Finite Group Databasebeta

← #29647369

Subgroups — #29647369

Order 15616.

1470 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C22×C22⋊#92418C211yesmaximal, characteristic, complemented
3#21444390C212yesmaximal, complemented
4#21444386C212yesmaximal, complemented
5#21444373C214yesmaximal, complemented
6#21444308C214yesmaximal, complemented
7C61×#2280C211yesmaximal, characteristic, complemented
8C22×#11758222C411yescharacteristic, complemented
9C23×#92418—21no—
10#16840273—21no—
11#16840273—21no—
12#16840273—21no—
13#16840273—21no—
14#16840273C412yescomplemented
15#16840273C412yescomplemented
16#16840273C2212yes—
17#16840273C2212yes—
18C2×#14519760—21no—
19C2×#14519756C411yescharacteristic, complemented
20C2×#14519756C2211yescharacteristic
21C2×#14519751C411yescharacteristic, complemented
22C2×#14519751C2211yescharacteristic
23C2×#14519746—21no—
24C2×C4×C22⋊D61—21no—
25C2×C4×C22⋊D61—21no—
26C2×#14519736C411yescharacteristic, complemented
27C2×C22⋊#92418—21no—
28C2×C22⋊#92418—21no—
29C2×C22⋊#92418—21no—
30C2×C22⋊#92418C2212yes—
31C2×C22⋊#92418C2212yescomplemented
32C2×C22⋊#92418C2212yescomplemented
33#16839498C2218yescomplemented
34#16839495C2218yescomplemented
35C24×C4×C61C2211yescharacteristic
36C2×#117×C61—21no—
37C61×#381C2212yescomplemented
38C61×#380—21no—
39C61×#380C2212yes—
40C61×#379—21no—
41C4×C22⋊C4×C61—21no—
42C4×C22⋊C4×C61C2212yescomplemented
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—44no—
46C2×#11758222C2×C412yes—
47C2×#11758222C2×C412yes—
48C22×Dic122C2×C411yescharacteristic
49C22×D244C2×C411yescharacteristic
50C22×C22⋊D61—21no—
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C22×C4×D61—21no—
54C22×#92418—22no—
55C22×#92418—22no—
56C22×#92418—22no—
57C22×#92418—44no—
58#14519760—22no—
59#14519760—22no—
60#14519760—22no—
61#14519760—22no—
62#14519756—21no—
63#14519756—21no—
64#14519756—21no—
65#14519756—21no—
66#14519756C2×C412yes—
67#14519756C2×C412yes—
68#14519756C2×C412yes—
69#14519756C2312yes—
70#14519751—21no—
71#14519751—21no—
72#14519751—21no—
73#14519751—21no—
74#14519751C2×C412yes—
75#14519751C2×C412yes—
76#14519751C2×C412yes—
77#14519751C2312yes—
78#14519746—22no—
79#14519746—22no—
80#14519746—22no—
81#14519746—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86C4×C22⋊D61—22no—
87C4×C22⋊D61—22no—
88C4×C22⋊D61—22no—
89C4×C22⋊D61—22no—
90#14519736—21no—
91#14519736—21no—
92#14519736C2×C412yes—
93#14519736C2×C412yes—
94C2×C4⋊Dic61C2×C411yescharacteristic
95C2×C4⋊Dic61C2×C411yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×C4×Dic61—21no—
104C22⋊#92418—22no—
105C22⋊#92418—22no—
106C22⋊#92418—22no—
107C22⋊#92418C2314yes—
108C25×C61D411yescharacteristic
109C23×C4×C61—44no—
110C23×C4×C61C2×C411yescharacteristic
111C23×C4×C61C2×C411yescharacteristic
112C23×C4×C61C2×C411yescharacteristic
113C23×C4×C61C2×C411yescharacteristic
114C23×C4×C61D411yescharacteristic
115C23×C4×C61D411yescharacteristic
116C23×C4×C61D411yescharacteristic
117C23×C4×C61D411yescharacteristic
118C23×C4×C61D411yescharacteristic
119C23×C4×C61D411yescharacteristic
120C23×C4×C61D411yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124#117×C61—44no—
125C2×C4⋊C4×C61—22no—
126C2×C22⋊C4×C61—22no—
127C2×C22⋊C4×C61—22no—
128C2×C22⋊C4×C61—22no—
129C2×C42×C61—22no—
130#95×C61—22no—
131#95×C61C2314yes—
132C24×C61—24no—
133C24×C61—42no—
134C24×C61—42no—
135C24×C61C22⋊C411yescharacteristic
136C24×C61C22⋊C411yescharacteristic
137C24×C61C22⋊C411yescharacteristic
