Finite Group Databasebeta

← #29841056

Subgroups — #29841056

Order 15616.

5682 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519823C211yesmaximal, characteristic
2C2×#16840244C211yesmaximal, characteristic, complemented
3C2×C4×#11758226C211yesmaximal, characteristic, complemented
4#21448660C211yesmaximal, characteristic, complemented
5#21448657C211yesmaximal, characteristic, complemented
6#21448657C211yesmaximal, characteristic, complemented
7C22⋊C4×D244C213yesmaximal, complemented
8#21448640C213yesmaximal, complemented
9#21448640C213yesmaximal, complemented
10#21448639C213yesmaximal, complemented
11#21448408C213yesmaximal, complemented
12#21448398C213yesmaximal, complemented
13#21448305C213yesmaximal, complemented
14#390×D61C213yesmaximal, complemented
15C61×#2341C211yesmaximal, characteristic, complemented
16C2×#14519823—28no—
17C2×#14519823—28no—
18C2×#14519823C4116yescomplemented
19C22×#11758226C2211yescharacteristic
20C22×#11758226C2211yescharacteristic
21C22×#11758222C2213yes—
22C23×D244C2213yes—
23C22×D4×D61C2213yes—
24C22×D4×D61C2213yes—
25#16840244—28no—
26C4×#11758226—28no—
27C2×Q8×Dic61C2211yescharacteristic, complemented
28C2×Q8×Dic61C2211yescharacteristic, complemented
29C2×C4×D244C2213yescomplemented
30C2×C4×D244C2213yescomplemented
31C2×#14519739C2213yescomplemented
32C2×#14519739C2213yescomplemented
33C2×#14519735C2213yescomplemented
34C2×#14519734C2213yescomplemented
35C2×C4⋊C4×D61C2213yescomplemented
36C2×C22⋊C4×D61C2216yescomplemented
37C2×C22⋊C4×D61C2216yescomplemented
38C2×C42×D61C2213yescomplemented
39#16839666C2211yescharacteristic, complemented
40#16839666C2213yescomplemented
41#16839665C2213yescomplemented
42#16839665C2213yescomplemented
43#16839664C2213yescomplemented
44#16839664C2213yescomplemented
45#16839663C2213yescomplemented
46#16839663C2213yescomplemented
47#16839662C2213yescomplemented
48#16839662C2216yescomplemented
49#16839662C2213yescomplemented
50#16839640C2213yescomplemented
51#16839640C2213yescomplemented
52#16839640C2216yescomplemented
53#16839638C2213yescomplemented
54#16839638C2213yescomplemented
55#16839638C2216yescomplemented
56#16839622C2213yescomplemented
57#16839619C2213yescomplemented
58#16839619C2213yescomplemented
59#16839617C2216yescomplemented
60#16839617C2216yescomplemented
61C4×#11758198C2213yescomplemented
62C4×#11758198C2213yescomplemented
63C4×C22⋊Dic61C2213yescomplemented
64C22×#41×C61C2211yescharacteristic
65C2×C4×Q8×C61C2211yescharacteristic, complemented
66C2×C4×Q8×C61C2211yescharacteristic, complemented
67C61×#390C2213yescomplemented
68C61×#390C2213yescomplemented
69C61×#380C2213yescomplemented
70C4×C22⋊C4×C61C2213yescomplemented
71C24×D61C2316yes—
72#14519823—2128no—
73C2×#11758226—24no—
74C2×#11758226—24no—
75C2×#11758226C2×C418yes—
