Finite Group Databasebeta

← #30620354

Subgroups — #30620354

Order 15616.

1226 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D61⋊C8C211yesmaximal, characteristic, complemented
2#21462335C211yesmaximal, characteristic, complemented
3#21462001C211yesmaximal, characteristic, complemented
4#21461999C211yesmaximal, characteristic, complemented
5#21461833C211yesmaximal, characteristic, complemented
6#21461833C211yesmaximal, characteristic, complemented
7#21461807C211yesmaximal, characteristic, complemented
8#21461806C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461723C211yesmaximal, characteristic, complemented
11#21461689C211yesmaximal, characteristic, complemented
12C4×#14519839C211yesmaximal, characteristic, complemented
13#21461504C211yesmaximal, characteristic, complemented
14C2×#16840635C211yesmaximal, characteristic, complemented
15#553×D61C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840790—21no—
21#16840789—21no—
22#16840789—21no—
23D4×#92420—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29D61⋊(C22⋊C8)C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31C4×D61⋊C8C2211yescharacteristic
32#16840712—21no—
33#16840711—21no—
34#16840710—21no—
35#16840706C2211yescharacteristic
36#16840704C2211yescharacteristic
37#16840704C2211yescharacteristic
38C4×C4⋊#6923C2211yescharacteristic
39C22⋊C4×#6923—21no—
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840465C411yescharacteristic, complemented
53#16840464C411yescharacteristic, complemented
54#16840463—21no—
55#16840462C411yescharacteristic, complemented
56#16840461—21no—
57#16840460C411yescharacteristic, complemented
58#16840459C411yescharacteristic, complemented
59#16840458C411yescharacteristic, complemented
60#16840457—21no—
61#16840456C411yescharacteristic, complemented
62#16840455—21no—
63#126×D61—21no—
64#125×D61C2211yescharacteristic
65#123×D61—21no—
66#121×D61—21no—
67#121×D61C2211yescharacteristic
68#121×D61C2211yescharacteristic
69C4×D4×D61—21no—
70C4×D4×D61C2211yescharacteristic
71C4×D4×D61C2211yescharacteristic
72#117×D61C2211yescharacteristic
73C2×C4⋊C4×D61C2211yescharacteristic
74C61×#553C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×D61⋊C8—22no—
77C2×D61⋊C8—22no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—21no—
80C2×D61⋊C8—41no—
81C2×D61⋊C8—41no—
82C2×D61⋊C8C2311yescharacteristic
83C2×D61⋊C8C2311yescharacteristic
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C22×#92420—21no—
87C22×#92420—21no—
88#14519856—22no—
89#14519856—41no—
90C2×C4⋊#6923—22no—
91C2×C4⋊#6923—21no—
92C2×C4⋊#6923—41no—
93C2×C4⋊#6923C2311yescharacteristic
94C2×C4⋊#6923C2311yescharacteristic
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2311yescharacteristic
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102#14519844—21no—
103C4⋊#92420—21no—
104#14519839—22no—
105#14519839—22no—
106#14519839—41no—
107#14519839—41no—
108#14519834—21no—
109#14519834—21no—
