Finite Group Databasebeta

← #30620319

Subgroups — #30620319

Order 15616.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462325C212yesmaximal, complemented
2#21462010C212yesmaximal, complemented
3#21461842C212yesmaximal, complemented
4#21461840C212yesmaximal
5#21461716C211yesmaximal, characteristic, complemented
6#21461714C211yesmaximal, characteristic, complemented
7#21461679C211yesmaximal, characteristic, complemented
8C4×#14519835C211yesmaximal, characteristic, complemented
9#21461518C211yesmaximal, characteristic, complemented
10C2×#16840640C211yesmaximal, characteristic, complemented
11C2×#16840441C211yesmaximal, characteristic
12C2×#14519856C2212yes—
13C22×C22⋊#6923C2212yes—
14C2×#14519835C2212yes—
15C2×#14519835C2212yes—
16#16840712—22no—
17#16840712—22no—
18#16840709—22no—
19#16840705C2212yes—
20#16840704C2212yes—
21#16840703C2212yes—
22C22⋊C4×#6923—22no—
23C4×C22⋊#6923C2212yes—
24#16840640C2211yescharacteristic
25#16840640C2212yes—
26#16840640C2211yescharacteristic
27#16840640C2212yes—
28#16840640C2211yescharacteristic
29#16840640C2211yescharacteristic
30#16840640C2212yes—
31#16840640C2212yes—
32#16840441—22no—
33#16840441—22no—
34#16840441—22no—
35#16840441—22no—
36C2×#14519772C411yescharacteristic, complemented
37C2×#14519771C411yescharacteristic, complemented
38C2×#14519763C411yescharacteristic, complemented
39C2×#14519760C411yescharacteristic, complemented
40C2×#14519759C2211yescharacteristic
41C2×#14519758C411yescharacteristic, complemented
42C2×#14519756C411yescharacteristic, complemented
43C2×#14519755C2211yescharacteristic
44C2×#14519745C2211yescharacteristic
45C2×C4×C22⋊D61C2211yescharacteristic
46C2×#14519734C2211yescharacteristic
47C2×#14519733C411yescharacteristic, complemented
48C22×#11758198C2211yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×C4×D4×C61C411yescharacteristic, complemented
51C23×#6923—22no—
52#14519856—24no—
53#14519856—42no—
54C2×C4⋊#6923—22no—
55C2×C4⋊#6923—22no—
56C2×C22⋊#6923—24no—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—22no—
59C2×C22⋊#6923—22no—
60C2×C22⋊#6923—42no—
61C2×C22⋊#6923C2312yes—
62C2×C22⋊#6923C2312yes—
63C2×C22⋊#6923C2312yes—
64C2×C22⋊#6923C2312yes—
65C2×C4×#6923—22no—
66C2×C4×#6923—22no—
67#14519835—24no—
68#14519835—42no—
69(C2×#6923)⋊C4—22no—
70(C2×#6923)⋊C4—22no—
71(C2×#6923)⋊C4—22no—
72(C2×#6923)⋊C4—22no—
73C24×D61C2311yescharacteristic
74C22×Dic122C2×C411yescharacteristic, complemented
75C22×C22⋊D61C2×C411yescharacteristic
76C22×C22⋊D61C2311yescharacteristic
77C23×Dic61C2×C411yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C22×C4×D61C2311yescharacteristic
80#14519772—22no—
81#14519772—22no—
82#14519771—22no—
83#14519771—22no—
84#14519763—22no—
85#14519763—22no—
86#14519760—22no—
87#14519760—22no—
88#14519759—22no—
89#14519759—22no—
90#14519758—22no—
91#14519758—22no—
92#14519756—22no—
93#14519756—22no—
94#14519755—22no—
95#14519755—22no—
96#14519745—22no—
97#14519745—22no—
98C4×C22⋊D61—22no—
99C4×C22⋊D61—22no—
100#14519734—22no—
101#14519734—22no—
102#14519733—21no—
103#14519733—21no—
104#14519733—21no—
105#14519733—21no—
106C2×C4⋊Dic61C2×C411yescharacteristic, complemented
107C2×#11758196C2×C411yescharacteristic, complemented
108C2×#11758196C2×C411yescharacteristic, complemented
109C2×#11758196C2×C411yescharacteristic, complemented
110C2×#11758196C2×C411yescharacteristic, complemented
111C2×#11758196C2×C411yescharacteristic, complemented
112C2×#11758196C2×C411yescharacteristic, complemented
113C2×C22⋊Dic61C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic, complemented
116C2×C22⋊Dic61C2×C411yescharacteristic, complemented
117C2×#11758198—22no—
118C2×#11758198—22no—
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2311yescharacteristic
125C2×#11758198C2311yescharacteristic
126C2×#11758198C2311yescharacteristic
127C22⋊C4×D61D412yes—
128C22⋊C4×D61D412yes—
129C22⋊C4×D61D412yes—
130C22⋊C4×D61D412yes—
131C2×C4×Dic61C2×C411yescharacteristic, complemented
