Finite Group Databasebeta

← #29718800

Subgroups — #29718800

Order 15616.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839895C211yesmaximal, characteristic
2C2×#16839823C211yesmaximal, characteristic, complemented
3#21448399C211yesmaximal, characteristic, complemented
4#21447204C211yesmaximal, characteristic, complemented
5#21447190C211yesmaximal, characteristic, complemented
6#21447129C211yesmaximal, characteristic, complemented
7#21447129C211yesmaximal, characteristic, complemented
8#21446694C211yesmaximal, characteristic, complemented
9#21446684C211yesmaximal, characteristic, complemented
10#21446515C211yesmaximal, characteristic, complemented
11#21446501C211yesmaximal, characteristic, complemented
12#21446142C211yesmaximal, characteristic, complemented
13#21446016C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic, complemented
15C61×#2624C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839895—24no—
21#16839823—24no—
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24C2×C4⋊#92418C2211yescharacteristic, complemented
25C2×C4⋊#92418C2211yescharacteristic, complemented
26C2×#14519698C2211yescharacteristic, complemented
27C2×#14519698C2211yescharacteristic, complemented
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic, complemented
37C2×C4×#92418C2211yescharacteristic, complemented
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839664C2211yescharacteristic
42#16839663—21no—
43#16839663—21no—
44#16839617—21no—
45#16839617—21no—
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50C2×#121×C61C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C61×#399—21no—
53C61×#397—21no—
54C61×#394—21no—
55C61×#394—21no—
56C61×#390C2211yescharacteristic, complemented
57C61×#390C2211yescharacteristic, complemented
58C61×#389C2211yescharacteristic, complemented
59C61×#389C2211yescharacteristic, complemented
60C61×#380C2211yescharacteristic
61C24×D61—21no—
62C22×D244—21no—
63C22×D244—22no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—41no—
68C22×D244—41no—
69C22×D244C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C2×#11758199—22no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—22no—
75C2×#11758199—41no—
76C2×#11758199—41no—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81#14519736—41no—
82#14519736—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×C4×Dic61—21no—
95#14519710—41no—
96#14519708—41no—
97C4⋊#92418—22no—
98C4⋊#92418—22no—
99#14519698—41no—
100#14519698—41no—
101#14519697—22no—
102#14519697—22no—
103#14519697—22no—
104#14519697—22no—
105#14519697—41no—
106#14519697—41no—
107C22⋊#92418—22no—
108C22⋊#92418D414yes—
109#14519688—22no—
110C4×#92418—22no—
111C22×D4×C61—21no—
112C22×D4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114#121×C61—22no—
115#121×C61—22no—
116#117×C61—22no—
117#117×C61—22no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61D411yescharacteristic
121C2×C4⋊C4×C61D411yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61D411yescharacteristic
132C2×C22⋊C4×C61D411yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C2×C42×C61C2311yescharacteristic
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C23×D61—21no—
141C23×D61—21no—
142C23×D61—24no—
143C23×D61—42no—
144C23×D61—42no—
145C23×D61—81no—
146C23×D61—81no—
147C23×D61—81no—
148C23×D61—81no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—42no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D412yes—
171C22×C4×C61#4112yes—
172C22×C4×C61C2411yescharacteristic
173C22×Dic61—21no—
174C22×Dic61—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—24no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—44no—
187C2×D244—44no—
188C2×D244—44no—
189C2×D244—44no—
190C2×D244—42no—
191C2×D244—42no—
192C2×D244#4112yes—
193C2×D244#4112yes—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—81no—
203C4⋊C4×C61—81no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—81no—
208C22⋊C4×C61—81no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C22⋊C4×C61—81no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—21no—
216C22⋊Dic61—42no—
217#11758199—44no—
218#11758199—44no—
219#11758198—81no—
220#11758198—81no—
221#11758198—81no—
222#11758198—81no—
223#11758198—81no—
224#11758198—81no—
225#11758198—81no—
226#11758198—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4×Dic61—42no—
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×#92418C2×D412yes—
243C2×#92418C2×D412yes—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61#12112yes—
258C23×C61C22×D411yescharacteristic
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—48no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—84no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—84no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61#12112yes—
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61H(5,𝔽2)11yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325D244—22no—
326D244—22no—
327D244—22no—
328D244—22no—
329D244—48no—
330D244—41no—
331D244—41no—
332D244—41no—
333D244—41no—
334#92418—22no—
335#92418—22no—
336#92418—41no—
337#92418—41no—
338#24512—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61C2×#12111yescharacteristic
354C22×C61#52511yescharacteristic
355C22×C61#53511yescharacteristic
356C22×C61#57611yescharacteristic
357C22×C61#57611yescharacteristic
358C22×C61#57611yescharacteristic
359C22×C61#57711yescharacteristic
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—816no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C4×C61—22no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61—41no—
380C4×C61—81no—
381C4×C61—81no—
382C4×C61—81no—
383C4×C61#54611yescharacteristic
384C4×C61#54611yescharacteristic
385C4×C61#55111yescharacteristic
386C4×C61#55111yescharacteristic
387Dic61—81no—
388Dic61—81no—
389C2×#447—611no—
390C2×#433—611no—
