Finite Group Databasebeta

← C2×#21454482 #30543773

Subgroups — C2×#21454482 #30543773

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840230C211yesmaximal, characteristic
2#21454482C2116yesmaximal, direct product factor
3C2×#16839823C211yesmaximal, characteristic, complemented
4C2×#16839822C211yesmaximal, characteristic, complemented
5C2×#16839822C211yesmaximal, characteristic, complemented
6C2×#16839817C211yesmaximal, characteristic, complemented
7C2×#16839816C211yesmaximal, characteristic, complemented
8C2×#16839813C211yesmaximal, characteristic, complemented
9C2×#16839812C211yesmaximal, characteristic, complemented
10C2×#16839784C211yesmaximal, characteristic, complemented
11C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
12C2×#16839727C211yesmaximal, characteristic
13C2×#16839727C211yesmaximal, characteristic
14C2×#16839719C211yesmaximal, characteristic, complemented
15C2×#16839716C211yesmaximal, characteristic, complemented
16C2×C61×#433C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22#16840230C418yes—
23#16840230C2218yes—
24C2×#14519742C411yescharacteristic
25C2×#14519742C411yescharacteristic
26C2×#14519739C411yescharacteristic
27C2×#14519739C411yescharacteristic
28C2×#14519737C411yescharacteristic
29C2×#14519737C411yescharacteristic
30C2×#14519737C411yescharacteristic
31C2×#14519737C411yescharacteristic
32C2×#14519734C2211yescharacteristic
33C2×#14519734C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C2×C42×D61C2211yescharacteristic
36C2×C42×D61C2211yescharacteristic
37#16839823C2218yescomplemented
38#16839822C2218yescomplemented
39#16839822C2218yescomplemented
40#16839817C2218yescomplemented
41#16839816C2218yescomplemented
42#16839813C2218yescomplemented
43#16839812C2218yescomplemented
44#16839784C2218yescomplemented
45C2×C4⋊#92418C2211yescharacteristic
46C2×C4⋊#92418C2211yescharacteristic
47C2×#14519706C2211yescharacteristic
48C2×#14519706C2211yescharacteristic
49C2×#14519706C2211yescharacteristic
50C2×#14519706C2211yescharacteristic
51C4⋊C8×D61C2218yescomplemented
52#16839727C2218yes—
53#16839727C2218yes—
54C2×C22⋊#92418C2211yescharacteristic
55C2×C22⋊#92418C2211yescharacteristic
56C2×#14519689C2211yescharacteristic
57C2×#14519689C2211yescharacteristic
58C2×#14519689C2211yescharacteristic
59C2×#14519689C2211yescharacteristic
60#16839719C2218yescomplemented
61#16839716C2218yescomplemented
62C2×#14519688C2211yescharacteristic
63C2×#14519687C2211yescharacteristic
64C2×#14519687C2211yescharacteristic
65C2×C4×#92418C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×#117×C61C2211yescharacteristic
69C61×#433C2218yescomplemented
70C2×C4⋊C8×C61C2211yescharacteristic
71C2×C4⋊C8×C61C2211yescharacteristic
72C2×C22⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×#97×C61C2211yescharacteristic
75C2×C4×C8×C61C2211yescharacteristic
76C2×#11758222—24no—
77C2×#11758222—24no—
78C2×#11758222C2×C414yes—
79C2×#11758222C2314yes—
80C22×Dic122C2×C411yescharacteristic
81C22×D244C2×C411yescharacteristic
82C22×C22⋊D61C2×C411yescharacteristic
83C22×C22⋊D61C2×C411yescharacteristic
84C23×Dic61C2×C411yescharacteristic
85C23×Dic61C2×C411yescharacteristic
86C22×C4×D61C2×C411yescharacteristic
87C22×C4×D61C2×C411yescharacteristic
88C22×C4×D61C2×C411yescharacteristic
89C22×C4×D61C2×C411yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C2×#11758189—24no—
93C2×#11758189—24no—
94C2×#11758189C2314yes—
