Finite Group Databasebeta

← #29737097

Subgroups — #29737097

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic, complemented
2C22×#14519697C211yesmaximal, characteristic
3C22⋊C4×D244C211yesmaximal, characteristic
4#21447343C211yesmaximal, characteristic, complemented
5#21447204C211yesmaximal, characteristic, complemented
6#21447190C211yesmaximal, characteristic, complemented
7#21446962C211yesmaximal, characteristic, complemented
8#21446079C211yesmaximal, characteristic, complemented
9#21446065C211yesmaximal, characteristic, complemented
10#21446012C211yesmaximal, characteristic, complemented
11#21445999C211yesmaximal, characteristic, complemented
12#21445846C211yesmaximal, characteristic, complemented
13#21445826C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic
15C61×#2442C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C22⋊C4×D61—21no—
21#16840059—24no—
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519708C2211yescharacteristic, complemented
25C2×#14519708C2211yescharacteristic, complemented
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×C4⋊#92418C2211yescharacteristic, complemented
28C2×#14519697—24no—
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839640—21no—
41#16839640—21no—
42#16839622C2211yescharacteristic
43#16839617—21no—
44#16839524C2211yescharacteristic, complemented
45#16839524C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839517C2211yescharacteristic, complemented
49#16839517C2211yescharacteristic, complemented
50C2×#125×C61C2211yescharacteristic, complemented
51C22×C4⋊C4×C61C2211yescharacteristic
52C61×#400—21no—
53C61×#398—21no—
54C61×#389C2211yescharacteristic, complemented
55C61×#389C2211yescharacteristic, complemented
56C61×#385—21no—
57C61×#382C2211yescharacteristic, complemented
58C61×#380—21no—
59C61×#380C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C24×D61—21no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—21no—
65C22×D244—22no—
66C22×D244—41no—
67C22×D244—41no—
68C22×D244Q814yes—
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×#92418—22no—
74C22×#92418—22no—
75C22×#92418—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C4×D244—22no—
81C4×D244—22no—
82C4×D244—41no—
83C4×D244—41no—
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C22⋊C4×D61—44no—
94#14519710—22no—
95#14519710—41no—
96#14519708—22no—
97#14519708—41no—
98C4⋊#92418—22no—
99C4⋊#92418—41no—
100#14519697—22no—
101#14519697—22no—
102#14519697—22no—
103#14519697—22no—
104#14519697—22no—
105#14519697—41no—
106#14519697—41no—
107#14519697D414yes—
108C22⋊#92418—22no—
109#14519684—21no—
110C23×C4×C61—21no—
111C23×C4×C61C2311yescharacteristic
112#125×C61—22no—
113#125×C61—41no—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—41no—
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C42×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61D411yescharacteristic
136#95×C61D411yescharacteristic
137C24×C61C2×D411yescharacteristic
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—24no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—81no—
146C23×D61—81no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—81no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×Q812yes—
164C22×C4×C61#4112yes—
165C22×C4×C61C2411yescharacteristic
166C22×Dic61—21no—
167C22×Dic61—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—28no—
176C2×D244—24no—
177C2×D244—21no—
178C2×D244—44no—
179C2×D244—44no—
180C2×D244—44no—
181C2×D244—42no—
182C2×D244—42no—
183C2×D244C2×D412yes—
184C2×D244C2×Q812yes—
185C2×D244C2×Q812yes—
186C2×D244#4112yes—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—81no—
192C2×C4×D61—81no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—42no—
201C4⋊C4×C61—42no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—81no—
204C4⋊C4×C61—81no—
205C4⋊C4×C61C2×D412yes—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—42no—
209C42×C61—21no—
210C42×C61—21no—
211C42×C61—21no—
212C42×C61—21no—
213C22⋊Dic61—42no—
214#11758198—42no—
215#11758198—42no—
216#11758198—42no—
217#11758198—42no—
218#11758198—81no—
219#11758198—81no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—44no—
236C2×#92418C2×D412yes—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61C22⋊Q812yes—
242C23×C61#13512yes—
