Finite Group Databasebeta

← #29700223

Subgroups — #29700223

Order 15616.

1144 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839840C211yesmaximal, characteristic, complemented
2C2×#16839834C211yesmaximal, characteristic, complemented
3C2×#16839729C211yesmaximal, characteristic, complemented
4C2×#16839729C211yesmaximal, characteristic, complemented
5#21446618C211yesmaximal, characteristic, complemented
6#21446434C211yesmaximal, characteristic, complemented
7#21446427C211yesmaximal, characteristic, complemented
8#21446117C211yesmaximal, characteristic, complemented
9#21446117C211yesmaximal, characteristic, complemented
10#21446112C211yesmaximal, characteristic, complemented
11#21446004C211yesmaximal, characteristic, complemented
12#21445999C211yesmaximal, characteristic, complemented
13#21445603C211yesmaximal, characteristic, complemented
14#21445597C211yesmaximal, characteristic, complemented
15C61×#2388C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21#16839840—24no—
22#16839834—24no—
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26#16839729—24no—
27#16839729—24no—
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×#14519688C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C22×#41×C61C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C2×C4×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C61×#395C411yescharacteristic
53C61×#394C411yescharacteristic
54C61×#394C411yescharacteristic
55C61×#394C411yescharacteristic
56C61×#393C411yescharacteristic
57C61×#392C411yescharacteristic
58C61×#392C411yescharacteristic
59C61×#392C411yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C4×C22⋊C4×C61C2211yescharacteristic
62C4×C22⋊C4×C61C2211yescharacteristic
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194—41no—
70C2×#11758194—41no—
71C2×#11758194—41no—
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—22no—
75C22×#92418—22no—
76C22×#92418—41no—
77C22×#92418—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C4⋊#92418—22no—
87C4⋊#92418—22no—
88C4⋊#92418—41no—
89C22⋊#92418—22no—
90C22⋊#92418—22no—
91C22⋊#92418—22no—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94C22⋊#92418—22no—
95C22⋊#92418—22no—
96C22⋊#92418—22no—
97C22⋊#92418—41no—
98C22⋊#92418D414yescomplemented
99C22⋊#92418D414yescomplemented
100#14519688—22no—
101#14519688—41no—
102C4×#92418—22no—
103C2×#41×C61—22no—
104C2×#41×C61—22no—
105C2×#41×C61—22no—
106C2×#41×C61—22no—
107C2×#41×C61—41no—
108C2×#41×C61—41no—
109C22×Q8×C61C2×C411yescharacteristic
110C22×D4×C61C2×C411yescharacteristic
111C22×D4×C61C2×C411yescharacteristic
112C22×D4×C61C2×C411yescharacteristic
113C22×D4×C61C2×C411yescharacteristic
114C22×D4×C61C2×C411yescharacteristic
115C22×D4×C61C2×C411yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C23×C4×C61C2311yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C4×D4×C61—22no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C4×D4×C61—41no—
125C4×D4×C61—41no—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130C2×C22⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2×C411yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C42×C61C2311yescharacteristic
142C2×C42×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#95×C61C2×C411yescharacteristic
145#95×C61C2×C411yescharacteristic
146#95×C61C2×C411yescharacteristic
147#95×C61C2×C411yescharacteristic
148#95×C61C2×C411yescharacteristic
149#95×C61C2×C411yescharacteristic
150C24×C61C22×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154#41×C61—44no—
155#41×C61—44no—
156#41×C61—44no—
157#41×C61—44no—
158C2×Q8×C61—22no—
159C2×Q8×C61—22no—
160C2×Q8×C61—41no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—41no—
171C2×D4×C61—41no—
172C2×D4×C61—41no—
173C2×D4×C61—41no—
174C2×D4×C61—41no—
175C2×D4×C61—41no—
176C2×D4×C61—41no—
177C2×D4×C61—41no—
178C2×D4×C61—41no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C22×C411yescharacteristic
207C22×C4×C61C22×C411yescharacteristic
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C2×D412yes—
210C22×C4×C61C2×D412yes—
211C22×C4×C61#4112yes—
212C22×C4×C61#4112yes—
213C22×C4×C61C2411yescharacteristic
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—41no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—41no—
224C22⋊C4×C61—41no—
225C22⋊C4×C61—41no—
226C22⋊C4×C61—41no—