76C2×#11758226C2×C418yescomplemented
77C2×#11758226D418yes—
78C2×#11758226D418yes—
79C2×#11758222—212no—
80C2×#11758222—212no—
81C2×#11758222C2×C4124yescomplemented
82C22×Dic122C2311yescharacteristic
83C22×D244—212no—
84C22×D244—212no—
85C22×D244C2×C4124yescomplemented
86C22×D244C2313yes—
87C22×D244C2313yes—
88C22×D244C2313yes—
89C22×C22⋊D61C2313yes—
90C22×C22⋊D61C2313yes—
91C2×D4×D61—212no—
92C2×D4×D61—212no—
93C2×D4×D61—212no—
94C2×D4×D61—212no—
95C2×D4×D61C2×C4124yescomplemented
96C2×D4×D61C2×C4124yescomplemented
97C22×C4×D61C2313yes—
98C22×C4×D61C2313yes—
99C22×C4×D61C2313yes—
100C22×C4×D61C2316yes—
101C22×C4×D61C2313yes—
102Q8×Dic61—24no—
103Q8×Dic61—24no—
104C4×D244—212no—
105C4×D244—212no—
106#14519739—212no—
107#14519739—212no—
108#14519735—212no—
109#14519734—212no—
110C2×C4⋊Dic61C2313yes—
111C2×C4⋊Dic61C2313yes—
112C2×#11758196C2313yes—
113C2×#11758196C2311yescharacteristic
114C4⋊C4×D61—212no—
115C2×C22⋊Dic61C2313yes—
116C2×C22⋊Dic61C2316yes—
117C2×C22⋊Dic61C2313yes—
118C2×#11758198C2313yes—
119C2×#11758198C2313yes—
120C2×#11758198C2313yes—
121C2×#11758198C2313yes—
122C2×#11758198C2316yes—
123C2×#11758198C2316yes—
124C2×#11758198C2316yes—
125C2×#11758198C2313yes—
126C2×#11758198C2313yes—
127C22⋊C4×D61—412no—
128C22⋊C4×D61—412no—
129C2×C4×Dic61C2311yescharacteristic
130C2×C4×Dic61C2313yes—
131C2×C4×Dic61C2313yes—
132C2×C4×Dic61C2313yes—
133C42×D61—212no—
134#14519684C2311yescharacteristic
135#14519684C2313yes—
136#14519684C2311yescharacteristic
137#14519684C2311yescharacteristic
138#14519684C2313yes—
139#14519684C2313yes—
140C2×#41×C61—24no—
141C2×#41×C61—24no—
142C2×#41×C61C2×C418yescomplemented
143C22×Q8×C61C2311yescharacteristic
144C22×D4×C61C2313yes—
145C23×C4×C61C2313yes—
146C4×Q8×C61—24no—
147C4×Q8×C61—24no—
148C2×C4⋊C4×C61C2313yes—
149C2×C4⋊C4×C61C2313yes—
150C2×C22⋊C4×C61C2313yes—
151C2×C22⋊C4×C61C2316yes—
152C2×C22⋊C4×C61C2313yes—
153C2×C42×C61C2313yes—
154C2×C42×C61C2313yes—
155#95×C61C2311yescharacteristic
156#95×C61C2313yes—
157C24×C61C2413yes—
158C23×D61—212no—
159C23×D61—212no—
160C23×D61—46no—
161C23×D61—46no—
162C23×D61—46no—
163C23×D61—46no—
164C23×D61C22×C4124yes—
165C23×D61C2413yes—
166C23×D61C2413yes—
167#41×C61—232no—
168C2×Q8×C61C22×C414yes—
169C2×Q8×C61C2×D414yes—
170C2×Q8×C61C2×D414yes—
171C2×D4×C61—26no—
172C2×D4×C61—26no—
173C2×D4×C61C22×C4112yes—
174C22×C4×C61—26no—
175C22×C4×C61—26no—
176C22×C4×C61C22×C4112yes—
177C22×C4×C61C2413yes—
178C22×C4×C61C2413yes—
179C22×C4×C61C2411yescharacteristic
180C22×C4×C61C2411yescharacteristic
181C22×C4×C61C2411yescharacteristic
182C22×C4×C61C2413yes—
183C2×C22⋊D61—26no—
184C2×C22⋊D61—26no—
185C2×C22⋊D61—26no—
186C2×C22⋊D61—26no—
187C2×C22⋊D61C22×C4112yes—
188C2×C22⋊D61C22×C4112yes—
189C22×Dic61C2413yes—
190C22×Dic61C2413yes—
191C22×Dic61C2411yescharacteristic