95C2×#11758189C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C2×C8×D61—24no—
101C2×C8×D61—24no—
102C2×C8×D61C2314yes—
103C2×C8×D61C2314yes—
104#14519742C2×C418yes—
105#14519742C2×C418yes—
106#14519739C2×C418yes—
107#14519739C2×C418yes—
108#14519737C2×C418yes—
109#14519737C2×C418yes—
110#14519737C2×C418yes—
111#14519737C2×C418yes—
112#14519734C2×C414yes—
113#14519734C2×C414yes—
114#14519734C2314yes—
115#14519734C2314yes—
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×C4×Dic61C2×C411yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2×C411yescharacteristic
129C2×C4×Dic61C2×C411yescharacteristic
130C2×C4×Dic61C2×C414yes—
131C2×C4×Dic61C2311yescharacteristic
132C2×C4×Dic61C2311yescharacteristic
133C2×C4×Dic61C2314yes—
134C42×D61C2×C414yes—
135C42×D61C2×C414yes—
136C42×D61C2314yes—
137C42×D61C2314yes—
138C4⋊#92418C2314yes—
139C4⋊#92418C2314yes—
140#14519706C2314yes—
141#14519706C2314yes—
142#14519706C2314yes—
143#14519706C2314yes—
144C22⋊#92418C2314yes—
145C22⋊#92418C2314yes—
146#14519689C2314yes—
147#14519689C2314yes—
148#14519689C2314yes—
149#14519689C2314yes—
150#14519688C2314yes—
151#14519687C2314yes—
152#14519687C2314yes—
153C4×#92418C2314yes—
154C8×Dic61C2314yes—
155C8×Dic61C2314yes—
156C23×C4×C61C2311yescharacteristic
157C22×C8×C61C2311yescharacteristic
158C22×C8×C61C2311yescharacteristic
159C22×C8×C61C2311yescharacteristic
160C22×C8×C61C2311yescharacteristic
161#117×C61C2×C414yes—
162#117×C61C2314yes—
163C2×C4⋊C4×C61C2×C411yescharacteristic
164C2×C4⋊C4×C61C2×C411yescharacteristic
165C2×C22⋊C4×C61C2×C411yescharacteristic
166C2×C22⋊C4×C61C2×C411yescharacteristic
167C2×C42×C61C2311yescharacteristic
168C2×C42×C61C2311yescharacteristic
169C4⋊C8×C61C2314yes—
170C4⋊C8×C61C2314yes—
171C22⋊C8×C61C2314yes—
172C22⋊C8×C61C2314yes—
173#97×C61C2314yes—
174C4×C8×C61C2314yes—
175C24×C61C22×C411yescharacteristic
176C23×D61C22×C411yescharacteristic
177C23×D61C22×C411yescharacteristic
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C412yes—
186C22×C4×C61C2412yes—
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61C22×C414yes—
191C2×C22⋊D61C22×C414yes—
192C22×Dic61—24no—
193C22×Dic61—42no—
194C22×Dic61C22×C411yescharacteristic
195C22×Dic61C22×C411yescharacteristic
196C22×Dic61C22×C411yescharacteristic
197C22×Dic61C22×C411yescharacteristic
198C22×Dic61C22×C414yes—
199C22×Dic61C22×C414yes—
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202#11758222—216no—
203#11758222—28no—
204#11758222—28no—
205C2×D244—24no—
206C2×D244C22×C414yes—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—24no—
210C2×C4×D61—24no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61C22×C414yes—
214C2×C4×D61C22×C414yes—
215C2×C4×D61C22×C412yes—
216C2×C4×D61C22×C414yes—
217C2×C4×D61C22×C414yes—
218C2×C4×D61C22×C412yes—
219C2×C4×D61#4114yes—
220C2×C4×D61#4114yes—
221C2×C4×D61C2412yes—
222C2×C4×D61C2412yes—
223C2×Dic122—24no—
224C2×Dic122C22×C414yes—
225C2×C8×C61—22no—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61C2412yes—
230C2×C8×C61C2412yes—
231C2×C8×C61C2412yes—
232C2×C8×C61C2412yes—
233C4⋊C4×C61C22×C414yes—
234C4⋊C4×C61C22×C414yes—
235C22⋊C4×C61C22×C414yes—
236C22⋊C4×C61C22×C414yes—
237C42×C61C22×C412yes—
238C42×C61C22×C412yes—
239C42×C61C2412yes—
240C42×C61C2412yes—
241#11758198C22×C414yes—
242#11758198C22×C414yes—
243#11758198C22×C414yes—
244#11758198C22×C414yes—
245#11758196C22×C414yes—
246#11758196C22×C414yes—
247#11758196C22×C414yes—
248#11758196C22×C414yes—