227C22⋊C4×C61—41no—
228C22⋊C4×C61—41no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—21no—
233C42×C61—21no—
234C42×C61—21no—
235#11758194—44no—
236#11758194—44no—
237#11758194—44no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—44no—
259C2×#92418—44no—
260C2×#92418C2×D412yes—
261C2×#92418C2×D412yes—
262C2×#92418C2×D412yes—
263C2×#92418C2×D412yes—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61C4×D412yes—
291C23×C61C4×D412yes—
292C23×C61C23×C411yescharacteristic
293Q8×C61—44no—
294D4×C61—44no—
295D4×C61—44no—
296D4×C61—44no—
297D4×C61—44no—
298D4×C61—44no—
299D4×C61—44no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61C4×D412yes—
344C2×C4×C61C4×D412yes—
345C2×C4×C61#13112yes—
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2×#4111yescharacteristic
349C2×C4×C61C2×#4111yescharacteristic
350C2×C4×C61H(5,𝔽2)11yescharacteristic
351C2×C4×C61H(5,𝔽2)11yescharacteristic
352#92418—22no—
353#92418—22no—
354#92418—22no—
355#92418—22no—
356#92418—41no—
357#92418—41no—
358#92418—41no—
359#92418—41no—
360#22849—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61C2×C4×D411yescharacteristic
390C22×C61C2×C4×D411yescharacteristic
391C22×C61#51811yescharacteristic
392C22×C61C2×#13111yescharacteristic
393C22×C61#56811yescharacteristic
394C22×C61#56811yescharacteristic
395C22×C61#56811yescharacteristic
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—41no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61D4211yescharacteristic
407C4×C61#54611yescharacteristic
408C4×C61#54611yescharacteristic
409C4×C61#55111yescharacteristic
410C2×#436—611no—
411C2×#435—611no—
412C2×#408—611no—
413C2×#408—611no—
414#2388D6111yescharacteristic
415#1955—611no—
416#1924—611no—
417#1923—611no—
418#1870—611no—
419#1870—611no—
420#1869—611no—
421#1851—611no—
422#1850—611no—
423#1753—611no—
424#1752—611no—
425C2×C61—42no—
426C2×C61—42no—
427C2×C61—81no—
428C2×C61—81no—
429C2×C61#235811yescharacteristic
430C2×C61#293011yescharacteristic
431C2×C61#293211yescharacteristic
432C2×C61#293311yescharacteristic
433C2×C61#293511yescharacteristic
434C2×C61#297811yescharacteristic
435C2×C61#298111yescharacteristic
436C22×#41C2×D6111yescharacteristic
437C22×M16—611no—
438C22×M16—611no—
439C22×M16—611no—
440C23×C8—611no—
441C23×C8—611no—
442C2×C4×D4C2×D6111yescharacteristic
443C2×C4×D4C2×D6111yescharacteristic
444C2×C4×D4C2×D6111yescharacteristic
445#436—1224no—
446#435—1224no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8—611no—
450#408—1224no—
451#408—1224no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—611no—
463C2×#97—611no—
464C2×#97—611no—
465C2×C4×C8—611no—
466#395Dic6111yescharacteristic
467#394Dic6111yescharacteristic
468#394Dic6111yescharacteristic
469#394Dic6111yescharacteristic
470#393Dic6111yescharacteristic
471#392Dic6111yescharacteristic
472#392Dic6111yescharacteristic
473#392Dic6111yescharacteristic
474C4×C22⋊C4C2×D6111yescharacteristic
475C4×C22⋊C4C2×D6111yescharacteristic
476C4×C22⋊C4C2×D6111yescharacteristic
477#336—611no—
478#336—611no—
479#336—611no—
480#336—611no—
481#336—611no—
482#336—611no—
483C61#2284911yescharacteristic, complemented, Sylow
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8C2×Dic6111yescharacteristic
491C22×D4C2×Dic6111yescharacteristic
492C22×D4C2×Dic6111yescharacteristic
493C22×D4C2×Dic6111yescharacteristic
494C22×D4C2×Dic6111yescharacteristic
495C22×D4C2×Dic6111yescharacteristic
496C22×D4C2×Dic6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C2×M16—1222no—
502C2×M16—1222no—
503C2×M16—1222no—
504C2×M16—1222no—
505C2×M16—1222no—
506C2×M16—1222no—
507C2×M16—2441no—
508C2×M16—2441no—
509C2×M16—2441no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—611no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—1222no—
519C22×C8—1222no—
520C22×C8—1222no—
521C22×C8—1222no—
522C22×C8—2441no—
523C22×C8—2441no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—41no—
529C4×D4—41no—
530C2×C4⋊C4C2×Dic6111yescharacteristic
531C2×C4⋊C4C2×Dic6111yescharacteristic
532C2×C4⋊C4C2×Dic6111yescharacteristic
533C2×C22⋊C4C2×Dic6111yescharacteristic
534C2×C22⋊C4C2×Dic6111yescharacteristic
535C2×C22⋊C4C2×Dic6111yescharacteristic
536C2×C22⋊C4C2×Dic6111yescharacteristic
537C2×C22⋊C4C2×Dic6111yescharacteristic
538C2×C22⋊C4C2×Dic6111yescharacteristic