138C24×C61C22⋊C411yescharacteristic
139C24×C61C2×D411yescharacteristic
140C24×C61C2×D411yescharacteristic
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C22×C4×C61—24no—
144C22×C4×C61—24no—
145C22×C4×C61—24no—
146C22×C4×C61—24no—
147C22×C4×C61—42no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—42no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61C22⋊C411yescharacteristic
159C22×C4×C61C22⋊C411yescharacteristic
160C22×C4×C61C22⋊C411yescharacteristic
161C22×C4×C61C22⋊C411yescharacteristic
162C22×C4×C61C22⋊C411yescharacteristic
163C22×C4×C61C22⋊C411yescharacteristic
164C22×C4×C61C22⋊C411yescharacteristic
165C22×C4×C61C22⋊C411yescharacteristic
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—44no—
193C2×C22⋊D61—44no—
194C2×C22⋊D61—44no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198#11758222—44no—
199#11758222—44no—
200#11758222—44no—
201#11758222—44no—
202C2×D244—21no—
203C2×D244—42no—
204C2×D244C22×C412yes—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—44no—
208C2×Dic122—21no—
209C2×Dic122—42no—
210C2×Dic122C22×C412yes—
211C4⋊C4×C61—44no—
212C22⋊C4×C61—44no—
213C22⋊C4×C61—44no—
214C22⋊C4×C61—44no—
215C42×C61—44no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220C22⋊Dic61—22no—
221C22⋊Dic61—22no—
222#11758198—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198—22no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61C22×C412yes—
229C4⋊Dic61C22×C412yes—
230#11758196—22no—
231#11758196—22no—
232#11758196—22no—
233#11758196—22no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236C2×#92418—24no—
237C2×#92418—44no—
238C2×#92418—44no—
239C2×#92418—44no—
240C23×C61—22no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—416no—
261C23×C61C2×C22⋊C411yescharacteristic
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61C2×C22⋊C411yescharacteristic
267C23×C61#13514yes—
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—42no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—44no—
301C2×C4×C61—44no—
302C2×C4×C61—44no—
303C2×C4×C61#9914yes—
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C2×C22⋊C411yescharacteristic
307C2×C4×C61C2×C22⋊C411yescharacteristic
308C2×C4×C61C2×C22⋊C411yescharacteristic
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C23×C411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C22⋊D61—44no—
313C22⋊D61—44no—
314C22⋊D61—44no—
315C22⋊D61—44no—
316C22⋊D61—44no—
317C22⋊D61—44no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324D244—42no—
325D244—42no—
326C4×D61—44no—
327C4×D61—44no—
328Dic122—42no—
329Dic122—42no—
330#92418—44no—
331#17572—611nomaximal, Sylow
332C22×C61—28no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—21no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—44no—
350C22×C61—44no—
351C22×C61—44no—
352C22×C61—44no—
353C22×C61—44no—
354C22×C61—44no—
355C22×C61C2×#9912yes—
356C22×C61#41612yes—
357C22×C61#41612yes—
358C22×C61#42112yes—
359C22×C61C22×C22⋊C411yescharacteristic
360C22×C61C2×#13512yes—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—84no—
365C4×C61—21no—
366C4×C61—21no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—84no—
372C4×C61C2×#9912yes—
373C4×C61C2×#9912yes—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377C2×#525—611no—
378C22×C22⋊C8—611no—
379#2280D6111yescharacteristic, complemented
380#1520—612no—
381#1519—612no—
382#1516—614no—
383#1501—614no—
384C2×C61—22no—
385C2×C61—22no—
386C2×C61—22no—
387C2×C61—22no—
388C2×C61—22no—
389C2×C61—41no—
390C2×C61—41no—