249C4×Dic61C22×C412yes—
250C4×Dic61C22×C414yes—
251C4×Dic61C22×C414yes—
252C4×Dic61C22×C414yes—
253C4×Dic61C22×C414yes—
254C4×Dic61C22×C412yes—
255C4×Dic61C22×C414yes—
256C4×Dic61C22×C414yes—
257C4×Dic61C2412yes—
258C4×Dic61C2412yes—
259C2×#92418—22no—
260C2×#92418—22no—
261C2×#92418—22no—
262C2×#92418—22no—
263C2×#92418C2412yes—
264C2×#92418C2412yes—
265C2×#92418C2412yes—
266C2×#92418C2412yes—
267#11758189—28no—
268#11758189—28no—
269C8×D61—28no—
270C8×D61—28no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61C23×C412yes—
275C23×C61C23×C411yescharacteristic
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61#11714yes—
282C22×D61C23×C412yes—
283C22×D61C23×C412yes—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61C23×C412yes—
293C2×C4×C61C23×C412yes—
294C2×C4×C61C23×C412yes—
295C2×C4×C61C23×C412yes—
296C2×C4×C61C23×C412yes—
297C2×C4×C61C23×C411yescharacteristic
298C2×C4×C61C2×#4112yes—
299C2×C4×C61C2×#4112yes—
300C2×C4×C61C2511yescharacteristic
301C22⋊D61—28no—
302C22⋊D61—28no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—28no—
308C2×Dic61—44no—
309C2×Dic61#11714yes—
310C2×Dic61#13114yes—
311C2×Dic61C23×C412yes—
312C2×Dic61C23×C412yes—
313C2×Dic61C23×C412yes—
314C2×Dic61C23×C412yes—
315C2×Dic61C23×C412yes—
316C2×Dic61C23×C412yes—
317D244—28no—
318C4×D61—24no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—28no—
322C4×D61—28no—
323C4×D61—44no—
324C4×D61—44no—
325C4×D61#11718yes—
326C4×D61C2×#4114yes—
327C4×D61C2×#4114yes—
328Dic122—28no—
329C8×C61—22no—
330C8×C61—22no—
331C8×C61—22no—
332C8×C61—22no—
333#92418—22no—
334#92418—22no—
335#92418—22no—
336#92418—22no—
337C2×#2925—611nomaximal, Sylow
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—44no—
342C22×C61C2×#11712yes—
343C22×C61C2×#13112yes—
344C22×C61#56812yes—
345C22×C61C24×C411yescharacteristic
346C2×D61—28no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—44no—
353C2×D61C2×#11714yes—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61C2×#11712yes—
360C4×C61C22×#4111yescharacteristic
361C4×C61C22×#4111yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
365Dic61—22no—
366Dic61C2×#11714yes—
367Dic61C2×#13114yes—
368C2×C4×#41—611no—
369#2925—6116no—
370C2×#433—611no—
371C2×#433—611no—
372C2×#433—611no—
373C2×#433D6111yescharacteristic, complemented
374C2×#432—611no—
375C2×#432—611no—
376C2×#431—611no—
377C2×#431—611no—
378C2×#423—611no—
379C22×C4⋊C8—611no—
380C2×#408—611no—
381C2×#408—611no—
382C2×#405—611no—
383C2×#405—611no—
384C2×C61—42no—
385C2×C61#292514yescomplemented
386C2×C61C22×#11711yescharacteristic
387C2×C61C22×#13111yescharacteristic
388C2×C61C2×#56811yescharacteristic
389D61—24no—
390D61—42no—
391C22×#41—611no—
392C22×M16—611no—
393C22×M16—611no—
394C23×C8—611no—
395C23×C8—611no—
396C4×#41—618no—
397C4×#41—618no—
398C2×C4×Q8—611no—
399C2×C4×Q8—611no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×C4×D4—611no—
403C2×C4×D4—611no—
404C2×C4×D4—611no—
405C2×C4×D4—611no—
406C2×#117—611no—
407C2×#117—611no—
408C2×#117C2×D6111yescharacteristic
409C22×C42—611no—
410C22×C42—611no—
411C22×C42—611no—
412#433—618no—
413#433—618no—
414#433—618no—
415#433C2×D6118yescomplemented
416#432—618no—
417#432—618no—
418#431—618no—
419#431—618no—
420#423—618no—
421C2×C4⋊C8—611no—
422C2×C4⋊C8—611no—
423C2×C4⋊C8—611no—
424C2×C4⋊C8—611no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×C4⋊C8—618no—
428C2×C4⋊C8C2×D6111yescharacteristic
429C2×C4⋊C8C2×D6111yescharacteristic
