Finite Group Databasebeta

← #29696194

Subgroups — #29696194

Order 15616.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic
2D4×#11758194C211yesmaximal, characteristic, complemented
3#21446812C211yesmaximal, characteristic, complemented
4#21446811C211yesmaximal, characteristic, complemented
5#21446282C211yesmaximal, characteristic, complemented
6#21446282C211yesmaximal, characteristic, complemented
7#21446280C211yesmaximal, characteristic, complemented
8#21446280C211yesmaximal, characteristic, complemented
9#21445900C211yesmaximal, characteristic, complemented
10#21445897C211yesmaximal, characteristic, complemented
11#21445808C211yesmaximal, characteristic, complemented
12C4×#14519693C211yesmaximal, characteristic, complemented
13#21445557C211yesmaximal, characteristic, complemented
14C2×#16839530C211yesmaximal, characteristic, complemented
15D4×M16×C61C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18#16840458—21no—
19#16840458—21no—
20#16840458—21no—
21#16840458—21no—
22#16840458—21no—
23#16840458—21no—
24#16840458—21no—
25#16840458—21no—
26C2×#14519772C412yes—
27C2×#14519769C2211yescharacteristic
28C2×#14519759C412yes—
29C2×#14519751C2211yescharacteristic
30C2×#14519751C2211yescharacteristic
31C2×#14519749C412yes—
32C2×C4×D244C2211yescharacteristic
33C2×#14519737C412yes—
34C2×#14519736C2211yescharacteristic
35C22×C4⋊Dic61C2211yescharacteristic
36#16839840—21no—
37#16839834—21no—
38#16839834—21no—
39D4×#92418—21no—
40#16839786C2211yescharacteristic
41C2×#14519693C2211yescharacteristic
42C2×#14519693C2211yescharacteristic
43C2×#14519693C2211yescharacteristic
44C2×#14519693C2211yescharacteristic
45#16839726C2211yescharacteristic
46#16839726C2211yescharacteristic
47C4×#11758194C2211yescharacteristic
48#16839530C2211yescharacteristic
49#16839530C2211yescharacteristic
50#16839530C2211yescharacteristic
51#16839530C2211yescharacteristic
52#16839530C2211yescharacteristic
53#16839530C2211yescharacteristic
54#16839530C2211yescharacteristic
55#16839530C2211yescharacteristic
56#16839530C2211yescharacteristic
57#16839530C2211yescharacteristic
58#16839530C2211yescharacteristic
59#16839530C2211yescharacteristic
60C22×M16×C61C2211yescharacteristic
61C22×M16×C61C2211yescharacteristic
62C2×C4×D4×C61C2211yescharacteristic
63C61×#436—21no—
64C61×#435—21no—
65C61×#435—21no—
66C8×D4×C61—21no—
67C61×#423C2211yescharacteristic
68C61×#407C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C4×M16×C61C2211yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C22⋊D61C2×C412yes—
73C22×C22⋊D61C2×C412yes—
74C23×Dic61C2×C412yes—
75C22×C4×D61C2×C412yes—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—22no—
79C2×#11758194—22no—
80C2×#11758194—41no—
81C2×#11758194—41no—
82C2×#11758194C2311yescharacteristic
83C2×#11758194C2311yescharacteristic
84C2×#11758194C2311yescharacteristic
85C2×#11758194C2311yescharacteristic
86C22×#92418—21no—
87C22×#92418—21no—
88#14519772—22no—
89#14519772—22no—
90#14519772—22no—
91#14519772—22no—
92#14519769—21no—
93#14519769—21no—
94#14519769—21no—
95#14519769—21no—
96#14519759—22no—
97#14519759—22no—
98#14519759—22no—
99#14519759—22no—
100#14519751—21no—
101#14519751—21no—
102#14519751—21no—
103#14519751—21no—
104#14519751—21no—
105#14519751—21no—
106#14519751—21no—
107#14519751—21no—
108#14519749—22no—
109#14519749—22no—
110#14519749—22no—
111#14519749—22no—
112C4×D244—21no—
113C4×D244—21no—
114C4×D244—21no—
115C4×D244—21no—
116#14519737—22no—
117#14519737—22no—
118#14519737—22no—
119#14519737—22no—
120#14519736—21no—
121#14519736—21no—
