Finite Group Databasebeta

← #30621757

Subgroups — #30621757

Order 15616.

1134 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840753C211yesmaximal, characteristic
3#21462343C211yesmaximal, characteristic, complemented
4#21462322C211yesmaximal, characteristic
5#21461967C211yesmaximal, characteristic, complemented
6#21461908C211yesmaximal, characteristic, complemented
7#21461898C211yesmaximal, characteristic, complemented
8#21461834C211yesmaximal, characteristic, complemented
9#21461813C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461769C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic, complemented
15#452×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21SD16×#6923—24no—
22C2×#14519845C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24#16840753—24no—
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35(C2×#6923)⋊Q8C2211yescharacteristic
36#16840713—21no—
37#16840713C2211yescharacteristic
38#16840711—21no—
39#16840710—21no—
40#16840710—21no—
41#16840709—21no—
42#16840705—21no—
43#16840704C2211yescharacteristic
44C4⋊C4×#6923C2211yescharacteristic
45C22⋊C4×#6923—21no—
46C4×C22⋊#6923C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C2×Q16×D61C2211yescharacteristic
56C2×SD16×D61C2211yescharacteristic
57C22⋊Q8×D61C2211yescharacteristic
58#16839927C411yescharacteristic, complemented
59#16839926C411yescharacteristic, complemented
60#16839925C411yescharacteristic, complemented
61#16839924C411yescharacteristic, complemented
62#16839923C411yescharacteristic, complemented
63#16839922C411yescharacteristic, complemented
64#16839921C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#452C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C2×#11758213—21no—
73D61⋊M16—22no—
74D61⋊M16—41no—
75C2×#11758217—21no—
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78Q8×#6923—22no—
79Q8×#6923—41no—
80D4×#6923—22no—
81D4×#6923—22no—
82D4×#6923—41no—
83D4×#6923—41no—
84C2×C4⋊#6923—22no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923—21no—
88C2×C4⋊#6923—41no—
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C4⋊#6923C2311yescharacteristic
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923D411yescharacteristic
97C2×C22⋊#6923D411yescharacteristic
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102#14519845—22no—
103#14519845—41no—
104#14519840—22no—
105#14519840—22no—
106#14519840—22no—
107#14519840—41no—
108#14519839—22no—
109#14519839D414yes—
110#14519831—41no—
111C8×#6923—22no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—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—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4D411yescharacteristic
122(C2×#6923)⋊C4D411yescharacteristic
123C2×#11758226C2×C411yescharacteristic
124C2×#11758222—21no—
125C2×#11758222C2×C411yescharacteristic
126C2×#11758224—21no—
127C2×#11758224C2×C411yescharacteristic
128#41×D61—22no—
129#41×D61—22no—
130#41×D61—41no—
131#41×D61—41no—
132C2×Q8×D61C2311yescharacteristic
133C2×Q8×D61C2311yescharacteristic
134C2×D4×D61—21no—
135C2×D4×D61C2311yescharacteristic
136C22×C4×D61—21no—
137C22×C4×D61C2311yescharacteristic
138C2×Dic244C2×C411yescharacteristic, complemented
139C2×#11758202C2×C411yescharacteristic, complemented
140C2×#11758202C2×C411yescharacteristic, complemented
141Q16×D61—41no—
142Q16×D61—41no—
143C2×#11758190C2×C411yescharacteristic, complemented
144C2×#11758200C2×C411yescharacteristic, complemented
145C2×#11758201C2×C411yescharacteristic, complemented
146SD16×D61—22no—
147SD16×D61—22no—
148C2×C8×D61C2311yescharacteristic
149C2×C8×D61C2311yescharacteristic
150#14519757C2×C411yescharacteristic, complemented
151#14519756C2×C411yescharacteristic, complemented
152#14519755—21no—
153#14519754—21no—
154#14519753C2×C411yescharacteristic, complemented
155C4⋊C4×D61—21no—
156C4⋊C4×D61C2311yescharacteristic
157C22⋊C4×D61—21no—
158#14519702C2×C411yescharacteristic, complemented
159#14519701C2×C411yescharacteristic, complemented
160#14519700C2×C411yescharacteristic, complemented
161#14519699C2×C411yescharacteristic, complemented
162#14519698C2×C411yescharacteristic, complemented
163#14519697C2×C411yescharacteristic, complemented
164C22⋊#92418C2×C411yescharacteristic, complemented
165#14519689C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167C2×#41×C61C2×C411yescharacteristic
168C2×Q16×C61C2×C411yescharacteristic, complemented
169C2×SD16×C61C2×C411yescharacteristic, complemented
170C22⋊Q8×C61C2×C411yescharacteristic, complemented
171#103×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic, complemented