192C22×Dic61C2411yescharacteristic
193C22×Dic61C2411yescharacteristic
194C22×Dic61C2411yescharacteristic
195#11758226—232no—
196#11758226C22⋊C4164yescomplemented
197D4×D61—296no—
198D4×D61—296no—
199#11758222—296no—
200C2×D244—26no—
201C2×D244—26no—
202C2×D244—26no—
203C2×D244—26no—
204C2×D244—296no—
205C2×D244C22×C4112yes—
206C2×D244C22×C4112yes—
207C2×D244C22×C4112yes—
208C2×D244C2×D4112yes—
209C2×D244C2×D4112yes—
210C2×C4×D61—26no—
211C2×C4×D61—26no—
212C2×C4×D61—26no—
213C2×C4×D61—26no—
214C2×C4×D61—26no—
215C2×C4×D61—26no—
216C2×C4×D61—212no—
217C2×C4×D61—43no—
218C2×C4×D61—43no—
219C2×C4×D61—46no—
220C2×C4×D61—46no—
221C2×C4×D61C22×C4112yes—
222C2×C4×D61C22×C4112yes—
223C2×C4×D61C2×D4112yes—
224C2×C4×D61C2×D4112yes—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122C22×C414yes—
228C4⋊C4×C61—26no—
229C4⋊C4×C61—26no—
230C22⋊C4×C61—26no—
231C22⋊C4×C61—43no—
232C22⋊C4×C61—46no—
233C42×C61—26no—
234C42×C61—26no—
235C22⋊Dic61—26no—
236C22⋊Dic61—46no—
237C22⋊Dic61—43no—
238#11758198—26no—
239#11758198—26no—
240#11758198—212no—
241#11758198—26no—
242#11758198—26no—
243#11758198—46no—
244#11758198—46no—
245#11758198—43no—
246#11758198—43no—
247C4⋊Dic61—26no—
248C4⋊Dic61—26no—
249#11758196—26no—
250#11758196—22no—
251C4×Dic61—26no—
252C4×Dic61—26no—
253C4×Dic61—22no—
254C4×Dic61—26no—
255C23×C61—23no—
256C23×C61—23no—
257C23×C61—23no—
258C23×C61—23no—
259C23×C61—23no—
260C23×C61—23no—
261C23×C61C23×C416yes—
262C23×C61C2511yescharacteristic
263C22×D61—23no—
264C22×D61—23no—
265C22×D61—23no—
266C22×D61—23no—
267C22×D61—23no—
268C22×D61—23no—
269C22×D61—23no—
270C22×D61—23no—
271C22×D61—23no—
272C22×D61—23no—
273C22×D61—248no—
274C22×D61—424no—
275C22×D61—424no—
276C22×D61—812no—
277C22×D61—812no—
278C22×D61—812no—
279C22×D61—812no—
280C22×D61C23×C416yes—
281C22×D61C23×C416yes—
282C22×D61C22×D416yes—
283C22×D61C22×D416yes—
284Q8×C61C2×C22⋊C4116yescomplemented
285D4×C61—224no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—224no—
291C2×C4×C61—23no—
292C2×C4×C61—21no—
293C2×C4×C61—23no—
294C2×C4×C61—23no—
295C2×C4×C61—23no—
296C2×C4×C61—23no—
297C2×C4×C61—21no—
298C2×C4×C61—23no—
299C2×C4×C61—21no—
300C2×C4×C61C23×C412yes—
301C2×C4×C61C23×C416yes—
302C2×C4×C61C22×D416yes—
303C2×C4×C61C22×D416yes—
304C2×C4×C61H(5,𝔽2)12yescomplemented
305C22⋊D61—224no—
306C22⋊D61—224no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—23no—
313C2×Dic61—23no—
314C2×Dic61—23no—
315C2×Dic61—23no—
316C2×Dic61—23no—
317C2×Dic61—21no—
318C2×Dic61—23no—
319C2×Dic61—21no—
320C2×Dic61C23×C412yes—
321C2×Dic61C23×C412yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61H(5,𝔽2)12yescomplemented
325D244—224no—
326D244—224no—
327D244C2×C22⋊C4148yescomplemented
328C4×D61—224no—
329C4×D61—412no—
330C4×D61—412no—
331C4×D61—812no—
332C4×D61C2×C22⋊C4148yescomplemented