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112C4×#92420—21no—
113C4×#92420—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119C2×D4×D61—21no—
120C2×D4×D61—21no—
121C2×D4×D61D411yescharacteristic
122C2×D4×D61C2311yescharacteristic
123C22×C4×D61—21no—
124C22×C4×D61—21no—
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127#14519772—21no—
128#14519772—21no—
129#14519772—21no—
130#14519771—21no—
131#14519770—21no—
132#14519770—21no—
133#14519770—21no—
134#14519769C2×C411yescharacteristic, complemented
135#14519768C2×C411yescharacteristic, complemented
136#14519768C2×C411yescharacteristic, complemented
137#14519767—21no—
138#14519767—21no—
139#14519762—21no—
140#14519762—21no—
141#14519761—21no—
142#14519760—21no—
143#14519759—21no—
144#14519759—21no—
145#14519758—21no—
146#14519752—21no—
147#14519752C2×C411yescharacteristic
148#14519752C2×C411yescharacteristic, complemented
149#14519751—21no—
150#14519751C2×C411yescharacteristic
151#14519751C2×C411yescharacteristic, complemented
152#14519750—21no—
153#14519750—21no—
154#14519750—21no—
155#14519750—21no—
156#14519749—21no—
157#14519749—21no—
158#14519749—21no—
159#14519749—21no—
160#14519748—21no—
161#14519748C2×C411yescharacteristic
162#14519748C2×C411yescharacteristic, complemented
163C4×D244—21no—
164C4×D244C2×C411yescharacteristic
165C4×D244C2×C411yescharacteristic, complemented
166D4×Dic61—21no—
167D4×Dic61C2×C411yescharacteristic, complemented
168D4×Dic61D411yescharacteristic
169#14519739—21no—
170#14519739C2×C411yescharacteristic, complemented
171#14519739D411yescharacteristic
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737—21no—
178#14519737—21no—
179#14519737—21no—
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519736C2×C411yescharacteristic, complemented
183#14519735C2×C411yescharacteristic, complemented
184#14519735C2×C411yescharacteristic, complemented
185#14519734—21no—
186#14519733—21no—
187C2×C4⋊Dic61C2×C411yescharacteristic
188C2×#11758196—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61C2×C411yescharacteristic
194C4⋊C4×D61C2×C411yescharacteristic
195C4⋊C4×D61D411yescharacteristic
196C4⋊C4×D61C2311yescharacteristic
197C4⋊C4×D61C2311yescharacteristic
198C4⋊C4×D61C2311yescharacteristic
199C22⋊C4×D61—21no—
200C22⋊C4×D61—21no—
201C22⋊C4×D61—21no—
202C22⋊C4×D61—21no—
203C22⋊C4×D61D411yescharacteristic
204C22⋊C4×D61D411yescharacteristic
205C42×D61—21no—
206C42×D61C2311yescharacteristic
207#126×C61—21no—
208#125×C61C2×C411yescharacteristic, complemented
209#123×C61—21no—
210#121×C61—21no—
211#121×C61C2×C411yescharacteristic
212#121×C61C2×C411yescharacteristic, complemented
213C4×D4×C61—21no—
214C4×D4×C61C2×C411yescharacteristic
215C4×D4×C61C2×C411yescharacteristic, complemented
216#117×C61C2×C411yescharacteristic, complemented
217C2×C4⋊C4×C61C2×C411yescharacteristic
218C23×D61—21no—
219C23×D61C2×D411yescharacteristic
220C23×D61C2×D411yescharacteristic
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—42no—
