Finite Group Databasebeta

← #29718798

Subgroups — #29718798

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×#16839896C211yesmaximal, characteristic
2C2×#16839823C211yesmaximal, characteristic, complemented
3#21451608C211yesmaximal, characteristic, complemented
4#21447207C211yesmaximal, characteristic, complemented
5#21447193C211yesmaximal, characteristic, complemented
6#21447129C211yesmaximal, characteristic, complemented
7#21447129C211yesmaximal, characteristic, complemented
8#21446694C211yesmaximal, characteristic, complemented
9#21446684C211yesmaximal, characteristic, complemented
10#21446519C211yesmaximal, characteristic, complemented
11#21446505C211yesmaximal, characteristic, complemented
12#21446141C211yesmaximal, characteristic, complemented
13#21446018C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C61×#2309C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19#16839896—24no—
20#16839823—24no—
21C2×#14519710C2211yescharacteristic, complemented
22C2×#14519708C2211yescharacteristic, complemented
23C2×C4⋊#92418C2211yescharacteristic, complemented
24C2×C4⋊#92418C2211yescharacteristic, complemented
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519697C2211yescharacteristic, complemented
32C2×#14519697C2211yescharacteristic, complemented
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519688C2211yescharacteristic, complemented
36C2×C4×#92418C2211yescharacteristic, complemented
37#16839697—21no—
38#16839688—21no—
39#16839677—21no—
40#16839677—21no—
41#16839664C2211yescharacteristic, complemented
42#16839664C2211yescharacteristic, complemented
43#16839660C2211yescharacteristic, complemented
44#16839660C2211yescharacteristic, complemented
45#16839622C2211yescharacteristic
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50C23×D4×C61C2211yescharacteristic
51C2×#117×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C61×#390—21no—
54C61×#390—21no—
55C61×#390C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#379—21no—
60C61×#379—21no—
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C2×#11758199—22no—
64C2×#11758199—22no—
65C2×#11758199—22no—
66C2×#11758199—22no—
67C2×#11758199—41no—
68C2×#11758199—41no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519751—22no—
74#14519751—22no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C22⋊Dic61—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86#14519710—41no—
87#14519708—41no—
88C4⋊#92418—22no—
89C4⋊#92418—22no—
90#14519698—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—22no—
94#14519698—41no—
95#14519698—41no—
96#14519697—41no—
97#14519697—41no—
98C22⋊#92418—22no—
99C22⋊#92418D414yes—
100#14519688—22no—
101C4×#92418—22no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C25×C61—21no—
106C22×D4×C61—22no—
107C22×D4×C61—22no—
108C22×D4×C61—21no—
109C22×D4×C61—22no—
110C22×D4×C61—22no—
111C22×D4×C61—41no—
112C22×D4×C61—41no—
113C22×D4×C61C2311yescharacteristic
114C22×D4×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116#117×C61—22no—
117#117×C61—22no—
118#117×C61—41no—
119#117×C61—41no—
120C2×C4⋊C4×C61D411yescharacteristic
121C2×C4⋊C4×C61D411yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
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×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61D411yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C42×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C24×C61—24no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—42no—
142C24×C61—42no—
143C24×C61—81no—
144C24×C61—81no—
145C24×C61—81no—
146C24×C61—81no—
147C24×C61C2×D411yescharacteristic
148C23×D61—21no—
149C2×D4×C61—24no—
150C2×D4×C61—21no—
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—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—44no—
161C2×D4×C61—44no—
162C2×D4×C61—44no—
163C2×D4×C61—44no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61#4112yes—
167C2×D4×C61#4112yes—
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×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D412yes—
180C22×C4×C61#4112yes—
181C22×C4×C61C2411yescharacteristic
182C2×C22⋊D61—42no—
183C2×C22⋊D61—81no—
184C2×C22⋊D61—81no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—42no—
203C22⋊C4×C61—81no—
204C22⋊C4×C61—81no—
205C22⋊C4×C61—81no—
206C22⋊C4×C61—81no—
207C22⋊C4×C61—81no—
208C22⋊C4×C61—81no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—42no—
216C22⋊Dic61—81no—
217#11758199—44no—
218#11758199—44no—
219#11758198—42no—
220#11758198—81no—
221#11758198—81no—
222#11758198—81no—
223#11758198—81no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230#11758196—81no—
231#11758196—81no—
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—22no—
251C23×C61—22no—
252C23×C61—48no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—84no—
266C23×C61—84no—
267C23×C61—84no—
268C23×C61—84no—
269C23×C61—84no—
270C23×C61—84no—
271C23×C61#12112yes—
272C23×C61C22×D411yescharacteristic
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280D4×C61—22no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—48no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—41no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
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—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61#12112yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C2×C4×C61H(5,𝔽2)11yescharacteristic
319C2×C4×C61H(5,𝔽2)11yescharacteristic
320C22⋊D61—84no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