132C2×C4×Dic61C2×C411yescharacteristic, complemented
133C22×D4×C61C2×C411yescharacteristic
134C23×C4×C61C2×C411yescharacteristic
135C23×C4×C61C2×C411yescharacteristic, complemented
136C4×D4×C61—21no—
137C4×D4×C61—21no—
138C4×D4×C61—21no—
139C4×D4×C61—21no—
140C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
143C2×C42×C61C2×C411yescharacteristic, complemented
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61—22no—
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—42no—
150C23×D61—81no—
151C23×D61C22×C411yescharacteristic
152C23×D61C2×D412yes—
153C23×D61C2×D412yes—
154C23×D61C2411yescharacteristic
155C22×#6923—22no—
156C22×#6923—22no—
157C22×#6923—22no—
158C22×#6923—22no—
159C22×#6923—44no—
160C22×#6923—44no—
161C22×#6923—82no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—42no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—81no—
170C22×C4×C61—81no—
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C22×C4×C61C22×C411yescharacteristic
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—22no—
181C2×C22⋊D61—81no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—42no—
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C2×C4×D61—22no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—81no—
195C2×C4×D61C2×D412yes—
196C2×C4×D61C2×D412yes—
197C2×C4×D61C2×D412yes—
198C2×C4×D61C2×D412yes—
199C2×Dic122—22no—
200C2×Dic122—81no—
201C22⋊#6923—22no—
202C22⋊#6923—22no—
203C22⋊#6923—22no—
204C22⋊#6923—22no—
205C22⋊#6923—22no—
206C22⋊#6923—22no—
207C22⋊#6923—22no—
208C22⋊#6923—44no—
209C22⋊#6923—44no—
210C22⋊#6923—82no—
211C22⋊#6923#4114yes—
212C4⋊#6923—44no—
213C4⋊#6923—82no—
214C4×#6923—44no—
215C4×#6923—82no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—21no—
220C22⋊C4×C61C22⋊C411yescharacteristic
221C22⋊C4×C61C22⋊C411yescharacteristic
222C22⋊C4×C61C22⋊C411yescharacteristic
223C22⋊C4×C61C22⋊C411yescharacteristic
224C42×C61—21no—
225C42×C61—21no—
226C22⋊Dic61—21no—
227C22⋊Dic61—21no—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61C22⋊C412yes—
231C22⋊Dic61C22⋊C412yes—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198C22⋊C412yes—
239#11758198C22⋊C412yes—
240#11758198C22⋊C412yes—
241#11758198C22⋊C412yes—
242C4⋊Dic61—22no—
243#11758196—21no—
244#11758196—21no—
245#11758196—21no—
246#11758196—21no—
247#11758196—22no—
248#11758196—22no—
249#11758196—22no—
250#11758196—22no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—22no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61C2×C22⋊C411yescharacteristic
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61C23×C411yescharacteristic
267C22×D61—24no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—41no—
275C22×D61—42no—
276C22×D61—41no—
277C22×D61—42no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—42no—
281C22×D61—84no—
282C22×D61—82no—
283C22×D61—82no—
284C22×D61C2×C22⋊C412yes—
285C22×D61C22×D412yes—
286C22×D61C2×#4112yes—
287C22×D61H(5,𝔽2)11yescharacteristic
288C22×D612−1+411yescharacteristic
289C2×#6923—24no—
290C2×#6923—42no—
291C2×#6923—42no—
292C2×#6923—42no—
293C2×#6923—42no—
294C2×#6923—42no—
295C2×#6923—42no—
296C2×#6923—42no—
297C2×#6923—42no—
298C2×#6923—42no—
299C2×#6923—42no—
300C2×#6923—42no—
301C2×#6923—88no—
302D4×C61—42no—
303D4×C61—42no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—81no—
314C2×C4×C61—81no—
315C2×C4×C61—81no—
316C2×C4×C61—81no—
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C22⋊D61—42no—
322C22⋊D61—42no—
323C22⋊D61—82no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—41no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61C2×C22⋊C412yes—
339C2×Dic61C2×C22⋊C412yes—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—42no—
345C4×D61—42no—
346Dic122—82no—
347#22477—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61#41012yes—
363C22×C61C22×C22⋊C411yescharacteristic
364C22×C61C4×#4111yescharacteristic
365C22×C61#52011yescharacteristic
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—42no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—44no—