539C2×C22⋊C4C2×Dic6111yescharacteristic
540C2×C22⋊C4C2×Dic6111yescharacteristic
541C2×C22⋊C4C2×Dic6111yescharacteristic
542C2×C22⋊C4C2×Dic6111yescharacteristic
543C2×C22⋊C4C2×Dic6111yescharacteristic
544C2×C22⋊C4C2×Dic6111yescharacteristic
545C2×C42C22×D6111yescharacteristic
546C2×C42C22×D6111yescharacteristic
547C2×C42C22×D6111yescharacteristic
548C4⋊C8—1222no—
549C4⋊C8—1222no—
550C4⋊C8—2441no—
551C22⋊C8—614no—
552C22⋊C8—614no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560C22⋊C8—1222no—
561C22⋊C8—2441no—
562#97—1222no—
563#97—2441no—
564C4×C8—1222no—
565#95C2×Dic6111yescharacteristic
566#95C2×Dic6111yescharacteristic
567#95C2×Dic6111yescharacteristic
568#95C2×Dic6111yescharacteristic
569#95C2×Dic6111yescharacteristic
570#95C2×Dic6111yescharacteristic
571C24C22×Dic6111yescharacteristic
572C24C22×Dic6111yescharacteristic
573C24C22×Dic6111yescharacteristic
574C24C22×Dic6111yescharacteristic
575#41—44no—
576#41—44no—
577#41—44no—
578#41—44no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—41no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C22×C4—21no—
601C22×C4—21no—
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—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4D4×D6112yes—
621C22×C4D4×D6112yes—
622C22×C4#1175822412yes—
623C22×C4#1175822412yes—
624C22×C4C22×Dic6111yescharacteristic
625C22×C4C22×Dic6111yescharacteristic
626C22×C4C22×Dic6111yescharacteristic
627C22×C4C22×Dic6111yescharacteristic
628C22×C4C22×Dic6111yescharacteristic
629C22×C4C22×Dic6111yescharacteristic
630C22×C4C22×Dic6111yescharacteristic
631C22×C4C22×Dic6111yescharacteristic
632C22×C4C22×Dic6111yescharacteristic
633C22×C4C22×Dic6111yescharacteristic
634C22×C4C23×D6111yescharacteristic
635M16—2444no—
636M16—2444no—
637M16—2444no—
638C2×C8—612no—
639C2×C8—612no—
640C2×C8—612no—
641C2×C8—612no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—2444no—
663C2×C8—2444no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23D4×Dic6112yes—
712C23D4×Dic6112yes—
713C23C23×Dic6111yescharacteristic
714Q8—44no—
715D4—44no—
716D4—44no—
717D4—44no—
718D4—44no—
719D4—44no—
720D4—44no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
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—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4D4×Dic6112yes—
765C2×C4D4×Dic6112yes—
766C2×C4#1451978412yes—
767C2×C4C2×D4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4C2×#1175822411yescharacteristic
770C2×C4C2×#1175822411yescharacteristic
771C2×C4#1451982211yescharacteristic
772C2×C4#1451982211yescharacteristic
773C8—1222no—
774C8—1222no—
775C8—1222no—
776C8—1222no—
777C8—2441no—
778C8—2441no—
779C8—2441no—
780C8—2441no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22C2×D4×Dic6111yescharacteristic
810C22C2×D4×Dic6111yescharacteristic
811C22#1684023711yescharacteristic
812C22C2×#1451978411yescharacteristic
813C22#1684052911yescharacteristic
814C22#1684052911yescharacteristic
815C22#1684052911yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4#1684039411yescharacteristic
827C4#1684039911yescharacteristic
828C4#1684039911yescharacteristic
829C4#1684044311yescharacteristic
830C2—42no—
831C2—42no—
832C2—81no—
833C2—81no—
834C2#2144880311yescharacteristic
835C2#2145452311yescharacteristic
836C2#2145453711yescharacteristic
837C2#2145454611yescharacteristic
838C2#2145456311yescharacteristic
839C2#2145488111yescharacteristic
840C2#2145489511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
Fitting, prime radicalC61×#2388C2
cosocleC22×C4×C61C24
hypercenter#2388D61
hypocenterC61#22849
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C2×#16839840C2semidirect
2. C2×#16839834C2semidirect
3. C2×#16839729C2semidirect
4. C2×#16839729C2semidirect
5. #21446618C2semidirect
6. #21446434C2semidirect
7. #21446427C2semidirect
8. #21446117C2semidirect
9. #21446117C2semidirect
10. #21446112C2semidirect
11. #21446004C2semidirect
12. #21445999C2semidirect
13. #21445603C2semidirect
14. #21445597C2semidirect
98. C22⋊#92418D4semidirect
99. C22⋊#92418D4semidirect
483. C61#22849semidirect

Maximal subgroups

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

subgroupindex
C2×#168398402
C2×#168398342
C2×#168397292
#214466182
#214464342
#214464272
#214461172
#214461122
#214460042
#214459992
#214456032
#214455972
C61×#23882
#2284961