430#408—618no—
431#408—618no—
432C2×C22⋊C8—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C22⋊C8—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8C2×D6111yescharacteristic
439C2×C22⋊C8C2×D6111yescharacteristic
440#405—618no—
441#405—618no—
442C2×#97—611no—
443C2×#97—611no—
444C2×#97—611no—
445C2×#97C2×D6111yescharacteristic
446C2×C4×C8—611no—
447C2×C4×C8—611no—
448C2×C4×C8—611no—
449C2×C4×C8C2×D6111yescharacteristic
450C61C2×#292511yescharacteristic, complemented, Sylow
451C2×#41—614no—
452C2×#41—614no—
453C2×#41—1224no—
454C2×#41—1224no—
455C22×Q8—611no—
456C22×D4—611no—
457C22×D4—611no—
458C22×D4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4C22×D6111yescharacteristic
468C2×M16—614no—
469C2×M16—614no—
470C2×M16—1224no—
471C2×M16—1224no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—614no—
477C22×C8—614no—
478C22×C8—1224no—
479C22×C8—1224no—
480C22×C8C22×D6111yescharacteristic
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C4×Q8—618no—
485C4×Q8—618no—
486C4×D4—618no—
487C4×D4—618no—
488C4×D4—618no—
489C4×D4—618no—
490C4×D4—618no—
491C4×D4—618no—
492#117—614no—
493#117—614no—
494#117—614no—
495#117—614no—
496#117C4×D6114yes—
497#117C22×D6114yes—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4C4×D6111yescharacteristic
503C2×C4⋊C4C4×D6111yescharacteristic
504C2×C22⋊C4—611no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4C4×D6111yescharacteristic
509C2×C22⋊C4C4×D6111yescharacteristic
510C2×C42—611no—
511C2×C42—611no—
512C2×C42—611no—
513C2×C42—611no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—614no—
517C2×C42—614no—
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—614no—
521C2×C42—614no—
522C2×C42—614no—
523C2×C42—614no—
524C2×C42C22×D6111yescharacteristic
525C2×C42C22×D6111yescharacteristic
526C4⋊C8—614no—
527C4⋊C8—614no—
528C4⋊C8—614no—
529C4⋊C8—614no—
530C4⋊C8—614no—
531C4⋊C8—614no—
532C4⋊C8C22×D6114yes—
533C4⋊C8C22×D6114yes—
534C22⋊C8—614no—
535C22⋊C8—614no—
536C22⋊C8—614no—
537C22⋊C8—614no—
538C22⋊C8—614no—
539C22⋊C8—614no—
540C22⋊C8C22×D6114yes—
541C22⋊C8C22×D6114yes—
542#97—614no—
543#97—614no—
544#97—614no—
545#97C22×D6114yes—
546C4×C8—614no—
547C4×C8—614no—
548C4×C8—614no—
549C4×C8C22×D6114yes—
550C24—611no—
551C24—611no—
552C24C2×C4×D6111yescharacteristic
553#41—12216no—
554#41—1228no—
555#41—1228no—
556C2×Q8—614no—
557C2×Q8—1224no—
558C2×D4—614no—
559C2×D4—614no—
560C2×D4—614no—
561C2×D4—1224no—
562C2×D4—1224no—
563C2×D4—1224no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—612no—
569C22×C4—614no—
570C22×C4—614no—
571C22×C4—612no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—614no—
577C22×C4—614no—
578C22×C4—612no—
579C22×C4—614no—
580C22×C4—614no—
581C22×C4—612no—
582C22×C4—614no—
583C22×C4—614no—
584C22×C4—1224no—
585C22×C4—1224no—
586C22×C4—1224no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4C2×C4×D6111yescharacteristic
593C22×C4C2×C4×D6112yes—
594C22×C4C2×C4×D6111yescharacteristic
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C23×D6112yes—
599C22×C4C23×D6111yescharacteristic
600M16—1228no—
601M16—1228no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1228no—
611C2×C8—1228no—
612C2×C8—1222no—
613C2×C8—1222no—
614C2×C8—1222no—
615C2×C8—1222no—
616C2×C8C23×D6112yes—
617C2×C8C23×D6112yes—
618C2×C8C23×D6112yes—
619C2×C8C23×D6112yes—
620C4⋊C4—614no—
621C4⋊C4—614no—
622C4⋊C4—614no—
623C4⋊C4—614no—
624C4⋊C4C2×C4×D6114yes—
