Finite Group Databasebeta

← #29690265

Subgroups — #29690265

Order 15616.

1030 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×#16839730C211yesmaximal, characteristic
2C2×#16839727C211yesmaximal, characteristic
3#21448305C211yesmaximal, characteristic
4#21446003C211yesmaximal, characteristic, complemented
5#21446003C211yesmaximal, characteristic, complemented
6#21446002C211yesmaximal, characteristic, complemented
7#21445999C211yesmaximal, characteristic, complemented
8#21445996C211yesmaximal, characteristic, complemented
9#21445995C211yesmaximal, characteristic, complemented
10#21445995C211yesmaximal, characteristic, complemented
11#21445802C211yesmaximal, characteristic, complemented
12#21445800C211yesmaximal, characteristic, complemented
13#21445798C211yesmaximal, characteristic, complemented
14#21445796C211yesmaximal, characteristic, complemented
15C61×#1851C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×C42×D61C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28#16839730—24no—
29#16839727—24no—
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519689C2211yescharacteristic
34C2×#14519689C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37#16839666C411yescharacteristic
38#16839666C411yescharacteristic
39#16839662C411yescharacteristic
40#16839662C411yescharacteristic
41#16839640C411yescharacteristic
42#16839640C411yescharacteristic
43#16839638C411yescharacteristic
44#16839638C411yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×C22⋊Dic61C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C2×#11758222—41no—
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222D414yes—
66C2×#11758222Q814yes—
67C22×Dic122C2×C411yescharacteristic
68C22×D244C2×C411yescharacteristic
69C22×C22⋊D61C2×C411yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C2×#11758189—22no—
76C2×#11758189—41no—
77C2×#11758189—41no—
78C22×#92418—22no—
79C22×#92418—41no—
80C22×#92418—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C2×C8×D61—22no—
86C2×C8×D61—41no—
87C2×C8×D61—41no—
88#14519734—41no—
89#14519734—41no—
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×C22⋊Dic61C2×C411yescharacteristic
93C2×C22⋊Dic61C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×#11758198C2×C411yescharacteristic
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C42×D61—41no—
105C42×D61—41no—
106C4⋊#92418—41no—
107C4⋊#92418—41no—
108#14519706—41no—
109#14519706—41no—
110#14519706—41no—
111#14519706—41no—
112C22⋊#92418—22no—
113#14519689—22no—
114#14519689—22no—
115#14519689—22no—
116#14519689—22no—
117#14519689—22no—
118#14519689—22no—
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C2×M16×C61—22no—
127C2×M16×C61—41no—
128C2×M16×C61—41no—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—41no—
138C4⋊C8×C61—41no—
139C22⋊C8×C61—22no—
140#95×C61C2×C411yescharacteristic
141#95×C61C2×C411yescharacteristic
142C24×C61C22×C411yescharacteristic
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×Q812yes—
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—41no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61C4⋊C414yes—
162C2×C22⋊D61C4⋊C414yes—
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169#11758222—44no—
170#11758222—44no—
171#11758222—44no—
172#11758222—44no—
173C2×D244—41no—
174C2×D244—41no—
175C2×D244C4⋊C414yes—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—41no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
189C2×C4×D61—41no—
190C2×C4×D61C2×D412yes—
191C2×C4×D61C2×D412yes—
192C2×C4×D61C2×Q812yes—
193C2×C4×D61C2×Q812yes—
194C2×Dic122—41no—
195C2×Dic122—41no—
196C2×Dic122C4⋊C414yes—
197M16×C61—44no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—41no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C22⋊Dic61—22no—
217C22⋊Dic61—41no—
218#11758198—22no—
219#11758198—22no—
220#11758198—41no—
221#11758198—41no—
222#11758198—41no—
223#11758198—41no—
224#11758196—41no—
225#11758196—41no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—41no—
231C4×Dic61—41no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—44no—