333Dic122—28no—
334#34258—611nomaximal, Sylow
335C22×C61—26no—
336C22×C61—26no—
337C22×C61—26no—
338C22×C61—43no—
339C22×C61—43no—
340C22×C61—43no—
341C22×C61—43no—
342C22×C61C24×C411yescharacteristic
343C22×C61C23×D411yescharacteristic
344C22×C61C23×D411yescharacteristic
345C22×C61C2×H(5,𝔽2)11yescharacteristic
346C22×C61C2×H(5,𝔽2)11yescharacteristic
347C22×C61#58511yescharacteristic
348C22×C61#58511yescharacteristic
349C2×D61—26no—
350C2×D61—26no—
351C2×D61—26no—
352C2×D61—26no—
353C2×D61—26no—
354C2×D61—26no—
355C2×D61—26no—
356C2×D61—26no—
357C2×D61—26no—
358C2×D61—43no—
359C2×D61—43no—
360C2×D61—43no—
361C2×D61—43no—
362C2×D61—848no—
363C2×D61C22×C22⋊C4112yes—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—43no—
367C4×C61—43no—
368C4×C61—41no—
369C4×C61C22×C22⋊C4112yes—
370Dic61—22no—
371Dic61—22no—
372Dic61—43no—
373Dic61—43no—
374Dic61—41no—
375Dic61C22×C22⋊C414yes—
376C22×H(5,𝔽2)—611no—
377C2×#520—611no—
378C2×C4×#41—611no—
379#2341—611no—
380#2341—611no—
381#2341—611no—
382#2341D6111yescharacteristic, complemented
383D4×C22⋊C4—613no—
384D4×C22⋊C4—613no—
385D4×C22⋊C4—613no—
386D4×C22⋊C4—613no—
387#2311—613no—
388#2309—613no—
389#2297—613no—
390C2×#390—613no—
391C2×C61—46no—
392C2×C61C23×C22⋊C411yescharacteristic
393C2×C61C4×H(5,𝔽2)11yescharacteristic
394C2×C61C4×H(5,𝔽2)11yescharacteristic
395C2×C61#348811yescharacteristic
396C2×C61#348811yescharacteristic
397C2×C61#349811yescharacteristic
398C2×C61#350011yescharacteristic
399D61—212no—
400D61—46no—
401C2×H(5,𝔽2)—6116no—
402C2×H(5,𝔽2)—1228no—
403C2×H(5,𝔽2)—1228no—
404C22×#41—611no—
405C22×#41—611no—
406C22×#41—613no—
407C22×#41C2×D6111yescharacteristic
408C23×D4—613no—
409C23×D4—613no—
410C23×D4—613no—
411#520—1228no—
412C4×#41—1228no—
413C2×C4×Q8—611no—
414C2×C4×Q8—611no—
415C2×C4×Q8C2×D6111yescharacteristic, complemented
416C2×C4×Q8C2×D6111yescharacteristic, complemented
417C2×C4×D4—613no—
418C2×C4×D4—613no—
419C2×C4×D4—613no—
420C2×C4×D4—613no—
421C2×#117—613no—
422C2×#117—613no—
423C22×C4⋊C4—613no—
424C22×C22⋊C4—616no—
425C22×C22⋊C4—616no—
426C22×C42—613no—
427#391—613no—
428#391—611no—
429#390—613no—
430#390—613no—
431#390—613no—
432#390—613no—
433#390—613no—
434#390—616no—
435#390—613no—
436#390—613no—
437#390—613no—
438#390C2×D6113yescomplemented
439#390C2×D6113yescomplemented
440#386—616no—
441#386—613no—
442#386—613no—
443#386—616no—
444#386—613no—
445#386—613no—
446#380—613no—
447#380—613no—
448#380—613no—
449#380C2×D6113yescomplemented
450#379—616no—
451#379—616no—
452C4×C22⋊C4—613no—
453C4×C22⋊C4—613no—
454C4×C22⋊C4—613no—
455C4×C22⋊C4C2×D6113yescomplemented
456C61#3425811yescharacteristic, complemented, Sylow
457C25—616no—
458H(5,𝔽2)—122128no—
459C2×#41—24no—
460C2×#41—24no—
461C2×#41—618no—
462C2×#41—618no—
463C2×#41—618no—
464C2×#41—618no—