625C4⋊C4C2×C4×D6114yes—
626C22⋊C4—614no—
627C22⋊C4—614no—
628C22⋊C4—614no—
629C22⋊C4—614no—
630C22⋊C4C2×C4×D6114yes—
631C22⋊C4C2×C4×D6114yes—
632C42—612no—
633C42—612no—
634C42—614no—
635C42—614no—
636C42—614no—
637C42—614no—
638C42—614no—
639C42—614no—
640C42—612no—
641C42—612no—
642C42C2×C4×D6112yes—
643C42C2×C4×D6112yes—
644C42C23×D6112yes—
645C42C23×D6112yes—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—614no—
650C23—612no—
651C23—612no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23C22×C4×D6112yes—
658C23C22×C4×D6111yescharacteristic
659Q8—1228no—
660D4—1228no—
661D4—1228no—
662D4—1228no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—614no—
672C2×C4—614no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—618no—
676C2×C4—614no—
677C2×C4—614no—
678C2×C4—612no—
679C2×C4—612no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—1228no—
683C2×C4—1228no—
684C2×C4—1228no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1224no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—2444no—
693C2×C4—2444no—
694C2×C4—2444no—
695C2×C4C22×C4×D6112yes—
696C2×C4C22×C4×D6112yes—
697C2×C4C22×C4×D6112yes—
698C2×C4C22×C4×D6112yes—
699C2×C4C22×C4×D6112yes—
700C2×C4C22×C4×D6111yescharacteristic
701C2×C4#41×D6112yes—
702C2×C4#41×D6112yes—
703C2×C4C24×D6111yescharacteristic
704C8—22no—
705C8—22no—
706C8—22no—
707C8—22no—
708C8—1222no—
709C8—1222no—
710C8—1222no—
711C8—1222no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—44no—
716C22—614no—
717C22—1222no—
718C22—1222no—
719C22—1228no—
720C22—1222no—
721C22—1222no—
722C22—1222no—
723C22—2444no—
724C22#117×D6112yes—
725C22#131×D6112yes—
726C22#1684052712yes—
727C22C23×C4×D6111yescharacteristic
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—614no—
734C4—614no—
735C4—1222no—
736C4—1222no—
737C4—1222no—
738C4—1222no—
739C4#117×D6112yes—
740C4C2×#41×D6111yescharacteristic
741C4C2×#41×D6111yescharacteristic
742C2—42no—
743C2—1224no—
744C2—2442no—
745C2#2145448214yesdirect product factor
746C2C2×#117×D6111yescharacteristic
747C2C2×#131×D6111yescharacteristic
748C2C2×#1684052711yescharacteristic
subgroupG/H
centerC22×C4C23×D61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C61×#433C2
socleC23×C61C23×C4
prime radicalC22×#11758222C22
cosocleC2×C4×C61C25
hypercenterC2×#433D61
hypocenterC61C2×#2925
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #21454482C2direct (N × H)
3. C2×#16839823C2semidirect
4. C2×#16839822C2semidirect
5. C2×#16839822C2semidirect
6. C2×#16839817C2semidirect
7. C2×#16839816C2semidirect
8. C2×#16839813C2semidirect
9. C2×#16839812C2semidirect
10. C2×#16839784C2semidirect
11. C2×C4⋊C8×D61C2semidirect
14. C2×#16839719C2semidirect
15. C2×#16839716C2semidirect
16. C2×C61×#433C2semidirect
37. #16839823C22semidirect
38. #16839822C22semidirect
39. #16839822C22semidirect
40. #16839817C22semidirect
41. #16839816C22semidirect
42. #16839813C22semidirect
43. #16839812C22semidirect
44. #16839784C22semidirect
51. C4⋊C8×D61C22semidirect
60. #16839719C22semidirect
61. #16839716C22semidirect
69. C61×#433C22semidirect
373. C2×#433D61semidirect
385. C2×C61#2925semidirect
415. #433C2×D61semidirect
450. C61C2×#2925semidirect
745. C2#21454482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402302
#214544822
C2×#168398232
C2×#168398222
C2×#168398172
C2×#168398162
C2×#168398132
C2×#168398122
C2×#168397842
C2×C4⋊C8×D612
C2×#168397272
C2×#168397192
C2×#168397162
C2×C61×#4332
C2×#292561