122#14519736—21no—
123#14519736—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61C2×C412yes—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196C2×C412yes—
133C2×#11758196C2×C412yes—
134C2×C22⋊Dic61C2×C412yes—
135C2×#11758198C2×C412yes—
136C2×#11758198C2×C412yes—
137C2×#11758198C2×C412yes—
138C2×C4×Dic61C2×C412yes—
139C4⋊#92418—21no—
140C4⋊#92418—21no—
141#14519693—22no—
142#14519693—22no—
143#14519693—41no—
144#14519693—41no—
145C22⋊#92418—21no—
146C22⋊#92418—21no—
147C22⋊#92418—21no—
148C22⋊#92418—21no—
149#14519688—21no—
150C4×#92418—21no—
151C22×D4×C61C2×C411yescharacteristic
152C23×C4×C61C2311yescharacteristic
153C23×C4×C61C2311yescharacteristic
154C2×M16×C61—21no—
155C2×M16×C61—21no—
156C2×M16×C61—22no—
157C2×M16×C61—22no—
158C2×M16×C61—41no—
159C2×M16×C61—41no—
160C2×M16×C61C2311yescharacteristic
161C2×M16×C61C2311yescharacteristic
162C2×M16×C61C2311yescharacteristic
163C2×M16×C61C2311yescharacteristic
164C22×C8×C61—21no—
165C22×C8×C61—21no—
166C4×D4×C61D411yescharacteristic
167C4×D4×C61D411yescharacteristic
168C4×D4×C61D411yescharacteristic
169C4×D4×C61D411yescharacteristic
170C4×D4×C61D411yescharacteristic
171C4×D4×C61D411yescharacteristic
172C4×D4×C61D411yescharacteristic
173C4×D4×C61D411yescharacteristic
174C2×C4⋊C4×C61C2×C411yescharacteristic
175C2×C22⋊C4×C61C2×C411yescharacteristic
176C2×C22⋊C4×C61C2×C411yescharacteristic
177C2×C42×C61C2311yescharacteristic
178C4⋊C8×C61—21no—
179C4⋊C8×C61—21no—
180C22⋊C8×C61—21no—
181C22⋊C8×C61—21no—
182C22⋊C8×C61—21no—
183C22⋊C8×C61—21no—
184#97×C61—21no—
185C4×C8×C61—21no—
186C24×C61C22×C411yescharacteristic
187C24×C61C22×C411yescharacteristic
188C23×D61C22×C412yes—
189C2×D4×C61—42no—
190C2×D4×C61C22⋊C411yescharacteristic
191C2×D4×C61C22⋊C411yescharacteristic
192C2×D4×C61C22⋊C411yescharacteristic
193C2×D4×C61C22⋊C411yescharacteristic
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C22×C411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—22no—
216C2×C22⋊D61—22no—
217C2×C22⋊D61—22no—
218C2×C22⋊D61—22no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—82no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—82no—
224C22×Dic61C22×C412yes—
225C22×Dic61C22×C412yes—
226C22×Dic61C22×C412yes—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×C4×D61—22no—
234C2×C4×D61—22no—
235C2×C4×D61—82no—
236M16×C61—21no—
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—42no—
244M16×C61—42no—
245M16×C61#4112yes—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—42no—
251C2×C8×C61—42no—
252C4⋊C4×C61C22⋊C411yescharacteristic
253C4⋊C4×C61C22⋊C411yescharacteristic
254C4⋊C4×C61C22⋊C411yescharacteristic
255C4⋊C4×C61C22⋊C411yescharacteristic
256C22⋊C4×C61C22⋊C411yescharacteristic
257C22⋊C4×C61C22⋊C411yescharacteristic
258C22⋊C4×C61C22⋊C411yescharacteristic
259C22⋊C4×C61C22⋊C411yescharacteristic
260C22⋊C4×C61C22⋊C411yescharacteristic
261C22⋊C4×C61C22⋊C411yescharacteristic
262C22⋊C4×C61C22⋊C411yescharacteristic
263C22⋊C4×C61C22⋊C411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2×D411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C22⋊Dic61—22no—
269C22⋊Dic61—22no—
270#11758198—22no—
271#11758198—22no—
272#11758198—22no—
273#11758198—22no—
274#11758198—22no—
275#11758198—22no—
276C4⋊Dic61—22no—
277C4⋊Dic61—22no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284#11758196—22no—
285#11758196—22no—
286#11758196—22no—
287#11758196—22no—
288C4×Dic61—22no—
289C4×Dic61—22no—
290#11758194—21no—
291#11758194—21no—
292#11758194—21no—
293#11758194—21no—
294#11758194—21no—
295#11758194—21no—