465C2×#41—6124no—
466C2×#41—12212no—
467C2×#41—12212no—
468C2×#41—1224no—
469C2×#41—1224no—
470C2×#41C4×D6118yescomplemented
471C22×Q8—611no—
472C22×Q8C22×D6111yescharacteristic
473C22×D4—613no—
474C22×D4—613no—
475C22×D4—6124no—
476C22×D4—6124no—
477C22×D4—6124no—
478C22×D4—613no—
479C22×D4—613no—
480C22×D4—613no—
481C22×D4—12212no—
482C22×D4—12212no—
483C22×D4—12212no—
484C22×D4—12212no—
485C22×D4—12212no—
486C22×D4—12212no—
487C22×D4C22×D6113yes—
488C23×C4—613no—
489C23×C4—613no—
490C23×C4—613no—
491C23×C4—613no—
492C23×C4—616no—
493C23×C4C22×D6113yes—
494C4×Q8—24no—
495C4×Q8—24no—
496C4×Q8—1224no—
497C4×Q8—1224no—
498C4×D4—12212no—
499C4×D4—12212no—
500C4×D4—12212no—
501C4×D4—12212no—
502#117—12212no—
503#117—12212no—
504C2×C4⋊C4—613no—
505C2×C4⋊C4—613no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—613no—
508C2×C4⋊C4—12212no—
509C2×C4⋊C4C22×D6113yes—
510C2×C4⋊C4C22×D6113yes—
511C2×C22⋊C4—613no—
512C2×C22⋊C4—613no—
513C2×C22⋊C4—613no—
514C2×C22⋊C4—613no—
515C2×C22⋊C4—616no—
516C2×C22⋊C4—613no—
517C2×C22⋊C4—616no—
518C2×C22⋊C4—613no—
519C2×C22⋊C4—616no—
520C2×C22⋊C4—616no—
521C2×C22⋊C4—613no—
522C2×C22⋊C4—613no—
523C2×C22⋊C4—24412no—
524C2×C22⋊C4—24412no—
525C2×C22⋊C4C22×D6113yes—
526C2×C22⋊C4C22×D6116yes—
527C2×C22⋊C4C22×D6113yes—
528C2×C42—613no—
529C2×C42—613no—
530C2×C42—613no—
531C2×C42—611no—
532C2×C42—12212no—
533C2×C42C22×D6113yes—
534C2×C42C22×D6113yes—
535#95—611no—
536#95—611no—
537#95—611no—
538#95—613no—
539#95—613no—
540#95—613no—
541#95C22×D6111yescharacteristic
542#95C22×D6113yes—
543C24—613no—
544C24—613no—
545C24—6124no—
546C24—12212no—
547C24—12212no—
548C24—2446no—
549C24—2446no—
550C24—2446no—
551C24—2446no—
552C24C23×D6113yes—
553#41—232no—
554#41—6164no—
555#41—12296no—
556#41—12232no—
557C2×Q8—614no—
558C2×Q8—1222no—
559C2×Q8—1222no—
560C2×Q8C2×C4×D6114yes—
561C2×Q8D4×D6114yes—
562C2×Q8D4×D6114yes—
563C2×D4—26no—
564C2×D4—26no—
565C2×D4—6112no—
566C2×D4—6112no—
567C2×D4—6112no—
568C2×D4—6112no—
569C2×D4—6112no—
570C2×D4—6112no—
571C2×D4—6112no—
572C2×D4—12296no—
573C2×D4—1226no—
574C2×D4—1226no—
575C2×D4—12296no—
576C2×D4—1226no—
577C2×D4—1226no—
578C2×D4—12296no—
579C2×D4—1226no—
580C2×D4—1226no—
581C2×D4—1226no—
582C2×D4—1226no—
583C2×D4C2×C4×D61112yes—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—611no—
587C22×C4—6112no—
588C22×C4—6112no—
589C22×C4—6112no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—6112no—
593C22×C4—611no—
594C22×C4—613no—
595C22×C4—613no—
596C22×C4—1226no—
597C22×C4—12212no—
598C22×C4—1226no—
599C22×C4—1226no—
600C22×C4—1226no—
601C22×C4—1226no—
602C22×C4—1226no—
603C22×C4—2446no—
604C22×C4—2446no—
605C22×C4—2443no—
606C22×C4—2443no—
607C22×C4C2×C4×D61112yes—
608C22×C4C23×D6113yes—
609C22×C4C23×D6111yescharacteristic
610C22×C4C23×D6113yes—
