Finite Group Databasebeta

← #29722395

Subgroups — #29722395

Order 15616.

1076 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840013C211yesmaximal, characteristic, complemented
2C2×#16840013C211yesmaximal, characteristic, complemented
3C2×#16839840C211yesmaximal, characteristic, complemented
4C2×#16839802C211yesmaximal, characteristic, complemented
5#21449237C211yesmaximal, characteristic, complemented
6#21447204C211yesmaximal, characteristic, complemented
7#21447193C211yesmaximal, characteristic, complemented
8#21447008C211yesmaximal, characteristic, complemented
9#21446998C211yesmaximal, characteristic, complemented
10#21446684C211yesmaximal, characteristic, complemented
11#21446544C211yesmaximal, characteristic, complemented
12#21446142C211yesmaximal, characteristic, complemented
13#21446136C211yesmaximal, characteristic, complemented
14#21445850C211yesmaximal, characteristic, complemented
15C61×#2416C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16840013—24no—
23#16840013—24no—
24#16839840—24no—
25#16839802—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41#16839677—21no—
42#16839670—21no—
43#16839664C2211yescharacteristic
44#16839662—21no—
45#16839660C2211yescharacteristic
46#16839652—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×#121×C61—21no—
53C2×#121×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C61×#396—21no—
58C61×#394—21no—
59C61×#390C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#386—21no—
62C61×#380C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C2×#11758199—22no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758194—22no—
70C2×#11758194—22no—
71C2×#11758194—22no—
72C2×#11758194—22no—
73C2×#11758194—22no—
74C2×#11758194D414yescomplemented
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519751—22no—
80#14519751—22no—
81#14519751—22no—
82#14519751—41no—
83#14519736—22no—
84#14519736—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×C4×Dic61—21no—
96#14519710—22no—
97#14519710—22no—
98#14519708—22no—
99#14519708—22no—
100#14519708D414yescomplemented
101C4⋊#92418—22no—
102#14519698—22no—
103#14519698—22no—
104#14519698—41no—
105#14519697—22no—
106#14519697—22no—
107#14519697—41no—
108C22⋊#92418—22no—
109C22⋊#92418—22no—
110C4×#92418—22no—
111#14519684—21no—
112#14519684—21no—
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61D411yescharacteristic
116C22×D4×C61C2311yescharacteristic
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C23×C4×C61C2311yescharacteristic
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61—41no—
124#121×C61—44no—
125C4×D4×C61—22no—
126C4×D4×C61—22no—
127C2×C4⋊C4×C61—22no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—41no—
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61D411yescharacteristic
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C42×C61C2311yescharacteristic
143#95×C61—21no—
144#95×C61—21no—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147C24×C61C2×D411yescharacteristic
148C23×D61—21no—
149C2×D4×C61—22no—
150C2×D4×C61—22no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—41no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—81no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61—81no—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61#4112yes—
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—81no—
191C2×C22⋊D61—81no—
192C2×C22⋊D61—81no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—42no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61C2×D412yes—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—81no—
218C42×C61—21no—
219C42×C61—21no—
220C22⋊Dic61—42no—
221C22⋊Dic61—81no—
222#11758199—44no—
223#11758198—42no—
224#11758198—42no—
225#11758198—42no—
226#11758198—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61C2×D412yes—
233#11758196—81no—
234C4×Dic61—42no—
235#11758194—28no—
236#11758194—44no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418C2×D412yes—
246C2×#92418C2×D412yes—
247C2×#92418C2×D412yes—
248C2×#92418#4112yes—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61#12112yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278D4×C61—44no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—84no—
284D4×C61—84no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
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—84no—
313C2×C4×C61#12112yes—
314C2×C4×C61AGL(1,ℤ/8)12yes—
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C2×C4×C612−1+411yescharacteristic
321C22⋊D61—84no—
322C22⋊D61—84no—
323C2×Dic61—22no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332D244—41no—
333D244—41no—
334D244—41no—
335D244—41no—
336#92418—22no—
337#92418—41no—
338#92418—41no—
339#92418#12114yescomplemented
340#24792—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61C2×#12111yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61#54711yescharacteristic
365C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C61#57511yescharacteristic
367C22×C61#57611yescharacteristic
368C22×C61#57711yescharacteristic
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—41no—
379C4×C61—42no—
380C4×C61—41no—
381C4×C61—81no—
382C4×C61—81no—
383C4×C61C2×#12111yescharacteristic
384C4×C61#53711yescharacteristic
385C4×C61#54811yescharacteristic
386C4×C61#55311yescharacteristic
387Dic61—42no—
388Dic61—81no—
389Dic61—81no—
390C2×#469—611no—
391C2×#469—611no—
392C2×#436—611no—
393C2×#428—611no—
394#2416D6111yescharacteristic, complemented
395#2414—611no—
396#2067—611no—
397#2065—611no—
398#2034—611no—
399#2033—611no—
400#1970—611no—
401#1941—611no—
402#1875—611no—
403#1874—611no—
404#1809—611no—
405C2×C61—42no—
406C2×C61—81no—
407C2×C61—161no—
408C2×C61#241611yescharacteristic
409C2×C61#305511yescharacteristic
410C2×C61#306211yescharacteristic
411C2×C61#327411yescharacteristic
412C2×C61#327511yescharacteristic
413C2×C61#335411yescharacteristic