245#11758189—44no—
246C8×D61—44no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61C2×C4⋊C412yes—
254C23×C61C23×C411yescharacteristic
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61C2×C4⋊C412yes—
268C22×D61C2×C4⋊C412yes—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61C2×C4⋊C412yes—
287C2×C4×C61#13112yes—
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C22×Q811yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×C4×C61H(5,𝔽2)11yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C22⋊D61—44no—
295C22⋊D61—44no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61C2×C4⋊C412yes—
312C2×Dic61C2×C4⋊C412yes—
313C2×Dic61#13112yes—
314D244—44no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—44no—
324C4×D61—44no—
325Dic122—44no—
326C8×C61—41no—
327C8×C61—41no—
328C8×C61—41no—
329C8×C61—41no—
330#92418—41no—
331#92418—41no—
332#92418—41no—
333#92418—41no—
334#21937—611nomaximal, Sylow
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61C22×C4⋊C411yescharacteristic
343C22×C61#51811yescharacteristic
344C22×C61#51811yescharacteristic
345C22×C61C2×#13111yescharacteristic
346C22×C61C2×#13111yescharacteristic
347C22×C61#56811yescharacteristic
348C22×C61#56811yescharacteristic
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—41no—
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61#53411yescharacteristic
369C4×C61#53411yescharacteristic
370C4×C61#54311yescharacteristic
371C4×C61#54311yescharacteristic
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—41no—
376Dic61—41no—
377Dic61—41no—
378C2×#408—611no—
379C2×#408—611no—
380#2297—611no—
381#1851—611no—
382#1851—611no—
383#1851—611no—
384#1851D6111yescharacteristic, complemented
385#1850—611no—
386#1850—611no—
387#1850—611no—
388#1850—611no—
389#1798—611no—
390#1798—611no—
391#1797—611no—
392#1797—611no—
393C2×C61—42no—
394C2×C61#231511yescharacteristic
395C2×C61#290611yescharacteristic
396C2×C61#290611yescharacteristic
397C2×C61#297711yescharacteristic
398C2×C61#297811yescharacteristic
399C2×C61#298111yescharacteristic
400C2×C61#298111yescharacteristic
401D61—42no—
402D61—42no—
403C22×#41—611no—
404C22×M16—611no—
405C22×M16C2×D6111yescharacteristic
406C23×C8—611no—
407C23×C8—611no—
408C2×#117—611no—
409C22×C42—611no—
410C2×C4⋊C8—611no—
411C2×C4⋊C8—611no—
412C2×C4⋊C8—611no—
413C2×C4⋊C8—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×C4⋊C8C2×D6111yescharacteristic
417C2×C4⋊C8C2×D6111yescharacteristic
418#408—1224no—
419#408—1224no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C22⋊C8C2×D6111yescharacteristic
428#391—611no—
429#391—611no—
430#390—611no—
431#390—611no—
432#386—611no—
433#386—611no—
434#386—611no—
435#386—611no—
436C4×C22⋊C4—611no—
437C4×C22⋊C4—611no—
438C4×C22⋊C4—611no—
439C4×C22⋊C4C2×D6111yescharacteristic
440#336—611no—
441#336—611no—
442#336—611no—
443#336—611no—
444#336—611no—
445#336—611no—
446#336C2×D6111yescharacteristic
447#336C2×D6111yescharacteristic
448C61#2193711yescharacteristic, complemented, Sylow
449C2×#41—614no—
450C2×#41—614no—
451C2×#41—2441no—
452C2×#41—2441no—
453C2×#41—2441no—
454C2×#41—2441no—
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×C4C22×D6111yescharacteristic
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—41no—
467C2×M16—1222no—
468C2×M16—2441no—
469C2×M16—2441no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—1222no—
475C22×C8—1222no—
476C22×C8—2441no—
477C22×C8—2441no—
478C22×C8—2441no—
479C22×C8—2441no—
480C22×C8C22×D6111yescharacteristic
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484#117—2441no—
485#117—2441no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4C4×D6111yescharacteristic
497C2×C22⋊C4C4×D6111yescharacteristic
498C2×C42—611no—
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—2441no—
503C2×C42—2441no—
504C2×C42C22×D6111yescharacteristic
505C2×C42C22×D6111yescharacteristic
506C4⋊C8—41no—
507C4⋊C8—41no—
508C4⋊C8—2441no—
509C4⋊C8—2441no—
510C4⋊C8—2441no—
511C4⋊C8—2441no—
512C4⋊C8—2441no—
513C4⋊C8—2441no—
514C22⋊C8—22no—
515C22⋊C8—1222no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C22⋊C8—1222no—