375C2×D61—44no—
376C2×D61—82no—
377C2×D61—82no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61#54612yes—
381C2×D61#54712yes—
382#6923—44no—
383#6923—82no—
384#6923—82no—
385#6923—82no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393Dic61—22no—
394Dic61—22no—
395Dic61—41no—
396Dic61—41no—
397Dic61—41no—
398Dic61—41no—
399C2×#551—611no—
400#2342—612no—
401#1996—612no—
402#1899—612no—
403#1898—612no—
404#1820—611no—
405#1819—611no—
406#1799—611no—
407C4×#99—611no—
408#1740—611no—
409C2×#342—611no—
410C2×C61—22no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—41no—
414C2×C61—81no—
415C2×C61#233911yescharacteristic
416C2×C61C2×#41011yescharacteristic
417C2×C61#288311yescharacteristic
418D61—22no—
419D61—22no—
420D61—42no—
421#551—1222no—
422#551—1222no—
423#551—1222no—
424#551—1222no—
425C2×#126—611no—
426C2×#126—611no—
427C2×#124—611no—
428C2×#123—611no—
429C2×#123—611no—
430C2×#123—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—611no—
433C2×#120—611no—
434C2×C4×D4—611no—
435C2×C4×D4#692311yescharacteristic, complemented
436C2×#117—611no—
437C2×#117—611no—
438C2×#117—612no—
439C22×C22⋊C4—611no—
440C22×C22⋊C4—611no—
441C22×C22⋊C4—612no—
442C2×#99—612no—
443C2×#99—612no—
444#388—1222no—
445#388—1222no—
446#385—1222no—
447#381—612no—
448#380—612no—
449#379—612no—
450C4×C22⋊C4—612no—
451C4×C22⋊C4—1222no—
452#342—611no—
453#342—611no—
454#342—611no—
455#342—612no—
456#342—612no—
457#342—612no—
458#342—612no—
459#342—611no—
460C61#2247711yescharacteristic, complemented, Sylow
461C25—611no—
462C22×Q8—611no—
463C22×D4—611no—
464C22×D4—611no—
465C22×D4C2×#692311yescharacteristic
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—1222no—
470C23×C4C2×#692311yescharacteristic
471C23×C4C2×#692311yescharacteristic, complemented
472#126—1222no—
473#126—1222no—
474#126—1222no—
475#126—1222no—
476#124—1222no—
477#124—1222no—
478#123—1222no—
479#123—1222no—
480#123—1222no—
481#123—1222no—
482#123—1222no—
483#123—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#120—1222no—
489#120—1222no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—1222no—
495C4×D4—1222no—
496#117—1222no—
497#117—1222no—
498#117—1221no—
499#117—1221no—
500#117—1221no—
501#117—1221no—
502#117—1224no—
503#117—2442no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4C2×#692311yescharacteristic, complemented
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4—612no—
520C2×C22⋊C4—612no—
521C2×C22⋊C4—612no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—612no—
532C2×C22⋊C4—612no—
533C2×C22⋊C4—612no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1222no—
536C2×C22⋊C4—1222no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4—2442no—
541C2×C22⋊C4C2×#692311yescharacteristic
542C2×C22⋊C4C2×#692311yescharacteristic, complemented
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—1222no—
546C2×C42—1222no—
547C2×C42C2×#692311yescharacteristic, complemented
548#99—1224no—
549#99—2442no—
550#95—1222no—
551#95—1222no—
552#95—1222no—
553#95—1222no—
554C24—611no—
555C24—612no—
556C24—612no—
557C24—611no—
558C24—1222no—
559C24—1221no—
560C24—1221no—
561C24—4881no—
562C24—2442no—
563C24C22×#692311yescharacteristic
564C24C22×#692311yescharacteristic
565C2×Q8—1222no—
566C2×Q8—4881no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1221no—
573C2×D4—1222no—
574C2×D4—1221no—
575C2×D4—4881no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—1222no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—4881no—
602C22×C4—4882no—
603C22×C4—2444no—
604C22×C4—2444no—
605C22×C4—2442no—
606C22×C4C22×#692311yescharacteristic
607C22×C4C22×#692311yescharacteristic
608C22×C4C22×#692311yescharacteristic
609C22×C4C22×#692311yescharacteristic
610C22×C4C22×#692311yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—1222no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—4882no—
623C4⋊C4—2444no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—612no—
