Finite Group Databasebeta

← #29733091

Subgroups — #29733091

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic, complemented
2C2×#16840073C211yesmaximal, characteristic, complemented
3#21449238C211yesmaximal, characteristic
4#21447145C211yesmaximal, characteristic, complemented
5#21447020C211yesmaximal, characteristic, complemented
6#21446953C211yesmaximal, characteristic, complemented
7#21446819C211yesmaximal, characteristic, complemented
8#21446176C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446132C211yesmaximal, characteristic, complemented
11#21446116C211yesmaximal, characteristic, complemented
12#21446071C211yesmaximal, characteristic, complemented
13#21446005C211yesmaximal, characteristic, complemented
14#21445539C211yesmaximal, characteristic, complemented
15C2×C61×#468C211yesmaximal, characteristic, complemented
16#16840470—24no—
17#16840470—24no—
18C2×#14519776C2211yescharacteristic
19C2×#14519767—21no—
20C2×#14519757—21no—
21C2×#14519754—21no—
22C2×#14519753C2211yescharacteristic
23C2×#14519748C2211yescharacteristic
24C2×Q8×Dic61C2211yescharacteristic
25C2×C4×C22⋊D61C2211yescharacteristic
26C2×#14519737—21no—
27C2×#14519736C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30#16840073—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519710C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40#16839676—21no—
41#16839670—21no—
42#16839665C2211yescharacteristic
43#16839662—21no—
44#16839658C2211yescharacteristic
45#16839656—21no—
46#16839619C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C61×#468—24no—
60C2×#107×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C22×C4×D61C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71#14519776—22no—
72#14519776—22no—
73#14519767—28no—
74#14519757—28no—
75#14519754—28no—
76#14519753—22no—
77#14519753—22no—
78#14519748—22no—
79#14519748—41no—
80Q8×Dic61—22no—
81Q8×Dic61—22no—
82C4×C22⋊D61—22no—
83C4×C22⋊D61—22no—
84#14519737—28no—
85#14519736—22no—
86#14519736—41no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61D414yescomplemented
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196D411yescharacteristic
100C4⋊C4×D61—22no—
101C4⋊C4×D61—22no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61D411yescharacteristic
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198D411yescharacteristic
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61C2311yescharacteristic
113#14519710—22no—
114#14519710—22no—
115#14519701—22no—
116#14519701—41no—
117#14519698—22no—
118#14519698—22no—
119C22⋊#92418—22no—
120#14519689—22no—
121#14519689—41no—
122#14519684—21no—
123#14519684—21no—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×SD16×C61—22no—
129C2×SD16×C61—22no—
130C2×SD16×C61—41no—
131C2×M16×C61—22no—
132C2×M16×C61—22no—
133C2×M16×C61—41no—
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61D414yescomplemented
138#121×C61—22no—
139#121×C61—22no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145#107×C61—22no—
146#103×C61—22no—
147#102×C61—22no—
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C23×D61C2×D411yescharacteristic
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61C2×D412yes—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—42no—
164C2×D4×C61—81no—
165C2×D4×C61—81no—
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×C61C2×D411yescharacteristic
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2×D412yes—
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—22no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—81no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—24no—
187C22×Dic61—21no—
188C22×Dic61—81no—
189C22×Dic61—81no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—24no—
200C2×C4×D61—81no—
201C2×C4×D61—81no—
202C2×Dic122—24no—
203C2×Dic122—81no—
204C2×Dic122—81no—
205SD16×C61—44no—
206M16×C61—44no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61#4112yes—
213C4⋊C4×C61—24no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61C2×D412yes—
218C22⋊C4×C61—24no—
219C22⋊C4×C61—42no—
220C22⋊Dic61—22no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223C22⋊Dic61—42no—
224C22⋊Dic61—81no—