391C2×C61C22×#9911yescharacteristic
392C2×C61C2×#41611yescharacteristic
393C2×C61C2×#42111yescharacteristic
394D61—82no—
395C22×#41—611no—
396C24×C4C2×D6111yescharacteristic
397C23×C8—1221no—
398#525—612no—
399#525—612no—
400#525—612no—
401#525—612no—
402#525—1221no—
403#525—1221no—
404#525—1221no—
405#525—1221no—
406C2×#123—1221no—
407C2×C22⋊Q8—611no—
408C2×C22⋊Q8—611no—
409C2×#121—611no—
410C2×#121—611no—
411C2×#120—1221no—
412C2×C4×D4—1221no—
413C2×C4×D4—1221no—
414C2×#117—21no—
415C2×#117—611no—
416C2×C22⋊C8—612no—
417C2×C22⋊C8—612no—
418C2×C22⋊C8—612no—
419C2×C22⋊C8—1221no—
420C2×C22⋊C8—1221no—
421C2×C22⋊C8—1221no—
422#381C2×D6112yescomplemented
423#380—21no—
424#380C2×D6112yes—
425#379—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4C2×D6112yescomplemented
428#328—618no—
429#327—618no—
430C61#1757211yescharacteristic, complemented, Sylow
431C25C22⋊D6111yescharacteristic
432C2×#41—612no—
433C2×#41—612no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—2444no—
437C22×Q8—611no—
438C22×D4—611no—
439C22×D4—1221no—
440C22×D4—1221no—
441C22×D4—1221no—
442C23×C4—44no—
443C23×C4—1221no—
444C23×C4C4×D6111yescharacteristic
445C23×C4C4×D6111yescharacteristic
446C23×C4C4×D6111yescharacteristic
447C23×C4C4×D6111yescharacteristic
448C23×C4D24411yescharacteristic
449C23×C4D24411yescharacteristic
450C23×C4D24411yescharacteristic
451C23×C4D24411yescharacteristic
452C23×C4C22⋊D6111yescharacteristic
453C23×C4C22⋊D6111yescharacteristic
454C23×C4C22⋊D6111yescharacteristic
455C23×C4C22×D6111yescharacteristic
456C23×C4C22×D6111yescharacteristic
457C23×C4C22×D6111yescharacteristic
458C22×C8—1222no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—2444no—
462#123—1222no—
463#123—1222no—
464#123—1222no—
465#123—1222no—
466C22⋊Q8—612no—
467C22⋊Q8—612no—
468C22⋊Q8—612no—
469C22⋊Q8—612no—
470C22⋊Q8—1221no—
471C22⋊Q8—1221no—
472C22⋊Q8—1221no—
473C22⋊Q8—1221no—
474#121—612no—
475#121—612no—
476#121—612no—
477#121—612no—
478#121—1221no—
479#121—1221no—
480#121—1221no—
481#121—1221no—
482#120—1222no—
483#120—1222no—
484#120—1222no—
485#120—1222no—
486C4×D4—1222no—
487C4×D4—1222no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494#117—44no—
495#117—612no—
496#117—612no—
497#117—1221no—
498#117—1221no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C42—22no—
513C2×C42—1221no—
514C22⋊C8—614no—
515C22⋊C8—1222no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518#95—22no—
519#95C22×D6114yes—
520C24—24no—
521C24—42no—
522C24—42no—
523C24—1221no—
524C24#1175819811yescharacteristic
525C24#1175819811yescharacteristic
526C24#1175819811yescharacteristic
527C24#1175819811yescharacteristic
528C24C2×C22⋊D6111yescharacteristic
529C24C2×C22⋊D6111yescharacteristic
530C24C2×C22⋊D6111yescharacteristic
531#41—2444no—
532#41—2444no—
533#41—2444no—
534#41—2444no—
535C2×Q8—612no—
536C2×Q8—1221no—
537C2×Q8—2442no—
538C2×D4—612no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—1221no—
546C2×D4—2442no—
547C2×D4—2444no—
548C2×D4—2444no—
549C2×D4—2444no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—2444no—
571C22×C4#1175819811yescharacteristic
572C22×C4#1175819811yescharacteristic
573C22×C4#1175819811yescharacteristic
574C22×C4#1175819811yescharacteristic
575C22×C4#1175819811yescharacteristic
576C22×C4#1175819811yescharacteristic
577C22×C4#1175819811yescharacteristic
578C22×C4#1175819811yescharacteristic
579C22×C4#1175819811yescharacteristic
580C22×C4#1175819811yescharacteristic