391#2624D6111yescharacteristic, complemented
392#2309—611no—
393#2067—611no—
394#2065—611no—
395#2054—611no—
396#2054—611no—
397#1972—611no—
398#1970—611no—
399#1936—611no—
400#1934—611no—
401#1875—611no—
402#1854—611no—
403#1786—611no—
404C2×C61—42no—
405C2×C61—161no—
406C2×C61#241111yescharacteristic
407C2×C61#305811yescharacteristic
408C2×C61#306211yescharacteristic
409C2×C61#311811yescharacteristic
410C2×C61#312211yescharacteristic
411C2×C61#322011yescharacteristic
412C2×C61#322411yescharacteristic
413D61—82no—
414D61—82no—
415C23×D4—611no—
416C22×D8—611no—
417C22×D8—611no—
418C2×#121C2×D6111yescharacteristic
419C2×#117—611no—
420C2×#117C2×D6111yescharacteristic
421#447—1224no—
422#433—1224no—
423C2×#107—611no—
424C2×#106—611no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×C22⋊C8—611no—
436C2×C22⋊C8—611no—
437C2×#97—611no—
438C2×C4×C8—611no—
439#399—21no—
440#397—21no—
441#394—21no—
442#394—21no—
443#390—611no—
444#390—611no—
445#390—611no—
446#390—611no—
447#390—1221no—
448#390—1221no—
449#390C2×D6111yescharacteristic, complemented
450#390C2×D6111yescharacteristic, complemented
451#389C2×D6111yescharacteristic, complemented
452#389C2×D6111yescharacteristic, complemented
453#380C2×D6111yescharacteristic
454#379—1221no—
455#379—1221no—
456#340—611no—
457#340—611no—
458#340—611no—
459#340—611no—
460C61#2451211yescharacteristic, complemented, Sylow
461C25—1221no—
462C22×D4—21no—
463C22×D4—611no—
464C22×D4—611no—
465C22×D4—1222no—
466C22×D4—1222no—
467C22×D4—1222no—
468C22×D4—1222no—
469C22×D4—1221no—
470C22×D4—2441no—
471C22×D4—2441no—
472C22×D4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C2×D8—1222no—
475C2×D8—1222no—
476C2×D8—1222no—
477C2×D8—1222no—
478C2×D8—2441no—
479C2×D8—2441no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484#121—22no—
485#121—22no—
486#117—22no—
487#117—22no—
488#117—2441no—
489#117—2441no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4C22⋊D6111yescharacteristic
495C2×C4⋊C4C22⋊D6111yescharacteristic
496C2×C4⋊C4C22×D6111yescharacteristic
497C2×C4⋊C4C22×D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4C22⋊D6111yescharacteristic
515C2×C22⋊C4C22⋊D6111yescharacteristic
516C2×C42—1221no—
517C2×C42C22×D6111yescharacteristic
518C2×C42C22×D6111yescharacteristic
519#107—2441no—
520#106—2441no—
521C4⋊C8—1222no—
522C4⋊C8—1222no—
523#102—1222no—
524#102—1222no—
525#102—1222no—
526#102—1222no—
527#102—2441no—
528#102—2441no—
529#102—2441no—
530#102—2441no—
531C22⋊C8—614no—
532C22⋊C8—1222no—
533#97—1222no—
534C4×C8—1222no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24—1224no—
540C24—1221no—
541C24—1221no—
542C24—4881no—
543C24—4881no—
544C24—4881no—
545C24—4881no—
546C24—2442no—
547C24—2442no—
548C24C2×C22⋊D6111yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—42no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—1224no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—2444no—
572C2×D4—2444no—
573C2×D4—2444no—
574C2×D4—2444no—
575C2×D4—2442no—
576C2×D4—2442no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4D4×D6112yes—
587C22×C4#1175822412yes—
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C2×C22⋊D6111yescharacteristic
590C22×C4C2×C22⋊D6111yescharacteristic
591C22×C4C2×C22⋊D6111yescharacteristic
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C23×D6111yescharacteristic
594D8—2444no—
595D8—2444no—
596C2×C8—612no—
597C2×C8—612no—
598C2×C8—1221no—
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—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—81no—
617C4⋊C4—81no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—4881no—
631C22⋊C4—4881no—
632C22⋊C4—4881no—
633C22⋊C4—4881no—
634C22⋊C4—4881no—
635C22⋊C4—4881no—
636C22⋊C4—4881no—
637C22⋊C4—4881no—
638C22⋊C4—2442no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—2442no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—1222no—
658C23—1222no—
659C23—4884no—
660C23—4884no—
661C23—4884no—
662C23—4884no—
663C23—4884no—
664C23—4884no—
665C23—2448no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23#1451974912yes—
679C23C22×C22⋊D6111yescharacteristic
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—1222no—
686D4—1222no—
687D4—1222no—
688D4—1222no—
689D4—2448no—
690D4—2441no—
691D4—2441no—
692D4—2441no—
693D4—2441no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4#1451974912yes—
728C2×C4C2×D4×D6111yescharacteristic
729C2×C4#41×D6111yescharacteristic
730C2×C4#41×D6111yescharacteristic
731C2×C4C2×#1175822411yescharacteristic
732C2×C4#1451982311yescharacteristic
733C2×C4#1451982311yescharacteristic
734C8—1222no—
735C8—1222no—
736C8—2441no—
737C8—2441no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—48816no—
753C22—4881no—
754C22—4881no—
755C22—4881no—
756C22—4881no—
757C22—4881no—
758C22—4881no—
759C22—4881no—
760C22—4881no—
761C22—2442no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22C2×#1451974911yescharacteristic
768C22#1684026911yescharacteristic
769C22#1684032611yescharacteristic
770C22#1684056511yescharacteristic
771C22#1684056511yescharacteristic
772C22#1684056511yescharacteristic
773C22#1684057011yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—4881no—
783C4—4881no—
784C4#1684040411yescharacteristic
785C4#1684040411yescharacteristic
786C4#1684043511yescharacteristic
787C4#1684043511yescharacteristic
788C2—42no—
789C2—161no—
790C2—4882no—
791C2—4882no—
792C2#2144920511yescharacteristic
793C2#2145546411yescharacteristic
794C2#2145550111yescharacteristic
795C2#2145599711yescharacteristic
796C2#2145605711yescharacteristic
797C2#2145686311yescharacteristic
798C2#2145690711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2624C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
hypercenter#2624D61
hypocenterC61#24512
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2624