296#11758194—21no—
297#11758194—42no—
298#11758194—42no—
299#11758194#4112yes—
300C2×#92418—21no—
301C2×#92418—21no—
302C2×#92418—21no—
303C2×#92418—21no—
304C2×#92418—42no—
305C2×#92418—42no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—22no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61C2×C22⋊C411yescharacteristic
315C23×C61C2×C22⋊C411yescharacteristic
316C23×C61C2×C22⋊C411yescharacteristic
317C23×C61C2×C22⋊C411yescharacteristic
318C23×C61C23×C411yescharacteristic
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—42no—
323C22×D61—42no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—41no—
327D4×C61—41no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2×#4111yescharacteristic
361C2×C4×C61C2×#4111yescharacteristic
362C2×C4×C61H(5,𝔽2)11yescharacteristic
363C2×C4×C612−1+411yescharacteristic
364C22⋊D61—44no—
365C22⋊D61—44no—
366C22⋊D61—82no—
367C22⋊D61—82no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—82no—
375C2×Dic61—82no—
376D244—41no—
377D244—41no—
378D244—41no—
379D244—41no—
380C4×D61—82no—
381C4×D61—82no—
382C8×C61—22no—
383C8×C61—41no—
384C8×C61—41no—
385C8×C61—41no—
386#92418—22no—
387#92418—41no—
388#92418—41no—
389#92418—41no—
390#22482—611nomaximal, Sylow
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—21no—
397C22×C61—21no—
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61#41312yes—
409C22×C61C22×C22⋊C411yescharacteristic
410C22×C61C4×#4111yescharacteristic
411C22×C61#52011yescharacteristic
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—82no—
416C2×D61—82no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61#54611yescharacteristic
426C4×C61#54611yescharacteristic
427C4×C61#54711yescharacteristic
428C4×C61#54711yescharacteristic
429Dic61—42no—
430Dic61—42no—
431Dic61—42no—
432C2×#553—611no—
433D4×M16—611no—
434D4×M16D6111yescharacteristic, complemented
435#1998—611no—
436#1998—611no—
437#1900—611no—
438#1900—611no—
439#1900—611no—
440#1900—611no—
441#1822—611no—
442#1821—611no—
443#1800—611no—
444C4×#100—611no—
445#1742—611no—
446C2×#343—611no—
447C2×C61—21no—
448C2×C61—21no—
449C2×C61—22no—
450C2×C61—41no—
451C2×C61—41no—
452C2×C61—41no—
453C2×C61#233911yescharacteristic
454C2×C61C2×#41311yescharacteristic
455C2×C61#288811yescharacteristic
456D61—82no—
457C22×M16—611no—
458C22×M16—611no—
459C22×M16C2×D6111yescharacteristic
460C22×M16C2×D6111yescharacteristic
461#553—1221no—
462#553—1221no—
463#553—1221no—
464#553—1221no—
465#553—1221no—
466#553—1221no—
467#553—1221no—
468#553—1221no—
469C2×#126—612no—
470C2×#125—611no—
471C2×#123—612no—
472C2×#121—612no—
473C2×#121—611no—
474C2×#121—611no—
475C2×C4×D4—612no—
476C2×C4×D4—611no—
477C2×C4×D4C2×D6111yescharacteristic
478C2×#117—611no—
479C22×C4⋊C4—611no—
480#436—21no—
481#436—1221no—
482#435—21no—
483#435—21no—
484#435—1221no—
485#435—1221no—
486C8×D4—21no—
487C8×D4—1221no—
488#423—611no—
489#423C2×D6111yescharacteristic
490C2×#100—611no—
491C2×#100—611no—
492C2×#100—611no—
493C2×#100—611no—
494#407—611no—
495#407—611no—
496#407C2×D6111yescharacteristic
497#407C2×D6111yescharacteristic
498C4×M16—611no—
499C4×M16C2×D6111yescharacteristic
500#343—611no—
501#343—611no—
502#343—611no—
503#343—611no—
504#343—611no—
505#343—611no—
506#343—611no—
507#343—611no—
508#343—611no—
509#343—611no—
510#343—611no—
511#343—611no—
512C61#2248211yescharacteristic, complemented, Sylow
513C22×D4—612no—
514C22×D4—612no—
515C22×D4—611no—
516C22×D4C4×D6111yescharacteristic
517C23×C4—612no—
518C23×C4—612no—
519C23×C4C22×D6111yescharacteristic
520C23×C4C22×D6111yescharacteristic