226C22×#6923—42no—
227C22×#6923—81no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61C22⋊C411yescharacteristic
231C2×D4×C61C22×C411yescharacteristic
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61C22×C411yescharacteristic
235C22×C4×C61C22×C411yescharacteristic
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247D4×D61—22no—
248D4×D61—22no—
249D4×D61—21no—
250D4×D61—21no—
251D4×D61—21no—
252D4×D61—21no—
253D4×D61—42no—
254D4×D61—42no—
255D4×D61—81no—
256D4×D61—81no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244C22⋊C411yescharacteristic
260C2×D244C22×C411yescharacteristic
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—81no—
277C2×C4×D61—81no—
278C2×C4×D61—81no—
279C2×C4×D61—81no—
280C2×C4×D61C22×C411yescharacteristic
281C2×C4×D61C22×C411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×C4×D61C2×D411yescharacteristic
285C2×C4×D61C2×D411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2411yescharacteristic
289C22⋊#6923—42no—
290C22⋊#6923—42no—
291C22⋊#6923—81no—
292C2×#92420—21no—
293C2×#92420—21no—
294C2×#92420—21no—
295C2×#92420—21no—
296C2×#92420—42no—
297C2×#92420—42no—
298C4⋊#6923—21no—
299C4⋊#6923—21no—
300C4⋊#6923—21no—
301C4⋊#6923—21no—
302C4⋊#6923—21no—
303C4⋊#6923—21no—
304C4⋊#6923—21no—
305C4⋊#6923—42no—
306C4⋊#6923#4112yes—
307C4×#6923—42no—
308C4×#6923—81no—
309D61⋊C8—21no—
310D61⋊C8—21no—
311D61⋊C8—21no—
312D61⋊C8—21no—
313D61⋊C8—21no—
314D61⋊C8—21no—
315D61⋊C8—21no—
316D61⋊C8—42no—
317D61⋊C8—42no—
318D61⋊C8#4112yes—
319C4⋊C4×C61—21no—
320C4⋊C4×C61—21no—
321C4⋊C4×C61—21no—
322C4⋊C4×C61C22⋊C411yescharacteristic
323C4⋊C4×C61C22×C411yescharacteristic
324C4⋊C4×C61C22×C411yescharacteristic
325C4⋊C4×C61C22×C411yescharacteristic
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—21no—
330C22⋊C4×C61C22⋊C411yescharacteristic
331C22⋊C4×C61C22⋊C411yescharacteristic
332C42×C61—21no—
333C42×C61C22×C411yescharacteristic
334C22⋊Dic61—21no—
335C22⋊Dic61—21no—
336C22⋊Dic61—21no—
337C22⋊Dic61—21no—
338C22⋊Dic61C22⋊C411yescharacteristic
339C22⋊Dic61C22⋊C411yescharacteristic
340#11758198—21no—
341#11758198—21no—
342#11758198—21no—
343#11758198—21no—
344#11758198—21no—
345#11758198—21no—
346#11758198—21no—
347#11758198—21no—
348#11758198C22⋊C411yescharacteristic
349#11758198C22⋊C411yescharacteristic
350#11758198C22⋊C411yescharacteristic
351#11758198C22⋊C411yescharacteristic
352C4⋊Dic61—21no—
353C4⋊Dic61—21no—
354C4⋊Dic61—21no—
355C4⋊Dic61C22⋊C411yescharacteristic
356C4⋊Dic61C22×C411yescharacteristic
357C4⋊Dic61C22×C411yescharacteristic
358C4⋊Dic61C22×C411yescharacteristic
359#11758196—21no—
360#11758196—21no—
361#11758196—21no—
362#11758196—21no—
363#11758196—21no—
364#11758196—21no—
365#11758196—21no—
366#11758196—21no—
367#11758196—21no—
368#11758196C22⋊C411yescharacteristic
369#11758196C22⋊C411yescharacteristic
370C4×Dic61—21no—
371C4×Dic61—21no—
372C4×Dic61—21no—
373C4×Dic61C22×C411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C4×Dic61C2×D411yescharacteristic