243C23×C61AGL(1,ℤ/8)12yes—
244C23×C61C22×D411yescharacteristic
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—48no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—48no—
261C22×D61—84no—
262C22×D61—84no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61—84no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
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—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
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—84no—
297C2×C4×C61C22⋊Q812yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×Q811yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310D244—22no—
311D244—22no—
312D244—22no—
313D244—22no—
314D244—22no—
315D244—48no—
316D244—41no—
317D244—41no—
318D244C22⋊Q814yes—
319C4×D61—84no—
320C4×D61—84no—
321#92418—22no—
322#92418—41no—
323#92418—41no—
324#92418—41no—
325#25952—611nomaximal, Sylow
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61#47814yescomplemented
333C22×C61C2×C22⋊Q811yescharacteristic
334C22×C61D4211yescharacteristic
335C22×C61#54611yescharacteristic
336C22×C61C2×#13511yescharacteristic
337C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C61#57611yescharacteristic
339C22×C61#57711yescharacteristic
340C2×D61—24no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—816no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C4×C61—22no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61—42no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61—81no—
364C4×C61C2×C22⋊Q811yescharacteristic
365C4×C61#54311yescharacteristic
366C4×C61#54611yescharacteristic
367C4×C61#55111yescharacteristic
368Dic61—81no—
369Dic61—81no—
370C2×#478—611no—
371C22×#102—611no—
372#2442D6111yescharacteristic, complemented
373D4×C22⋊C4—611no—
374#2092—611no—
375#2067—611no—
376#2065—611no—
377#2025—611no—
378#1864—611no—
379#1862—611no—
380#1853—611no—
381#1850—611no—
382#1808—611no—
383#1804—611no—
384#1786—611no—
385C2×C61—24no—
386C2×C61#243711yescharacteristic
387C2×C61C2×#47811yescharacteristic
388C2×C61#308111yescharacteristic
389C2×C61#326511yescharacteristic
390C2×C61#328011yescharacteristic
391C2×C61#329611yescharacteristic
392C2×C61#331811yescharacteristic
393D61—44no—
394D61—82no—
395C23×D4—611no—
396C23×C8—611no—
397C2×#125C2×D6111yescharacteristic, complemented
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C22×C4⋊C4C2×D6111yescharacteristic
401C22×C22⋊C4—1221no—
402#478—1224no—
403C2×#107—611no—
404C2×#107—611no—
405C2×#106—611no—
406C2×#106—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—1224no—
418C2×C22⋊C8—611no—
419#400—21no—
420#398—21no—
421#390—611no—
422#390—611no—
423#389C2×D6111yescharacteristic, complemented
424#389C2×D6111yescharacteristic, complemented
425#386—1221no—
426#386—1221no—
427#385—21no—
428#382C2×D6111yescharacteristic, complemented
429#380—21no—
430#380—611no—
431#380C2×D6111yescharacteristic
432#379—1221no—
433C4×C22⋊C4C2×D6111yescharacteristic
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#336—611no—
439#336—611no—
440C61#2595211yescharacteristic, complemented, Sylow
441C25—1221no—
442C22×D4—614no—
443C22×D4—611no—
444C22×D4—611no—
445C22×D4—1222no—
446C22×D4—1222no—
447C22×D4—1222no—
448C22×D4—1221no—
449C22×D4—2441no—
450C22×D4—2441no—
451C23×C4—21no—
452C23×C4—1221no—
453C23×C4—1221no—
454C23×C4C22×D6111yescharacteristic
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—2441no—
462#125—22no—
463#125—41no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—2441no—
467C4×D4—2441no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—2444no—
490C2×C22⋊C4C22⋊D6111yescharacteristic
491C2×C22⋊C4C22⋊D6111yescharacteristic
492C2×C42C22×D6111yescharacteristic
493C2×C42C22×D6111yescharacteristic
494#107—1222no—
495#107—2441no—
496#106—1222no—
497#106—2441no—
498C4⋊C8—1222no—
499C4⋊C8—2441no—
500#102—614no—
501#102—1222no—
502#102—1222no—
503#102—1222no—
504#102—1222no—
505#102—1222no—
506#102—2441no—
507#102—2441no—
508C22⋊C8—1222no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—1221no—
515#95C22⋊D6111yescharacteristic
516#95C22⋊D6111yescharacteristic
517C24—1221no—
518C24—1224no—
519C24—1221no—
520C24—4881no—
521C24—4881no—
522C24—2442no—
523C24—2442no—
524C24—2442no—
525C24—2442no—
526C24C2×C22⋊D6111yescharacteristic