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—611no—
528C2×M16—611no—
529C2×M16—611no—
530C2×M16—611no—
531C2×M16—1221no—
532C2×M16—1221no—
533C2×M16—1222no—
534C2×M16—1222no—
535C2×M16—2441no—
536C2×M16—2441no—
537C2×M16C22×D6111yescharacteristic
538C2×M16C22×D6111yescharacteristic
539C2×M16C22×D6111yescharacteristic
540C2×M16C22×D6111yescharacteristic
541C22×C8—21no—
542C22×C8—21no—
543C22×C8—1221no—
544C22×C8—1221no—
545#126—1222no—
546#126—1222no—
547#126—1222no—
548#126—1222no—
549#125—1221no—
550#125—1221no—
551#125—1221no—
552#125—1221no—
553#123—1222no—
554#123—1222no—
555#123—1222no—
556#123—1222no—
557#121—1222no—
558#121—1222no—
559#121—1222no—
560#121—1222no—
561#121—1221no—
562#121—1221no—
563#121—1221no—
564#121—1221no—
565#121—1221no—
566#121—1221no—
567#121—1221no—
568#121—1221no—
569C4×D4—1222no—
570C4×D4—1222no—
571C4×D4—1222no—
572C4×D4—1222no—
573C4×D4—1221no—
574C4×D4—1221no—
575C4×D4—1221no—
576C4×D4—1221no—
577C4×D4D24411yescharacteristic
578C4×D4D24411yescharacteristic
579C4×D4D24411yescharacteristic
580C4×D4D24411yescharacteristic
581C4×D4C22⋊D6111yescharacteristic
582C4×D4C22⋊D6111yescharacteristic
583C4×D4C22⋊D6111yescharacteristic
584C4×D4C22⋊D6111yescharacteristic
585#117—1221no—
586#117—1221no—
587#117—1221no—
588#117—1221no—
589C2×C4⋊C4—612no—
590C2×C4⋊C4—612no—
591C2×C4⋊C4—612no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—1221no—
596C2×C4⋊C4—1221no—
597C2×C4⋊C4—1221no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4C4×D6111yescharacteristic
600C2×C22⋊C4—612no—
601C2×C22⋊C4—612no—
602C2×C22⋊C4—612no—
603C2×C22⋊C4—612no—
604C2×C22⋊C4C4×D6111yescharacteristic
605C2×C22⋊C4C4×D6111yescharacteristic
606C2×C42—612no—
607C2×C42C22×D6111yescharacteristic
608C4⋊C8—21no—
609C4⋊C8—21no—
610C4⋊C8—1221no—
611C4⋊C8—1221no—
612#100—1222no—
613#100—1222no—
614#100—2441no—
615#100—2441no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—21no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622C22⋊C8—1221no—
623C22⋊C8—1221no—
624#97—21no—
625#97—1221no—
626C4×C8—21no—
627C4×C8—1221no—
628C24—612no—
629C24C2×C4×D6111yescharacteristic
630C24C2×C4×D6111yescharacteristic
631C2×D4—42no—
632C2×D4—1222no—
633C2×D4—1222no—
634C2×D4—1222no—
635C2×D4—1222no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—4882no—
643C2×D4—2444no—
644C2×D4#1175819811yescharacteristic
645C2×D4#1175819811yescharacteristic
646C2×D4#1175819811yescharacteristic
647C2×D4#1175819811yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—4882no—
664C22×C4—4882no—
665C22×C4C2×C4×D6111yescharacteristic
666C22×C4C2×C4×D6111yescharacteristic
667C22×C4C2×C4×D6111yescharacteristic
668C22×C4C2×C4×D6111yescharacteristic
669C22×C4C2×D24411yescharacteristic
670C22×C4C2×D24411yescharacteristic
671C22×C4C2×D24411yescharacteristic
672C22×C4C2×D24411yescharacteristic
673C22×C4C2×C22⋊D6111yescharacteristic
674C22×C4C2×C22⋊D6111yescharacteristic
675C22×C4C2×C22⋊D6111yescharacteristic
676C22×C4C2×C22⋊D6111yescharacteristic
677C22×C4C23×D6111yescharacteristic
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—612no—
688M16—1221no—
689M16—1221no—
690M16—1221no—
691M16—1221no—
692M16—1221no—
693M16—1221no—
694M16—1221no—
695M16—2442no—
696M16—2442no—
697M16#1175822412yes—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—2442no—
709C2×C8—2442no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1222no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4#1175819811yescharacteristic
723C4⋊C4#1175819811yescharacteristic
724C4⋊C4#1175819811yescharacteristic