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—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—816no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61C2×#12111yescharacteristic
362C22×C61#52511yescharacteristic
363C22×C61#53511yescharacteristic
364C22×C61#57611yescharacteristic
365C22×C61#57611yescharacteristic
366C22×C61#57611yescharacteristic
367C22×C61#57711yescharacteristic
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#54611yescharacteristic
383C4×C61#54611yescharacteristic
384C4×C61#55111yescharacteristic
385C4×C61#55111yescharacteristic
386Dic61—81no—
387Dic61—81no—
388Dic61—81no—
389C2×#447—611no—
390C2×#433—611no—
391#2624—611no—
392#2309D6111yescharacteristic, complemented
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—82no—
406C2×C61—82no—
407C2×C61#241111yescharacteristic
408C2×C61#305811yescharacteristic
409C2×C61#306211yescharacteristic
410C2×C61#311811yescharacteristic
411C2×C61#312211yescharacteristic
412C2×C61#322011yescharacteristic
413C2×C61#322411yescharacteristic
414D61—161no—
415C23×D4C2×D6111yescharacteristic
416C22×D8—611no—
417C22×D8—611no—
418C2×#121—611no—
419C2×#117C2×D6111yescharacteristic
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—1221no—
440#397—1221no—
441#394—1221no—
442#394—1221no—
443#390—21no—
444#390—21no—
445#390—611no—
446#390—611no—
447#390C2×D6111yescharacteristic
448#390C2×D6111yescharacteristic
449#390C2×D6111yescharacteristic
450#390C2×D6111yescharacteristic
451#389—611no—
452#389—611no—
453#380—611no—
454#379—21no—
455#379—21no—
456#340—611no—
457#340—611no—
458#340—611no—
459#340—611no—
460C61#2451211yescharacteristic, complemented, Sylow
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—21no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—611no—
470C22×D4—1221no—
471C22×D4C22×D6111yescharacteristic
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—1222no—
485#121—1222no—
486#117—22no—
487#117—22no—
488#117—41no—
489#117—41no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
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—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
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—21no—
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—1221no—
536#95—1221no—
537#95—1221no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—42no—
542C24—42no—
543C24—81no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—1221no—
548C24C2×C22⋊D6111yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—4881no—
573C2×D4—4881no—
574C2×D4—2442no—
575C2×D4#1175822212yes—
576C2×D4#1175822212yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—1221no—
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—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—4881no—
621C4⋊C4—4881no—
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—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
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—42no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—84no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23#1451974912yes—
679C23C22×C22⋊D6111yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—4884no—
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—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
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×C4C2×#1175822411yescharacteristic
730C2×C4C2×#1175822211yescharacteristic
731C2×C4C2×#1175822211yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982211yescharacteristic
734C8—1222no—
735C8—1222no—
736C8—2441no—
737C8—2441no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—4881no—
761C22—4881no—
762C22—4881no—
763C22—4881no—
764C22—4881no—
765C22—4881no—
766C22—4881no—
767C22C2×#1451974911yescharacteristic
768C22#1684027311yescharacteristic
769C22#1684032911yescharacteristic
770C22#1684056511yescharacteristic
771C22#1684056511yescharacteristic
772C22#1684056511yescharacteristic
773C22#1684057311yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—4881no—
782C4—4881no—
783C4—4881no—
784C4#1684040211yescharacteristic
785C4#1684040211yescharacteristic
786C4#1684043811yescharacteristic
787C4#1684043811yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—9761no—
792C2#2144920411yescharacteristic
793C2#2145546411yescharacteristic
794C2#2145549511yescharacteristic
795C2#2145600311yescharacteristic
796C2#2145606211yescharacteristic
797C2#2145686911yescharacteristic
798C2#2145691311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2309C2
socleC23×C61C22×D4
prime radicalC2×#16839896C2
hypercenter#2309D61
hypocenterC61#24512
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. C2×#16839823C2semidirect
3. #21451608C2semidirect
4. #21447207C2semidirect
5. #21447193C2semidirect
6. #21447129C2semidirect
7. #21447129C2semidirect
8. #21446694C2semidirect
9. #21446684C2semidirect
10. #21446519C2semidirect
11. #21446505C2semidirect
12. #21446141C2semidirect
13. #21446018C2semidirect
14. #21445750C2semidirect
15. C61×#2309C2semidirect
21. C2×#14519710C22semidirect
22. C2×#14519708C22semidirect
23. C2×C4⋊#92418C22semidirect
24. C2×C4⋊#92418C22semidirect
31. C2×#14519697C22semidirect
32. C2×#14519697C22semidirect
35. C2×#14519688C22semidirect
36. C2×C4×#92418C22semidirect
41. #16839664C22semidirect
42. #16839664C22semidirect
43. #16839660C22semidirect
44. #16839660C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
392. #2309D61semidirect
460. C61#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#168398962
C2×#168398232
#214516082
#214472072
#214471932
#214471292
#214466942
#214466842
#214465192
#214465052
#214461412
#214460182
#214457502
C61×#23092
#2451261