581C22×C4#1175819811yescharacteristic
582C22×C4#1175819811yescharacteristic
583C22×C4C2×C4×D6111yescharacteristic
584C22×C4C2×C4×D6111yescharacteristic
585C22×C4C2×C4×D6111yescharacteristic
586C22×C4C2×C4×D6111yescharacteristic
587C22×C4C2×C4×D6111yescharacteristic
588C22×C4C2×C4×D6111yescharacteristic
589C22×C4C2×D24411yescharacteristic
590C22×C4C2×D24411yescharacteristic
591C22×C4C2×D24411yescharacteristic
592C22×C4C2×D24411yescharacteristic
593C22×C4C2×D24411yescharacteristic
594C22×C4C2×D24411yescharacteristic
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C23×D6111yescharacteristic
599C2×C8—1224no—
600C2×C8—2444no—
601C2×C8—2444no—
602C2×C8—2444no—
603C4⋊C4—44no—
604C4⋊C4—612no—
605C4⋊C4—612no—
606C4⋊C4—1222no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1222no—
610C4⋊C4—1222no—
611C4⋊C4—1222no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C42—44no—
626C42—1222no—
627C42—1222no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—416no—
649C23—1222no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23C2×#1175819811yescharacteristic
654C23C2×#1175819811yescharacteristic
655C23C2×#1175819811yescharacteristic
656C23C2×#1175819811yescharacteristic
657C23C2×#1175819811yescharacteristic
658C23C2×#1175819811yescharacteristic
659C23#1451979714yes—
660C23C22×C22⋊D6111yescharacteristic
661Q8—2442no—
662Q8—2442no—
663D4—2442no—
664D4—2444no—
665D4—2444no—
666D4—2444no—
667D4—2444no—
668D4—2444no—
669D4—2444no—
670D4—2442no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—2444no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2444no—
709C2×C4#1451969114yes—
710C2×C4C2×#1175819811yescharacteristic
711C2×C4C2×#1175819811yescharacteristic
712C2×C4C2×#1175819811yescharacteristic
713C2×C4C2×#1175819811yescharacteristic
714C2×C4C2×#1175819811yescharacteristic
715C2×C4C2×#1175819811yescharacteristic
716C2×C4C22×C4×D6111yescharacteristic
717C2×C4C22×D24411yescharacteristic
718C8—2444no—
719C22—28no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—4884no—
743C22—2442no—
744C22—2442no—
745C22—2442no—
746C22C2×#1451969112yes—
747C22#1683975612yes—
748C22#1683975612yes—
749C22#1683978012yes—
750C22C22×#1175819811yescharacteristic
751C22C2×#1451979712yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—84no—
759C4—2442no—
760C4—2442no—
761C4—2442no—
762C4C2×#1451969112yes—
763C4C2×#1451969112yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—4882no—
772C2C22×#1451969111yescharacteristic
773C2C2×#1683975611yescharacteristic
774C2C2×#1683978011yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2280C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840273C2
cosocleC22×C4×C61C24
hypercenter#2280D61
hypocenterC61#17572
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊#92418C2semidirect
3. #21444390C2semidirect
4. #21444386C2semidirect
5. #21444373C2semidirect
6. #21444308C2semidirect
7. C61×#2280C2semidirect
8. C22×#11758222C4semidirect
14. #16840273C4semidirect
15. #16840273C4semidirect
19. C2×#14519756C4semidirect
21. C2×#14519751C4semidirect
26. C2×#14519736C4semidirect
31. C2×C22⋊#92418C22semidirect
32. C2×C22⋊#92418C22semidirect
33. #16839498C22semidirect
34. #16839495C22semidirect
37. C61×#381C22semidirect
42. C4×C22⋊C4×C61C22semidirect
379. #2280D61semidirect
422. #381C2×D61semidirect
427. C4×C22⋊C4C2×D61semidirect
430. C61#17572semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C22×C22⋊#924182
#214443902
#214443862
#214443732
#214443082
C61×#22802
#1757261