627C22⋊C4—612no—
628C22⋊C4—612no—
629C22⋊C4—612no—
630C22⋊C4—612no—
631C22⋊C4—612no—
632C22⋊C4—614no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1221no—
643C22⋊C4—1221no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—4882no—
651C22⋊C4—2444no—
652C22⋊C4—2444no—
653C22⋊C4C22⋊#692311yescharacteristic
654C22⋊C4C22⋊#692311yescharacteristic
655C22⋊C4C22⋊#692311yescharacteristic
656C22⋊C4C22⋊#692311yescharacteristic
657C42—21no—
658C42—21no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1221no—
663C42—4882no—
664C42—2444no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—612no—
675C23—612no—
676C23—611no—
677C23—611no—
678C23—612no—
679C23—1222no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1221no—
684C23—1221no—
685C23—1224no—
686C23—4882no—
687C23—4884no—
688C23—4882no—
689C23—2442no—
690C23—2441no—
691C23—2441no—
692C23—2442no—
693C23—2441no—
694C23—2442no—
695C23—2441no—
696C23C2×C22⋊#692311yescharacteristic
697C23C2×C22⋊#692311yescharacteristic
698C23C23×#692311yescharacteristic
699Q8—4882no—
700D4—42no—
701D4—42no—
702D4—4882no—
703D4—2442no—
704D4—2442no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—612no—
719C2×C4—612no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1224no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—4888no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2441no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4C2×C22⋊#692311yescharacteristic
754C2×C4C2×C22⋊#692311yescharacteristic
755C2×C4C2×C22⋊#692311yescharacteristic
756C2×C4C2×C22⋊#692311yescharacteristic
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—81no—
770C22—81no—
771C22—612no—
772C22—612no—
773C22—1222no—
774C22—1222no—
775C22—1222no—
776C22—1222no—
777C22—1222no—
778C22—4881no—
779C22—4881no—
780C22—4882no—
781C22—4882no—
782C22—2442no—
783C22—2441no—
784C22—2441no—
785C22—2444no—
786C22—2444no—
787C22#1684074112yes—
788C22C22×C22⋊#692311yescharacteristic
789C22#41×#692311yescharacteristic
790C22#1684083111yescharacteristic
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—1222no—
799C4—1222no—
800C4—4882no—
801C4—4882no—
802C4—4882no—
803C4—2444no—
804C4—2441no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C2—21no—
809C2—21no—
810C2—22no—
811C2—41no—
812C2—81no—
813C2—1222no—
814C2—1222no—
815C2—2442no—
816C2#2146232211yescharacteristic
817C2C2×#1684074111yescharacteristic
818C2#2146241811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519745C22
cosocleC23×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61#22477
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462325C2semidirect
2. #21462010C2semidirect
3. #21461842C2semidirect
5. #21461716C2semidirect
6. #21461714C2semidirect
7. #21461679C2semidirect
8. C4×#14519835C2semidirect
9. #21461518C2semidirect
10. C2×#16840640C2semidirect
36. C2×#14519772C4semidirect
37. C2×#14519771C4semidirect
38. C2×#14519763C4semidirect
39. C2×#14519760C4semidirect
41. C2×#14519758C4semidirect
42. C2×#14519756C4semidirect
47. C2×#14519733C4semidirect
50. C2×C4×D4×C61C4semidirect
74. C22×Dic122C2×C4semidirect
106. C2×C4⋊Dic61C2×C4semidirect
107. C2×#11758196C2×C4semidirect
108. C2×#11758196C2×C4semidirect
109. C2×#11758196C2×C4semidirect
110. C2×#11758196C2×C4semidirect
111. C2×#11758196C2×C4semidirect
112. C2×#11758196C2×C4semidirect
115. C2×C22⋊Dic61C2×C4semidirect
116. C2×C22⋊Dic61C2×C4semidirect
131. C2×C4×Dic61C2×C4semidirect
132. C2×C4×Dic61C2×C4semidirect
135. C23×C4×C61C2×C4semidirect
140. C2×C4⋊C4×C61C2×C4semidirect
142. C2×C22⋊C4×C61C2×C4semidirect
143. C2×C42×C61C2×C4semidirect
435. C2×C4×D4#6923semidirect
460. C61#22477semidirect
471. C23×C4C2×#6923semidirect
513. C2×C4⋊C4C2×#6923semidirect
542. C2×C22⋊C4C2×#6923semidirect
547. C2×C42C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623252
#214620102
#214618422
#214618402
#214617162
#214617142
#214616792
C4×#145198352
#214615182
C2×#168406402
C2×#168404412
#2247761