611C22×C4C23×D6111yescharacteristic
612C22×C4C23×D6111yescharacteristic
613C22×C4C23×D6113yes—
614C4⋊C4—26no—
615C4⋊C4—26no—
616C4⋊C4—1226no—
617C4⋊C4—1222no—
618C4⋊C4—1226no—
619C4⋊C4—1226no—
620C22⋊C4—26no—
621C22⋊C4—46no—
622C22⋊C4—43no—
623C22⋊C4—1226no—
624C22⋊C4—1226no—
625C22⋊C4—12212no—
626C22⋊C4—1226no—
627C22⋊C4—1226no—
628C22⋊C4—1226no—
629C22⋊C4—2446no—
630C22⋊C4—2446no—
631C22⋊C4—2443no—
632C22⋊C4—2443no—
633C22⋊C4—2446no—
634C22⋊C4—2443no—
635C42—26no—
636C42—26no—
637C42—1222no—
638C42—1226no—
639C42—1226no—
640C42—1226no—
641C23—23no—
642C23—23no—
643C23—23no—
644C23—23no—
645C23—23no—
646C23—23no—
647C23—616no—
648C23—616no—
649C23—616no—
650C23—616no—
651C23—12248no—
652C23—1223no—
653C23—1223no—
654C23—1223no—
655C23—1223no—
656C23—1223no—
657C23—1223no—
658C23—1223no—
659C23—1223no—
660C23—1223no—
661C23—1223no—
662C23—48812no—
663C23—48812no—
664C23—48812no—
665C23—48812no—
666C23—24424no—
667C23—24424no—
668C23C22×C4×D6116yes—
669C23C24×D6111yescharacteristic
670Q8—1228no—
671Q8C22⋊C4×D61116yescomplemented
672D4—224no—
673D4—6148no—
674D4—12224no—
675D4—12224no—
676D4—12224no—
677D4—12224no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—224no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—23no—
687C2×C4—23no—
688C2×C4—23no—
689C2×C4—21no—
690C2×C4—23no—
691C2×C4—21no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—6148no—
696C2×C4—612no—
697C2×C4—612no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—12224no—
703C2×C4—1221no—
704C2×C4—1223no—
705C2×C4—1223no—
706C2×C4—1223no—
707C2×C4—1223no—
708C2×C4—1223no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1223no—
712C2×C4—48812no—
713C2×C4—24412no—
714C2×C4—24412no—
715C2×C4C22×C4×D6112yes—
716C2×C4C22×C4×D6116yes—
717C2×C4C2×D4×D6116yes—
718C2×C4C2×D4×D6116yes—
719C2×C4#1451982312yescomplemented
720C22—26no—
721C22—26no—
722C22—26no—
723C22—43no—
724C22—43no—
725C22—43no—
726C22—43no—
727C22—6112no—
728C22—1226no—
729C22—1226no—
730C22—1226no—
731C22—1226no—
732C22—1226no—
733C22—1226no—
734C22—1226no—
735C22—1226no—
736C22—1226no—
737C22—48848no—
738C22—2443no—
739C22—2443no—
740C22—2443no—
741C22—2443no—
742C22C23×C4×D6111yescharacteristic
743C22C22×D4×D6111yescharacteristic
744C22C22×D4×D6111yescharacteristic
745C22H(5,𝔽2)×D6111yescharacteristic
746C22C2×#1451982311yescharacteristic
747C22#1684059811yescharacteristic
748C22#1684059911yescharacteristic
749C4—22no—
750C4—22no—
751C4—43no—
752C4—43no—
753C4—41no—
754C4—614no—
755C4—1222no—
756C4—1222no—
757C4—2443no—
758C4—2443no—
759C4—2441no—
760C4C2×C22⋊C4×D61112yes—
761C2—46no—
762C2—12212no—
763C2—2446no—
764C2C22×C22⋊C4×D6111yescharacteristic
765C2#2145902511yescharacteristic
766C2C4×#1451982311yescharacteristic
767C2#2145948511yescharacteristic
768C2#2145948711yescharacteristic