376C23×C61—21no—
377C23×C61C2×C22⋊C411yescharacteristic
378C23×C61C2×C22⋊C411yescharacteristic
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61—21no—
385C22×D61—21no—
386C22×D61—21no—
387C22×D61—21no—
388C22×D61—21no—
389C22×D61—21no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61C2×C22⋊C411yescharacteristic
397C22×D61C2×C22⋊C411yescharacteristic
398C22×D61#13512yes—
399C22×D61#13512yes—
400C22×D61C22×D411yescharacteristic
401C2×#6923—22no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—41no—
405C2×#6923—41no—
406C2×#6923—41no—
407C2×#6923—41no—
408C2×#6923—41no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—84no—
414D4×C61—22no—
415D4×C61—21no—
416D4×C61—21no—
417D4×C61—42no—
418D4×C61—81no—
419C2×C4×C61—21no—
420C2×C4×C61—21no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—81no—
427C2×C4×C61—81no—
428C2×C4×C61C2×C22⋊C411yescharacteristic
429C2×C4×C61C2×C22⋊C411yescharacteristic
430C2×C4×C61C2×C22⋊C411yescharacteristic
431C2×C4×C61C2×C22⋊C411yescharacteristic
432C2×C4×C61C23×C411yescharacteristic
433C22⋊D61—22no—
434C22⋊D61—22no—
435C22⋊D61—42no—
436C22⋊D61—42no—
437C22⋊D61—41no—
438C22⋊D61—41no—
439C22⋊D61—81no—
440C22⋊D61—81no—
441C2×Dic61—21no—
442C2×Dic61—21no—
443C2×Dic61—21no—
444C2×Dic61—21no—
445C2×Dic61—21no—
446C2×Dic61—21no—
447C2×Dic61—21no—
448C2×Dic61—81no—
449C2×Dic61—81no—
450C2×Dic61C2×C22⋊C411yescharacteristic
451C2×Dic61C2×C22⋊C411yescharacteristic
452C2×Dic61C2×C22⋊C411yescharacteristic
453C2×Dic61C2×C22⋊C411yescharacteristic
454C2×Dic61C22×D411yescharacteristic
455D244—22no—
456D244—21no—
457D244—21no—
458D244—42no—
459D244—81no—
460C4×D61—21no—
461C4×D61—21no—
462C4×D61—21no—
463C4×D61—21no—
464C4×D61—21no—
465C4×D61—21no—
466C4×D61—21no—
467C4×D61—21no—
468C4×D61—21no—
469C4×D61—21no—
470C4×D61—21no—
471C4×D61—21no—
472C4×D61—21no—
473C4×D61—21no—
474C4×D61—21no—
475C4×D61—21no—
476C4×D61—41no—
477C4×D61—41no—
478C4×D61—41no—
479C4×D61—41no—
480C4×D61—41no—
481C4×D61—41no—
482C4×D61—81no—
483C4×D61—81no—
484C4×D61—81no—
485C4×D61—81no—
486C4×D61C2×#4111yescharacteristic
487C4×D61C2×#4111yescharacteristic
488C4×D61H(5,𝔽2)11yescharacteristic
489C4×D612−1+411yescharacteristic
490#92420—22no—
491#92420—41no—
492#92420—41no—
493#92420—41no—
494#22488—611nomaximal, Sylow
495C22×C61—21no—
496C22×C61—21no—
497C22×C61—21no—
498C22×C61—21no—
499C22×C61—21no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61#41612yes—
504C22×C61C22×C22⋊C411yescharacteristic
505C2×D61—21no—
506C2×D61—21no—
507C2×D61—22no—
508C2×D61—22no—
509C2×D61—22no—
510C2×D61—22no—
511C2×D61—21no—
512C2×D61—21no—
513C2×D61—21no—
514C2×D61—41no—
515C2×D61—41no—
516C2×D61—41no—
517C2×D61—41no—
518C2×D61—41no—
519C2×D61—41no—
520C2×D61—41no—
521C2×D61—81no—
522C2×D61—81no—
523C2×D61—81no—
524C2×D61—81no—
525C2×D61#41612yes—
526C2×D61#54611yescharacteristic
527C2×D61#54711yescharacteristic
528C2×D61C2×#13511yescharacteristic
529C2×D61C2×#13511yescharacteristic
