yescharacteristic
772C22×C4C22×#692311yescharacteristic
773C22×C4C22×#692311yescharacteristic
774C22×C4C22×#692311yescharacteristic
775C22×C4C22×#692311yescharacteristic
776C22×C4C22×#692311yescharacteristic
777C22×C4C22×#692311yescharacteristic
778C4⋊C4—22no—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—1222no—
783C4⋊C4—1222no—
784C4⋊C4—1222no—
785C4⋊C4—1222no—
786C4⋊C4—1222no—
787C4⋊C4—1222no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1222no—
793C4⋊C4—1222no—
794C4⋊C4—2444no—
795C4⋊C4—2444no—
796C4⋊C4—2444no—
797C4⋊C4—2444no—
798C42—22no—
799C42—1222no—
800C42—1222no—
801C42—1222no—
802C42—2444no—
803C42—2444no—
804C23—611no—
805C23—611no—
806C23—611no—
807C23—611no—
808C23—611no—
809C23—611no—
810C23—611no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23—611no—
815C23—611no—
816C23—611no—
817C23—611no—
818C23C23×#692311yescharacteristic
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—612no—
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—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1222no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
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—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
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#1451985612yes—
943C2×C4D4×#692312yes—
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
975C22C2×D4×#692311yescharacteristic
976C22#1684083011yescharacteristic
977C22#1684083011yescharacteristic
978C22#1684083111yescharacteristic
979C22#1684083111yescharacteristic
980C4—22no—
981C4—22no—
982C4—22no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—1222no—
988C4—1222no—
989C4—1222no—
990C4—4881no—
991C4—4881no—
992C4—4881no—
993C4—4881no—
994C4—2442no—
995C4—2442no—
996C4—2442no—
997C4—2442no—
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#2146231011yescharacteristic
1013C2#2146232711yescharacteristic
1014C2#2146233511yescharacteristic
1015C2#2146234411yescharacteristic
1016C2#2146236511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#389C4
prime radical, cosocleC23×D61C24
hypercenter#389#6923
hypocenterC61#14385
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
53. #16839661C4semidirect
54. #16839660C4semidirect
55. #16839659C4semidirect
56. #16839659C4semidirect
57. #16839658C4semidirect
58. #16839657C4semidirect
59. #16839657C4semidirect
62. C61×#389C4semidirect
543. #389#6923semidirect
571. C61#14385semidirect

Maximal subgroups

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

subgroupindex
C2×#168407132
C2×#168407112
C2×#168407062
#214610082
#214610062
#214610052
#214610042
#214609992
#214609982
#214609952
#214609942
#389×D612
#1438561