769C2#2145959611yescharacteristic
770C2#2145961011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2341C2
socle, cosocleC23×C61C25
prime radicalC22×#14519823C2
hypercenter#2341D61
hypocenterC61#34258
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#16840244C2semidirect
3. C2×C4×#11758226C2semidirect
4. #21448660C2semidirect
5. #21448657C2semidirect
6. #21448657C2semidirect
7. C22⋊C4×D244C2semidirect
8. #21448640C2semidirect
9. #21448640C2semidirect
10. #21448639C2semidirect
11. #21448408C2semidirect
12. #21448398C2semidirect
13. #21448305C2semidirect
14. #390×D61C2semidirect
15. C61×#2341C2semidirect
18. C2×#14519823C4semidirect
27. C2×Q8×Dic61C22semidirect
28. C2×Q8×Dic61C22semidirect
29. C2×C4×D244C22semidirect
30. C2×C4×D244C22semidirect
31. C2×#14519739C22semidirect
32. C2×#14519739C22semidirect
33. C2×#14519735C22semidirect
34. C2×#14519734C22semidirect
35. C2×C4⋊C4×D61C22semidirect
36. C2×C22⋊C4×D61C22semidirect
37. C2×C22⋊C4×D61C22semidirect
38. C2×C42×D61C22semidirect
39. #16839666C22semidirect
40. #16839666C22semidirect
41. #16839665C22semidirect
42. #16839665C22semidirect
43. #16839664C22semidirect
44. #16839664C22semidirect
45. #16839663C22semidirect
46. #16839663C22semidirect
47. #16839662C22semidirect
48. #16839662C22semidirect
49. #16839662C22semidirect
50. #16839640C22semidirect
51. #16839640C22semidirect
52. #16839640C22semidirect
53. #16839638C22semidirect
54. #16839638C22semidirect
55. #16839638C22semidirect
56. #16839622C22semidirect
57. #16839619C22semidirect
58. #16839619C22semidirect
59. #16839617C22semidirect
60. #16839617C22semidirect
61. C4×#11758198C22semidirect
62. C4×#11758198C22semidirect
63. C4×C22⋊Dic61C22semidirect
65. C2×C4×Q8×C61C22semidirect
66. C2×C4×Q8×C61C22semidirect
67. C61×#390C22semidirect
68. C61×#390C22semidirect
69. C61×#380C22semidirect
70. C4×C22⋊C4×C61C22semidirect
76. C2×#11758226C2×C4semidirect
81. C2×#11758222C2×C4semidirect
85. C22×D244C2×C4semidirect
95. C2×D4×D61C2×C4semidirect
96. C2×D4×D61C2×C4semidirect
142. C2×#41×C61C2×C4semidirect
196. #11758226C22⋊C4semidirect
284. Q8×C61C2×C22⋊C4semidirect
304. C2×C4×C61H(5,𝔽2)semidirect
324. C2×Dic61H(5,𝔽2)semidirect
327. D244C2×C22⋊C4semidirect
332. C4×D61C2×C22⋊C4semidirect
382. #2341D61semidirect
415. C2×C4×Q8C2×D61semidirect
416. C2×C4×Q8C2×D61semidirect
438. #390C2×D61semidirect
439. #390C2×D61semidirect
449. #380C2×D61semidirect
455. C4×C22⋊C4C2×D61semidirect
456. C61#34258semidirect
470. C2×#41C4×D61semidirect
671. Q8C22⋊C4×D61semidirect
719. C2×C4#14519823semidirect

Maximal subgroups

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

subgroupindex
C22×#145198232
C2×#168402442
C2×C4×#117582262
#214486602
#214486572
C22⋊C4×D2442
#214486402
#214486392
#214484082
#214483982
#214483052
#390×D612
C61×#23412
#3425861