Complements

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

NH ≅ G/Ntype
2. C2×#16839823C2semidirect
3. #21448399C2semidirect
4. #21447204C2semidirect
5. #21447190C2semidirect
6. #21447129C2semidirect
7. #21447129C2semidirect
8. #21446694C2semidirect
9. #21446684C2semidirect
10. #21446515C2semidirect
11. #21446501C2semidirect
12. #21446142C2semidirect
13. #21446016C2semidirect
14. #21445749C2semidirect
15. C61×#2624C2semidirect
22. C2×#14519710C22semidirect
23. C2×#14519708C22semidirect
24. C2×C4⋊#92418C22semidirect
25. C2×C4⋊#92418C22semidirect
26. C2×#14519698C22semidirect
27. C2×#14519698C22semidirect
36. C2×#14519688C22semidirect
37. C2×C4×#92418C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
56. C61×#390C22semidirect
57. C61×#390C22semidirect
58. C61×#389C22semidirect
59. C61×#389C22semidirect
391. #2624D61semidirect
449. #390C2×D61semidirect
450. #390C2×D61semidirect
451. #389C2×D61semidirect
452. #389C2×D61semidirect
460. C61#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#168398952
C2×#168398232
#214483992
#214472042
#214471902
#214471292
#214466942
#214466842
#214465152
#214465012
#214461422
#214460162
#214457492
C61×#26242
#2451261