519C22⋊C8—1222no—
520C22⋊C8—1222no—
521C22⋊C8—1222no—
522#95—611no—
523#95—611no—
524#95—611no—
525#95—611no—
526#95—611no—
527#95—611no—
528#95C4×D6111yescharacteristic
529#95C4×D6111yescharacteristic
530C24—611no—
531C24—611no—
532C24C2×C4×D6111yescharacteristic
533#41—2444no—
534#41—2444no—
535#41—2444no—
536#41—2444no—
537C2×Q8—614no—
538C2×Q8—2441no—
539C2×Q8—2441no—
540C2×D4—614no—
541C2×D4—614no—
542C2×D4—614no—
543C2×D4—2441no—
544C2×D4—2441no—
545C2×D4—2441no—
546C2×D4—2441no—
547C2×D4—2441no—
548C2×D4—2441no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—1222no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1222no—
573C22×C4—2441no—
574C22×C4—2441no—
575C22×C4—2441no—
576C22×C4—2441no—
577C22×C4C2×C4×D6111yescharacteristic
578C22×C4C2×C4×D6111yescharacteristic
579C22×C4C2×C4×D6111yescharacteristic
580C22×C4C2×C4×D6111yescharacteristic
581C22×C4C2×C4×D6111yescharacteristic
582C22×C4D4×D6112yes—
583C22×C4Q8×D6112yes—
584C22×C4C23×D6111yescharacteristic
585M16—44no—
586M16—2444no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—2444no—
612C2×C8—2444no—
613C4⋊C4—2441no—
614C4⋊C4—2441no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—2441no—
621C22⋊C4—2441no—
622C22⋊C4—2441no—
623C22⋊C4—2441no—
624C22⋊C4—2441no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—1221no—
630C42—1221no—
631C42—1221no—
632C42—1221no—
633C42—2441no—
634C42—2441no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—612no—
642C23—612no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23C4⋊C4×D6112yes—
656C23C22×C4×D6111yescharacteristic
657Q8—2444no—
658D4—2444no—
659D4—2444no—
660D4—2444no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—612no—
679C2×C4—612no—
680C2×C4—612no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—2444no—
705C2×C4—2444no—
706C2×C4C4⋊C4×D6112yes—
707C2×C4#1451978512yes—
708C2×C4C2×D4×D6111yescharacteristic
709C2×C4C2×Q8×D6111yescharacteristic
710C2×C4#1451982211yescharacteristic
711C2×C4#1451982211yescharacteristic
712C2×C4#1451982311yescharacteristic
713C2×C4#1451982311yescharacteristic
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—2441no—
719C8—2441no—
720C8—2441no—
721C8—2441no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—1222no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—1222no—
734C22—1222no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22—2441no—
739C22—2441no—
740C22—2441no—
741C22—2441no—
742C22—2441no—
743C22C2×C4⋊C4×D6111yescharacteristic
744C22#1684023411yescharacteristic
745C22#1684023411yescharacteristic
746C22#131×D6111yescharacteristic
747C22C2×#1451978511yescharacteristic
748C22#1684052711yescharacteristic
749C22#1684052811yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—1222no—
756C4—1222no—
757C4—1222no—
758C4—2441no—
759C4—2441no—
760C4—2441no—
761C4#1684032211yescharacteristic
762C4#1684032311yescharacteristic
763C4#1684038711yescharacteristic
764C4#1684038711yescharacteristic
765C2—42no—
766C2—2442no—
767C2—2442no—
768C2#2144843011yescharacteristic
769C2#2145438611yescharacteristic
770C2#2145438811yescharacteristic
771C2#2145487011yescharacteristic
772C2#2145487611yescharacteristic
773C2#2145489111yescharacteristic
774C2#2145489611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1851C2
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1851D61
hypocenterC61#21937
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
4. #21446003C2semidirect
5. #21446003C2semidirect
6. #21446002C2semidirect
7. #21445999C2semidirect
8. #21445996C2semidirect
9. #21445995C2semidirect
10. #21445995C2semidirect
11. #21445802C2semidirect
12. #21445800C2semidirect
13. #21445798C2semidirect
14. #21445796C2semidirect
15. C61×#1851C2semidirect
384. #1851D61semidirect
448. C61#21937semidirect

Maximal subgroups

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

subgroupindex
C2×#168397302
C2×#168397272
#214483052
#214460032
#214460022
#214459992
#214459962
#214459952
#214458022
#214458002
#214457982
#214457962
C61×#18512
#2193761