225#11758198—24no—
226#11758198—22no—
227#11758198—81no—
228C4⋊Dic61—24no—
229C4⋊Dic61—24no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61C2×D412yes—
236C4⋊Dic61C2×D412yes—
237C4⋊Dic61#4112yes—
238#11758196—24no—
239#11758196—24no—
240#11758196—24no—
241#11758196—22no—
242#11758196—81no—
243C4×Dic61—24no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—42no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61#12012yes—
267C23×C61C22×D411yescharacteristic
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61#13712yes—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—41no—
278Q8×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—84no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61#12012yes—
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C612−1+411yescharacteristic
306C22⋊D61—28no—
307C22⋊D61—84no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—84no—
329C2×Dic61#13712yes—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—84no—
335Dic122—84no—
336C8×C61—22no—
337C8×C61—41no—
338#92418—41no—
339#92418—41no—
340#25559—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—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61C2×#12011yescharacteristic
356C22×C61#54611yescharacteristic
357C22×C61#54711yescharacteristic
358C22×C61C2×#13711yescharacteristic
359C22×C61C2×#13711yescharacteristic
360C22×C61#57611yescharacteristic
361C22×C61#57611yescharacteristic
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C4×C61—22no—
370C4×C61—42no—
371C4×C61—42no—
372C4×C61—81no—
373C4×C61#53211yescharacteristic
374C4×C61#53711yescharacteristic
375C4×C61#54611yescharacteristic
376C4×C61#54711yescharacteristic
377Dic61—22no—
378Dic61—41no—
379Dic61—41no—
380Dic61—42no—
381Dic61—42no—
382Dic61—42no—
383Dic61—81no—
384C2×#554—611no—
385C2×#480—611no—
386C2×#468D6111yescharacteristic, complemented
387#2414—611no—
388#2057—611no—
389#2036—611no—
390#2023—611no—
391#2000—611no—
392#1880—611no—
393#1874—611no—
394#1873—611no—
395#1870—611no—
396#1863—611no—
397#1852—611no—
398#1736—611no—
399C2×C61—42no—
400C2×C61—161no—
401C2×C61#243011yescharacteristic
402C2×C61#300411yescharacteristic
403C2×C61#300811yescharacteristic
404C2×C61#331411yescharacteristic
405C2×C61#333311yescharacteristic
406C2×C61#334611yescharacteristic
407C2×C61#335711yescharacteristic
408D61—42no—
409C22×SD16C2×D6111yescharacteristic
410C22×M16C2×D6111yescharacteristic
411#554—1224no—
412#554—1224no—
413C2×C4⋊Q8—611no—
414C2×#125—1221no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8—1221no—
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8C2×D6111yescharacteristic
419C2×#121—611no—
420C2×#121C2×D6111yescharacteristic
421C2×C4×Q8—611no—
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C2×#117—611no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427#480—1224no—
428#468—24no—
429C2×#107—611no—
430C2×#107—611no—
431C2×#107C2×D6111yescharacteristic
432C2×#103—611no—
433C2×#103—611no—
434C2×#103C2×D6111yescharacteristic
435C2×#102—611no—
436C2×#102—611no—
437C2×#102C2×D6111yescharacteristic
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441#394—1221no—
442#392—1221no—
443#390—611no—
444#390—1221no—
445#389—611no—
446#388—1221no—
447#380—611no—
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2555911yescharacteristic, complemented, Sylow
457C22×Q8—1221no—
458C22×Q8C22×D6111yescharacteristic
459C22×D4—21no—
460C22×D4—611no—
461C22×D4—1221no—
462C22×D4C22×D6111yescharacteristic
463C23×C4—611no—
464C23×C4—1221no—
465C23×C4—1221no—
466C23×C4C22×D6111yescharacteristic
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—41no—
470C2×M16—22no—
471C2×M16—22no—
472C2×M16—41no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477C4⋊Q8—1222no—
478C4⋊Q8—1222no—
479#125—1228no—
480C22⋊Q8—22no—
481C22⋊Q8—1228no—
482C22⋊Q8—1228no—
483C22⋊Q8—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8C22⋊D6114yescomplemented
486#121—22no—
487#121—22no—
488#121—1222no—
489#121—2441no—
490C4×Q8—1222no—
491C4×Q8—1222no—
492C4×D4—1228no—
493C4×D4—1222no—
494C4×D4—1222no—
495#117—1222no—
496#117—2441no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C42—611no—