530C2×D61#57611yescharacteristic
531C2×D61#57711yescharacteristic
532#6923—42no—
533#6923—81no—
534#6923—81no—
535#6923—81no—
536C4×C61—21no—
537C4×C61—21no—
538C4×C61—21no—
539C4×C61—21no—
540C4×C61—41no—
541C4×C61—41no—
542C4×C61—41no—
543C4×C61C4×#4111yescharacteristic
544C4×C61#52011yescharacteristic
545Dic61—21no—
546Dic61—21no—
547Dic61—21no—
548Dic61—21no—
549Dic61—41no—
550Dic61—41no—
551Dic61—41no—
552Dic61#54611yescharacteristic
553Dic61#54711yescharacteristic
554C2×#553—611no—
555C2×C8×D4—611no—
556#2352—611no—
557#1991—611no—
558#1989—611no—
559#1893—611no—
560#1893—611no—
561#1875—611no—
562#1874—611no—
563#1825—611no—
564#1824—611no—
565#1804—611no—
566C4×#102—611no—
567#1735—611no—
568C2×#340—611no—
569C2×C61—22no—
570C2×C61—41no—
571C2×C61—81no—
572C2×C61#233911yescharacteristic
573C2×C61C2×#41611yescharacteristic
574C2×C61#289711yescharacteristic
575D61—22no—
576D61—41no—
577D61—81no—
578D61#329711yescharacteristic
579D61#330111yescharacteristic
580D61#333711yescharacteristic
581D61#333911yescharacteristic
582C23×C8—611no—
583C23×C8—611no—
584#553—611no—
585#553—611no—
586#553—611no—
587#553—611no—
588#553—611no—
589#553—611no—
590#553—611no—
591#553—1221no—
592#553—1221no—
593#553—1221no—
594#553—1221no—
595#553#692311yescharacteristic, complemented
596C2×#126—1221no—
597C2×#125—611no—
598C2×#123—1221no—
599C2×#121—611no—
600C2×#121—611no—
601C2×#121—1221no—
602C2×C4×D4—611no—
603C2×C4×D4—611no—
604C2×C4×D4—1221no—
605C2×#117—611no—
606C2×#117—611no—
607C22×C4⋊C4—611no—
608C22×C4⋊C4—611no—
609C8×D4—1221no—
610C8×D4—1221no—
611C8×D4—1221no—
612C8×D4—1221no—
613C2×C4⋊C8—611no—
614C2×#102—611no—
615C2×#102—611no—
616C2×#102—611no—
617C2×#102—611no—
618C2×C22⋊C8—611no—
619C2×C22⋊C8—611no—
620C2×C4×C8—611no—
621#388—1221no—
622#387—1221no—
623#386—1221no—
624#382—611no—
625#380—611no—
626#380—611no—
627C4×C4⋊C4—611no—
628C4×C22⋊C4—1221no—
629#340—611no—
630#340—611no—
631#340—611no—
632#340—611no—
633#340—611no—
634#340—611no—
635#340—611no—
636#340—611no—
637#340—611no—
638#340—611no—
639#340—611no—
640#340—611no—
641C61#2248811yescharacteristic, complemented, Sylow
642C22×D4—611no—
643C22×D4—611no—
644C22×D4—1221no—
645C22×D4—1221no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—1221no—
649C23×C4—1221no—
650C23×C4—1221no—
651C22×C8—611no—
652C22×C8—611no—
653C22×C8—611no—
654C22×C8—611no—
655C22×C8—1222no—
656C22×C8—1222no—
657C22×C8—1221no—
658C22×C8—1221no—
659C22×C8—1221no—
660C22×C8—1221no—
661C22×C8—2441no—
662C22×C8—2441no—
663#126—21no—
664#126—1221no—
665#126—1221no—
666#126—1221no—
667#126—1221no—
668#126—1221no—
669#126—1221no—
670#126—1221no—
671#125—611no—
672#125—611no—
673#125—611no—
674#125—1221no—
675#125—1221no—
676#125C2×#692311yescharacteristic, complemented
677#123—21no—
678#123—1221no—
679#123—1221no—
680#123—1221no—
681#123—1221no—
682#123—1221no—
683#123—1221no—
684#123—1221no—
685#121—21no—
686#121—611no—
687#121—611no—