527C2×D4—612no—
528C2×D4—612no—
529C2×D4—612no—
530C2×D4—612no—
531C2×D4—1228no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1224no—
541C2×D4—2444no—
542C2×D4—2444no—
543C2×D4—2444no—
544C2×D4—2442no—
545C2×D4—2442no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—81no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—4881no—
560C22×C4—4881no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4Q8×D6112yes—
566C22×C4#1175822612yes—
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C2×C22⋊D6111yescharacteristic
570C22×C4C2×C22⋊D6111yescharacteristic
571C22×C4C2×C22⋊D6111yescharacteristic
572C22×C4C23×D6111yescharacteristic
573C2×C8—612no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—2444no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—81no—
597C4⋊C4—81no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4D4×D6112yes—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—42no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—2442no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—1222no—
625C23—4884no—
626C23—4884no—
627C23—4884no—
628C23—4884no—
629C23—4884no—
630C23—2448no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2448no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23#1451975312yes—
643C23#1451979712yes—
644C23#1451980212yes—
645C23C22×C22⋊D6111yescharacteristic
646D4—614no—
647D4—1222no—
648D4—1222no—
649D4—1222no—
650D4—1222no—
651D4—1222no—
652D4—2448no—
653D4—2441no—
654D4—2441no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—4884no—
687C2×C4—4884no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4#1451975312yes—
695C2×C4C2×D4×D6111yescharacteristic
696C2×C4C2×Q8×D6111yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4C2×#1175822611yescharacteristic
699C2×C4#1451982211yescharacteristic
700C2×C4#1451982311yescharacteristic
701C8—1222no—
702C8—2441no—
703C8—2441no—
704C8—2441no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—1224no—
712C22—48816no—
713C22—4881no—
714C22—4881no—
715C22—4881no—
716C22—4881no—
717C22—2442no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22—2442no—
726C22#1684005914yescomplemented
727C22C2×#1451975311yescharacteristic
728C22D4×C22⋊D6111yescharacteristic
729C22#1684040011yescharacteristic
730C22C2×#1451979711yescharacteristic
731C22C2×#1451980211yescharacteristic
732C22#1684056511yescharacteristic
733C22#1684057011yescharacteristic
734C4—22no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—4881no—
744C4—4881no—
745C4C22⋊Q8×D6111yescharacteristic
746C4#1684038711yescharacteristic
747C4#1684040311yescharacteristic
748C4#1684043911yescharacteristic
749C2—24no—
750C2—4882no—
751C2—2444no—
752C2#2144948211yescharacteristic
753C2C2×#1684005911yescharacteristic
754C2#2145564411yescharacteristic
755C2#2145731511yescharacteristic
756C2#2145750011yescharacteristic
757C2#2145764811yescharacteristic
758C2#2145795411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2442C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenter#2442D61
hypocenterC61#25952
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#16840059C2semidirect
4. #21447343C2semidirect
5. #21447204C2semidirect
6. #21447190C2semidirect
7. #21446962C2semidirect
8. #21446079C2semidirect
9. #21446065C2semidirect
10. #21446012C2semidirect
11. #21445999C2semidirect
12. #21445846C2semidirect
13. #21445826C2semidirect
15. C61×#2442C2semidirect
22. C2×#14519710C22semidirect
23. C2×#14519710C22semidirect
24. C2×#14519708C22semidirect
25. C2×#14519708C22semidirect
26. C2×C4⋊#92418C22semidirect
27. C2×C4⋊#92418C22semidirect
44. #16839524C22semidirect
45. #16839524C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839517C22semidirect
49. #16839517C22semidirect
50. C2×#125×C61C22semidirect
54. C61×#389C22semidirect
55. C61×#389C22semidirect
57. C61×#382C22semidirect
332. C22×C61#478semidirect
372. #2442D61semidirect
397. C2×#125C2×D61semidirect
423. #389C2×D61semidirect
424. #389C2×D61semidirect
428. #382C2×D61semidirect
440. C61#25952semidirect
726. C22#16840059semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C22×#145196972
C22⋊C4×D2442
#214473432
#214472042
#214471902
#214469622
#214460792
#214460652
#214460122
#214459992
#214458462
#214458262
#214457492
C61×#24422
#2595261