526C2×C42—1221no—
527C2×C42—1221no—
528#107—22no—
529#107—1222no—
530#107—1222no—
531#103—22no—
532#103—1222no—
533#103—2441no—
534#102—22no—
535#102—1222no—
536#102—1222no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—2441no—
540#95—1221no—
541#95—1221no—
542C24—21no—
543C24—611no—
544C24D4×D6111yescharacteristic
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—1224no—
551C2×Q8—4881no—
552C2×Q8—4881no—
553C2×Q8C2×C22⋊D6112yes—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—4881no—
567C2×D4—2442no—
568C2×D4—2442no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—1224no—
580C22×C4—1224no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—4881no—
592C22×C4—4881no—
593C22×C4—4881no—
594C22×C4—4881no—
595C22×C4D4×D6112yes—
596C22×C4D4×D6111yescharacteristic
597C22×C4C2×C22⋊D6112yes—
598C22×C4C23×D6111yescharacteristic
599SD16—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8#1175822412yes—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—612no—
618C4⋊C4—612no—
619C4⋊C4—612no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1224no—
628C4⋊C4—1222no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—4881no—
632C4⋊C4C2×C22⋊D6112yes—
633C22⋊C4—24no—
634C22⋊C4—42no—
635C22⋊C4—1224no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—4881no—
639C22⋊C4—4881no—
640C22⋊C4—2442no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C42—1224no—
644C42—1221no—
645C42—1221no—
646C42—2442no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—612no—
661C23—1221no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23#1451974512yes—
668C23C2×D4×D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673Q8—4884no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—84no—
679D4—1228no—
680D4—4884no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—612no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1222no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—4884no—
709C2×C4—4884no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4#1451974512yes—
724C2×C4C2×D4×D6111yescharacteristic
725C2×C4C22×C22⋊D6111yescharacteristic
726C2×C4#41×D6111yescharacteristic
727C2×C4C2×#1175822411yescharacteristic
728C2×C4#1451982211yescharacteristic
729C2×C4#1451982411yescharacteristic
730C8—22no—
731C8—41no—
732C8—2441no—
733C8—2441no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—1222no—
749C22—1222no—
750C22—1222no—
751C22—2441no—
752C22—2441no—
753C22—2441no—
754C22—2441no—
755C22C2×#1451974511yescharacteristic
756C22#1684040111yescharacteristic
757C22#1684041211yescharacteristic
758C22#137×D6111yescharacteristic
759C22#137×D6111yescharacteristic
760C22#1684056611yescharacteristic
761C22#1684056611yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—81no—
766C4—1222no—
767C4—4881no—
768C4—2441no—
769C4—2442no—
770C4—2441no—
771C4—2442no—
772C4—2442no—
773C4#1684030711yescharacteristic
774C4#1684033911yescharacteristic
775C4#1684040611yescharacteristic
776C4#1684041111yescharacteristic
777C2—42no—
778C2—161no—
779C2—2442no—
780C2#2144942511yescharacteristic
781C2#2145505111yescharacteristic
782C2#2145508611yescharacteristic
783C2#2145789511yescharacteristic
784C2#2145815211yescharacteristic
785C2#2145829911yescharacteristic
786C2#2145844011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#468C2
socleC23×C61C22×D4
prime radical#21449238C2
hypercenterC2×#468D61
hypocenterC61#25559
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16840470C2semidirect
2. C2×#16840073C2semidirect
4. #21447145C2semidirect
5. #21447020C2semidirect
6. #21446953C2semidirect
7. #21446819C2semidirect
8. #21446176C2semidirect
9. #21446133C2semidirect
10. #21446132C2semidirect
11. #21446116C2semidirect
12. #21446071C2semidirect
13. #21446005C2semidirect
14. #21445539C2semidirect
15. C2×C61×#468C2semidirect
90. C2×C4⋊Dic61D4semidirect
137. C22⋊Q8×C61D4semidirect
386. C2×#468D61semidirect
456. C61#25559semidirect
485. C22⋊Q8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
C2×#168400732
#214492382
#214471452
#214470202
#214469532
#214468192
#214461762
#214461332
#214461322
#214461162
#214460712
#214460052
#214455392
C2×C61×#4682
#2555961