688#121—611no—
689#121—611no—
690#121—611no—
691#121—611no—
692#121—1221no—
693#121—1221no—
694#121—1221no—
695#121—1221no—
696#121—1221no—
697#121—1221no—
698#121—1221no—
699#121—1221no—
700#121—1221no—
701#121—1221no—
702#121—1221no—
703#121C2×#692311yescharacteristic
704#121C2×#692311yescharacteristic, complemented
705C4×D4—21no—
706C4×D4—611no—
707C4×D4—611no—
708C4×D4—611no—
709C4×D4—611no—
710C4×D4—611no—
711C4×D4—611no—
712C4×D4—611no—
713C4×D4—611no—
714C4×D4—611no—
715C4×D4—611no—
716C4×D4—1221no—
717C4×D4—1221no—
718C4×D4—1221no—
719C4×D4—1221no—
720C4×D4—1221no—
721C4×D4—1221no—
722C4×D4—1221no—
723C4×D4—1221no—
724C4×D4—1221no—
725C4×D4C2×#692311yescharacteristic
726C4×D4C2×#692311yescharacteristic, complemented
727#117—611no—
728#117—611no—
729#117—611no—
730#117—1221no—
731#117—1221no—
732#117—1222no—
733#117—2441no—
734#117C2×#692311yescharacteristic, complemented
735C2×C4⋊C4—611no—
736C2×C4⋊C4—611no—
737C2×C4⋊C4—611no—
738C2×C4⋊C4—611no—
739C2×C4⋊C4—611no—
740C2×C4⋊C4—611no—
741C2×C4⋊C4—611no—
742C2×C4⋊C4—611no—
743C2×C4⋊C4—611no—
744C2×C4⋊C4—611no—
745C2×C4⋊C4—611no—
746C2×C4⋊C4—1221no—
747C2×C4⋊C4—1221no—
748C2×C4⋊C4—1221no—
749C2×C4⋊C4—1221no—
750C2×C4⋊C4—1222no—
751C2×C4⋊C4—1221no—
752C2×C4⋊C4—1221no—
753C2×C4⋊C4—2441no—
754C2×C4⋊C4C2×#692311yescharacteristic
755C2×C22⋊C4—611no—
756C2×C22⋊C4—611no—
757C2×C22⋊C4—1221no—
758C2×C22⋊C4—1221no—
759C2×C22⋊C4—1221no—
760C2×C22⋊C4—1221no—
761C2×C22⋊C4—1221no—
762C2×C22⋊C4—1221no—
763C2×C22⋊C4—1221no—
764C2×C42—611no—
765C2×C42—1221no—
766C2×C42—1221no—
767C2×C42—1221no—
768C4⋊C8—1221no—
769C4⋊C8—1221no—
770#102—1222no—
771#102—1222no—
772#102—2441no—
773#102—2441no—
774C22⋊C8—1221no—
775C22⋊C8—1221no—
776C22⋊C8—1221no—
777C22⋊C8—1221no—
778C4×C8—1221no—
779C4×C8—1221no—
780#95—1221no—
781#95—1221no—
782#95—1221no—
783#95—1221no—
784#95—1221no—
785C24—611no—
786C24—611no—
787C24—1221no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—611no—
791C2×D4—611no—
792C2×D4—611no—
793C2×D4—611no—
794C2×D4—1221no—
795C2×D4—1221no—
796C2×D4—1221no—
797C2×D4—1221no—
798C2×D4—1221no—
799C2×D4—1221no—
800C2×D4—1221no—
801C2×D4—1222no—
802C2×D4—1222no—
803C2×D4—1221no—
804C2×D4—1221no—
805C2×D4—1221no—
806C2×D4—1221no—
807C2×D4—4881no—
808C2×D4—4881no—
809C2×D4—2442no—
810C2×D4—2442no—
811C2×D4C22⋊#692311yescharacteristic
812C2×D4C22×#692311yescharacteristic
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—611no—
818C22×C4—611no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—611no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—4881no—
848C22×C4—4881no—
849C22×C4—4881no—
850C22×C4—4881no—
851C22×C4—4881no—
852C22×C4—2442no—
853C22×C4—2442no—
854C22×C4C22×#692311yescharacteristic
855C22×C4C22×#692311yescharacteristic
856C2×C8—612no—
857C2×C8—1221no—
858C2×C8—1221no—
859C2×C8—1221no—
860C2×C8—1221no—
861C2×C8—1221no—
862C2×C8—1221no—
863C2×C8—1221no—
864C2×C8—1221no—
865C2×C8—1221no—
866C2×C8—1221no—
867C2×C8—1221no—