725C4⋊C4#1175819811yescharacteristic
726C22⋊C4—1222no—
727C22⋊C4—1222no—
728C22⋊C4—1222no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C22⋊C4#1175819811yescharacteristic
735C22⋊C4#1175819811yescharacteristic
736C22⋊C4#1175819811yescharacteristic
737C22⋊C4#1175819811yescharacteristic
738C22⋊C4#1175819811yescharacteristic
739C22⋊C4#1175819811yescharacteristic
740C22⋊C4#1175819811yescharacteristic
741C22⋊C4#1175819811yescharacteristic
742C42—1222no—
743C42—1222no—
744C42C2×D24411yescharacteristic
745C42C2×D24411yescharacteristic
746C42C2×C22⋊D6111yescharacteristic
747C42C2×C22⋊D6111yescharacteristic
748C23—21no—
749C23—21no—
750C23—22no—
751C23—21no—
752C23—21no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—1222no—
757C23—1222no—
758C23—1222no—
759C23—2442no—
760C23—2442no—
761C23C2×#1175819811yescharacteristic
762C23C2×#1175819811yescharacteristic
763C23C2×#1175819811yescharacteristic
764C23C2×#1175819811yescharacteristic
765C23C22×C4×D6111yescharacteristic
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—4882no—
771D4—4882no—
772D4—2444no—
773D4—2444no—
774D4—2441no—
775D4—2441no—
776D4—2441no—
777D4—2441no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—4882no—
804C2×C4—4882no—
805C2×C4—4882no—
806C2×C4—4882no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4C2×#1175819811yescharacteristic
811C2×C4C2×#1175819811yescharacteristic
812C2×C4C2×#1175819811yescharacteristic
813C2×C4C2×#1175819811yescharacteristic
814C2×C4C2×#1175819811yescharacteristic
815C2×C4C2×#1175819811yescharacteristic
816C2×C4C2×#1175819811yescharacteristic
817C2×C4C2×#1175819811yescharacteristic
818C2×C4C22×C22⋊D6111yescharacteristic
819C2×C4C22×D24411yescharacteristic
820C2×C4#41×D6111yescharacteristic
821C2×C4C2×#1175822411yescharacteristic
822C2×C4#1451982211yescharacteristic
823C2×C4#1451982411yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C8—1222no—
829C8—2441no—
830C8—2441no—
831C8—2441no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—42no—
846C22—42no—
847C22—81no—
848C22—81no—
849C22—4882no—
850C22—4882no—
851C22—2442no—
852C22—2442no—
853C22—2442no—
854C22#1683974412yes—
855C22C22×#1175819811yescharacteristic
856C22C4×#1175822411yescharacteristic
857C22#1684024111yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—2442no—
867C4—2442no—
868C4—2442no—
869C4#1684040611yescharacteristic
870C4#1684040711yescharacteristic
871C4#1684041111yescharacteristic
872C4#1684041611yescharacteristic
873C2—21no—
874C2—21no—
875C2—22no—
876C2—41no—
877C2—41no—
878C2—41no—
879C2—4882no—
880C2#2144864411yescharacteristic
881C2C2×#1683974411yescharacteristic
882C2#2145429711yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×M16×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840458C2
cosocleC22×C4×C61C24
hypercenterD4×M16D61
hypocenterC61#22482
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#11758194C2semidirect
3. #21446812C2semidirect
4. #21446811C2semidirect
5. #21446282C2semidirect
6. #21446282C2semidirect
7. #21446280C2semidirect
8. #21446280C2semidirect
9. #21445900C2semidirect
10. #21445897C2semidirect
11. #21445808C2semidirect
12. C4×#14519693C2semidirect
13. #21445557C2semidirect
14. C2×#16839530C2semidirect
15. D4×M16×C61C2semidirect
434. D4×M16D61semidirect
512. C61#22482semidirect

Maximal subgroups

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

subgroupindex
C2×#168404582
D4×#117581942
#214468122
#214468112
#214462822
#214462802
#214459002
#214458972
#214458082
C4×#145196932
#214455572
C2×#168395302
D4×M16×C612
#2248261