414C2×C61#335511yescharacteristic
415D61—161no—
416C22×D8—611no—
417C22×M16—611no—
418C22×M16—611no—
419C2×#121—21no—
420C2×#121—611no—
421C2×#121—611no—
422C2×#121C2×D6111yescharacteristic
423C2×#121C2×D6111yescharacteristic
424C2×C4×D4C2×D6111yescharacteristic
425C2×#117—611no—
426C22×C4⋊C4C2×D6111yescharacteristic
427#469—1224no—
428#469—1224no—
429#436—1224no—
430#428—1224no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#106—611no—
434C2×#106—611no—
435C2×#106—611no—
436C2×C4⋊C8—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C4×C8—611no—
446#396—21no—
447#394—21no—
448#394—1221no—
449#392—1221no—
450#390—611no—
451#390—1221no—
452#390C2×D6111yescharacteristic
453#389—611no—
454#389C2×D6111yescharacteristic
455#388—1221no—
456#386—21no—
457#380—611no—
458#380C2×D6111yescharacteristic
459#340—611no—
460#340—611no—
461#340—611no—
462#340—611no—
463C61#2479211yescharacteristic, complemented, Sylow
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—611no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4C22⋊D6111yescharacteristic
470C22×D4C22×D6111yescharacteristic
471C23×C4—21no—
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C2×D8—1222no—
475C2×D8—1222no—
476C2×D8—1222no—
477C2×M16—614no—
478C2×M16—1222no—
479C2×M16—1222no—
480C2×M16—1222no—
481C2×M16—1222no—
482C2×M16—1222no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—611no—
486C22×C8—611no—
487#121—22no—
488#121—22no—
489#121—22no—
490#121—41no—
491#121—44no—
492#121—1222no—
493#121—1222no—
494#121—1222no—
495#121—2441no—
496C4×D4—22no—
497C4×D4—22no—
498#117—1222no—
499#117—2441no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4C22⋊D6111yescharacteristic
509C2×C4⋊C4C22×D6111yescharacteristic
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4C22⋊D6111yescharacteristic
524C2×C22⋊C4C22⋊D6111yescharacteristic
525C2×C42—1221no—
526C2×C42C22×D6111yescharacteristic
527#107—1222no—
528#107—1222no—
529#106—614no—
530#106—1222no—
531#106—1222no—
532C4⋊C8—1222no—
533#102—1222no—
534#102—1222no—
535#102—1222no—
536#102—1222no—
537#102—2441no—
538#102—2441no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C4×C8—1222no—
542#95—21no—
543#95—21no—
544#95—1221no—
545#95—1221no—
546C24—21no—
547C24—1221no—
548C24C2×C22⋊D6111yescharacteristic
549C24C2×C22⋊D6111yescharacteristic
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—41no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—4881no—
572C2×D4—4881no—
573C2×D4—4881no—
574C2×D4—2442no—
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—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—81no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4D4×D6112yes—
597C22×C4#1175822412yes—
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C23×D6111yescharacteristic
603D8—2444no—
604M16—1228no—
605M16—2444no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C4⋊C4—21no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—612no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—4881no—
633C4⋊C4D4×D6112yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—4881no—
642C22⋊C4—4881no—
643C22⋊C4—2442no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C42—21no—
648C42—21no—
649C42—2442no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23#1451974912yes—
678C23C22×C22⋊D6111yescharacteristic
679D4—44no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—4884no—
687D4—4884no—
688D4—2441no—
689D4—2441no—
690D4—2441no—
691D4—2441no—
692C2×C4—21no—
693C2×C4—21no—
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—22no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—84no—
720C2×C4—1222no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4#1451974912yes—
730C2×C4#1451980312yes—
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4#41×D6111yescharacteristic
734C2×C4C2×#1175822411yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982411yescharacteristic
737C8—614no—
738C8—1222no—
739C8—2441no—
740C8—2441no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—4881no—
763C22—4881no—
764C22—4881no—
765C22—4881no—
766C22—4881no—
767C22—4881no—
768C22—4881no—
769C22C2×#1451974911yescharacteristic
770C22D4×C22⋊D6111yescharacteristic
771C22#1684041111yescharacteristic
772C22C2×#1451980311yescharacteristic
773C22#1684056011yescharacteristic
774C22#1684056511yescharacteristic
775C22#1684057011yescharacteristic
776C4—22no—
777C4—22no—
778C4—42no—
779C4—41no—
780C4—41no—
781C4—81no—
782C4—81no—
783C4—4881no—
784C4—4881no—
785C4—2442no—
786C4#121×D6111yescharacteristic
787C4#1684033911yescharacteristic
788C4#1684041811yescharacteristic
789C4#1684045511yescharacteristic
790C2—42no—
791C2—81no—
792C2—161no—
793C2—9761no—
794C2#2144925611yescharacteristic
795C2#2145543411yescharacteristic
796C2#2145550111yescharacteristic
797C2#2145743511yescharacteristic
798C2#2145745111yescharacteristic
799C2#2145841411yescharacteristic
800C2#2145841911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2416C2
socleC23×C61C22×D4
hypercenter#2416D61
hypocenterC61#24792
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#16840013C2semidirect
2. C2×#16840013C2semidirect
3. C2×#16839840C2semidirect
4. C2×#16839802C2semidirect
5. #21449237C2semidirect
6. #21447204C2semidirect
7. #21447193C2semidirect
8. #21447008C2semidirect
9. #21446998C2semidirect
10. #21446684C2semidirect
11. #21446544C2semidirect
12. #21446142C2semidirect
13. #21446136C2semidirect
14. #21445850C2semidirect
15. C61×#2416C2semidirect
74. C2×#11758194D4semidirect
100. #14519708D4semidirect
339. #92418#121semidirect
394. #2416D61semidirect
463. C61#24792semidirect

Maximal subgroups

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

subgroupindex
C2×#168400132
C2×#168398402
C2×#168398022
#214492372
#214472042
#214471932
#214470082
#214469982
#214466842
#214465442
#214461422
#214461362
#214458502
C61×#24162
#2479261