868C2×C8—2442no—
869C2×C8—2442no—
870C2×C8—2442no—
871C2×C8—2442no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—611no—
876C4⋊C4—611no—
877C4⋊C4—611no—
878C4⋊C4—612no—
879C4⋊C4—611no—
880C4⋊C4—611no—
881C4⋊C4—611no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C4⋊C4—1221no—
885C4⋊C4—1221no—
886C4⋊C4—1221no—
887C4⋊C4—1221no—
888C4⋊C4—1221no—
889C4⋊C4—1221no—
890C4⋊C4—1221no—
891C4⋊C4—1221no—
892C4⋊C4—1221no—
893C4⋊C4—1221no—
894C4⋊C4—1221no—
895C4⋊C4—1221no—
896C4⋊C4—1221no—
897C4⋊C4—1221no—
898C4⋊C4—1221no—
899C4⋊C4—1221no—
900C4⋊C4—1221no—
901C4⋊C4—2442no—
902C4⋊C4C22⋊#692311yescharacteristic
903C4⋊C4C22×#692311yescharacteristic
904C4⋊C4C22×#692311yescharacteristic
905C4⋊C4C22×#692311yescharacteristic
906C22⋊C4—21no—
907C22⋊C4—21no—
908C22⋊C4—21no—
909C22⋊C4—21no—
910C22⋊C4—611no—
911C22⋊C4—611no—
912C22⋊C4—611no—
913C22⋊C4—611no—
914C22⋊C4—611no—
915C22⋊C4—611no—
916C22⋊C4—1221no—
917C22⋊C4—1221no—
918C22⋊C4—1221no—
919C22⋊C4—1221no—
920C22⋊C4—1221no—
921C22⋊C4—1221no—
922C22⋊C4—1221no—
923C22⋊C4—1221no—
924C22⋊C4—1221no—
925C22⋊C4—1221no—
926C22⋊C4—1221no—
927C22⋊C4—1221no—
928C22⋊C4—4881no—
929C22⋊C4—2442no—
930C22⋊C4—2442no—
931C22⋊C4C22⋊#692311yescharacteristic
932C22⋊C4C22⋊#692311yescharacteristic
933C42—21no—
934C42—611no—
935C42—611no—
936C42—611no—
937C42—1221no—
938C42—1221no—
939C42—1221no—
940C42—4881no—
941C42—2442no—
942C42C22×#692311yescharacteristic
943C23—21no—
944C23—611no—
945C23—612no—
946C23—612no—
947C23—611no—
948C23—611no—
949C23—1221no—
950C23—1221no—
951C23—1221no—
952C23—1221no—
953C23—1221no—
954C23—1221no—
955C23—1221no—
956C23—1221no—
957C23—1221no—
958C23—1221no—
959C23—1221no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23C2×C22⋊#692311yescharacteristic
967C23C2×C22⋊#692311yescharacteristic
968D4—22no—
969D4—21no—
970D4—21no—
971D4—42no—
972D4—81no—
973D4—1222no—
974D4—1222no—
975D4—1222no—
976D4—1221no—
977D4—1221no—
978D4—4881no—
979D4—4881no—
980D4—4881no—
981D4—2442no—
982D4—2441no—
983D4—2441no—
984D4—2442no—
985D4—2442no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—81no—
994C2×C4—81no—
995C2×C4—611no—
996C2×C4—611no—
997C2×C4—611no—
998C2×C4—611no—
999C2×C4—611no—
1000C2×C4—611no—
1001C2×C4—611no—
1002C2×C4—611no—
1003C2×C4—611no—
1004C2×C4—1221no—
1005C2×C4—1221no—
1006C2×C4—1221no—
1007C2×C4—1221no—
1008C2×C4—1221no—
1009C2×C4—1221no—
1010C2×C4—1221no—
1011C2×C4—1221no—
1012C2×C4—1221no—
1013C2×C4—1221no—
1014C2×C4—1221no—
1015C2×C4—1221no—
1016C2×C4—1221no—
1017C2×C4—1221no—
1018C2×C4—1221no—
1019C2×C4—1221no—
1020C2×C4—1221no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—1221no—
1024C2×C4—1222no—
1025C2×C4—1221no—
1026C2×C4—1221no—
1027C2×C4—1221no—
1028C2×C4—4881no—
1029C2×C4—4881no—
1030C2×C4—4881no—
1031C2×C4—4881no—
1032C2×C4—4881no—
1033C2×C4—4884no—
1034C2×C4—4881no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4C2×C22⋊#692311yescharacteristic
1053C2×C4C2×C22⋊#692311yescharacteristic
1054C2×C4C2×C22⋊#692311yescharacteristic
1055C2×C4C2×C22⋊#692311yescharacteristic
1056C2×C4C23×#692311yescharacteristic
1057C8—1222no—
1058C8—2441no—
1059C8—2441no—
1060C8—2441no—
1061C22—21no—
1062C22—21no—
1063C22—21no—
1064C22—21no—
1065C22—21no—
1066C22—41no—
1067C22—41no—
1068C22—41no—
1069C22—611no—
1070C22—611no—
1071C22—611no—
1072C22—611no—
1073C22—611no—
1074C22—611no—
1075C22—612no—
1076C22—1222no—
1077C22—1222no—
1078C22—1222no—
1079C22—1222no—
1080C22—1221no—
1081C22—1221no—
1082C22—1221no—
1083C22—1221no—
1084C22—1221no—
1085C22—4881no—
1086C22—4881no—
1087C22—4881no—
1088C22—4881no—
1089C22—2441no—
1090C22—2441no—
1091C22—2441no—
1092C22—2441no—
1093C22—2441no—
1094C22—2441no—
1095C22—2441no—
1096C22#1684075212yes—
1097C22C22×C22⋊#692311yescharacteristic
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—21no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—611no—
1106C4—611no—
1107C4—1221no—
1108C4—1221no—
1109C4—1221no—
1110C4—1221no—
1111C4—4881no—
1112C4—4881no—
1113C4—4881no—
1114C4—2442no—
1115C4—2441no—
1116C4—2441no—
1117C4—2441no—
1118C4#41×#692311yescharacteristic
1119C4#1684083111yescharacteristic
1120C2—22no—
1121C2—41no—
1122C2—81no—
1123C2—611no—
1124C2—611no—
1125C2—611no—
1126C2—611no—
1127C2—1222no—
1128C2—4881no—
1129C2—2441no—
1130C2#2146232211yescharacteristic
1131C2C2×#1684075211yescharacteristic
1132C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#553×D61C2
cosocleC2×C4×D61C24
hypercenter#553#6923
hypocenterC61#22488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×D61⋊C8C2semidirect
2. #21462335C2semidirect
3. #21462001C2semidirect
4. #21461999C2semidirect
5. #21461833C2semidirect
6. #21461833C2semidirect
7. #21461807C2semidirect
8. #21461806C2semidirect
9. #21461724C2semidirect
10. #21461723C2semidirect
11. #21461689C2semidirect
12. C4×#14519839C2semidirect
13. #21461504C2semidirect
14. C2×#16840635C2semidirect
52. #16840465C4semidirect
53. #16840464C4semidirect
55. #16840462C4semidirect
57. #16840460C4semidirect
58. #16840459C4semidirect
59. #16840458C4semidirect
61. #16840456C4semidirect
74. C61×#553C4semidirect
134. #14519769C2×C4semidirect
135. #14519768C2×C4semidirect
136. #14519768C2×C4semidirect
148. #14519752C2×C4semidirect
151. #14519751C2×C4semidirect
162. #14519748C2×C4semidirect
165. C4×D244C2×C4semidirect
167. D4×Dic61C2×C4semidirect
170. #14519739C2×C4semidirect
182. #14519736C2×C4semidirect
183. #14519735C2×C4semidirect
184. #14519735C2×C4semidirect
208. #125×C61C2×C4semidirect
212. #121×C61C2×C4semidirect
215. C4×D4×C61C2×C4semidirect
216. #117×C61C2×C4semidirect
595. #553#6923semidirect
641. C61#22488semidirect
676. #125C2×#6923semidirect
704. #121C2×#6923semidirect
726. C4×D4C2×#6923semidirect
734. #117C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D4×D61⋊C82
#214623352
#214620012
#214619992
#214618332
#214618072
#214618062
#214617242
#214617232
#214616892
C4×#145198392
#214615042
C2×#168406352
#553×D612
#2248861