173C22⋊C8×C61C2×C411yescharacteristic, complemented
174C23×D61—21no—
175C23×D61C2×D411yescharacteristic
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—42no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—42no—
185C22×#6923—42no—
186C22×#6923—81no—
187C22×#6923—81no—
188C22×#6923—81no—
189C22×#6923C2×D411yescharacteristic
190C22×#6923C2×D411yescharacteristic
191C22×#6923C2×D411yescharacteristic
192C22×#6923C2×D411yescharacteristic
193#41×C61—22no—
194#41×C61—41no—
195C2×Q8×C61C22×C411yescharacteristic
196C2×Q8×C61C22×C411yescharacteristic
197C2×D4×C61—21no—
198C2×D4×C61C22×C411yescharacteristic
199C22×C4×C61—21no—
200C22×C4×C61C22×C411yescharacteristic
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C22×Dic61—21no—
205C22×Dic61#4111yescharacteristic
206#11758226—22no—
207#11758226—41no—
208Q8×D61—21no—
209Q8×D61—21no—
210Q8×D61—21no—
211Q8×D61—21no—
212Q8×D61—21no—
213Q8×D61—21no—
214Q8×D61—21no—
215Q8×D61—21no—
216#11758224—22no—
217#11758224—41no—
218#11758224—42no—
219#11758224—42no—
220D4×D61—21no—
221D4×D61—21no—
222D4×D61—42no—
223D4×D61—42no—
224D4×D61C2×D412yes—
225D4×D61#4112yes—
226#11758222—22no—
227#11758222—41no—
228#11758222—42no—
229#11758222—42no—
230C2×D244—21no—
231C2×D244C22×C411yescharacteristic
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—42no—
242C2×C4×D61—42no—
243C2×C4×D61C22×C411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61#4111yescharacteristic
246C2×C4×D61C2411yescharacteristic
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122C22×C411yescharacteristic
250C2×Dic122C22×C411yescharacteristic
251C22⋊#6923—22no—
252C22⋊#6923—41no—
253C22⋊#6923—42no—
254C22⋊#6923—42no—
255C22⋊#6923—81no—
256#11758217—42no—
257C2×#92420—21no—
258C2×#92420—21no—
259C4⋊#6923—21no—
260C4⋊#6923—21no—
261C4⋊#6923—21no—
262C4⋊#6923—21no—
263C4⋊#6923—21no—
264C4⋊#6923—21no—
265C4⋊#6923—21no—
266C4⋊#6923—42no—
267C4⋊#6923—42no—
268C4⋊#6923—81no—
269C4⋊#6923C2×D412yes—
270C4×#6923—21no—
271C4×#6923—21no—
272C4×#6923—21no—
273C4×#6923—21no—
274C4×#6923—42no—
275C4×#6923—81no—
276#11758213—42no—
277D61⋊C8—21no—
278D61⋊C8—21no—
279D61⋊C8—21no—
280D61⋊C8C2×D412yes—
281Q16×C61—41no—
282SD16×C61—22no—
283C2×C8×C61C22×C411yescharacteristic
284C2×C8×C61C22×C411yescharacteristic
285C4⋊C4×C61—21no—
286C4⋊C4×C61C22×C411yescharacteristic
287C22⋊C4×C61—21no—
288C22⋊Dic61—21no—
289#11758202—41no—
290#11758202—41no—
291#11758201—22no—
292#11758200—22no—
293#11758198—21no—
294#11758198—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61C22×C411yescharacteristic
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300C2×#92418C22×C411yescharacteristic
301C2×#92418C22×C411yescharacteristic
302Dic244—41no—
303#11758190—22no—
304C8×D61—21no—
305C8×D61—21no—
306C8×D61—21no—
307C8×D61—21no—
308C23×C61—21no—
309C23×C61C4×D411yescharacteristic
310C22×D61—21no—
311C22×D61—22no—
312C22×D61—21no—
313C22×D61—22no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61C4×D411yescharacteristic
324C22×D61C22×D411yescharacteristic
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—21no—
328C2×#6923—22no—
329C2×#6923—21no—
330C2×#6923—21no—
331C2×#6923—21no—
332C2×#6923—21no—
333C2×#6923—21no—
334C2×#6923—21no—
335C2×#6923—21no—
336C2×#6923—21no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—84no—
349C2×#6923—84no—
350C2×#6923—84no—
351C2×#6923#13712yes—
352Q8×C61—21no—
353Q8×C61—21no—
354Q8×C61—21no—
355Q8×C61—21no—
356D4×C61—21no—
357D4×C61—42no—
358D4×C61C4×D412yes—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—42no—
365C2×C4×C61C4×D411yescharacteristic
366C2×C4×C61C23×C411yescharacteristic
367C22⋊D61—22no—
368C22⋊D61—22no—
369C22⋊D61—42no—
370C22⋊D61—42no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—42no—
377C2×Dic61C4×D411yescharacteristic
378C2×Dic61C2×#4111yescharacteristic
379D244—21no—
380D244—42no—
381D244C4×D412yes—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—42no—
389C4×D61—42no—
390C4×D61—41no—
391C4×D61—41no—
392C4×D61—41no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—41no—
396C4×D61C22×D411yescharacteristic
397C4×D61C2×#4111yescharacteristic
398C4×D61H(5,𝔽2)11yescharacteristic
399C4×D61H(5,𝔽2)11yescharacteristic
400Dic122—21no—
401Dic122—21no—
402Dic122—21no—
403Dic122—21no—
404Dic122—41no—
405Dic122—41no—
406Dic122—41no—
407Dic122—41no—
408#92420—22no—
409#92420—41no—
410C8×C61—21no—
411C8×C61—21no—
412#92418—21no—
413#92418—21no—
414#22882—611nomaximal, Sylow
415C22×C61—21no—
416C22×C61—22no—
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61C2×C4×D411yescharacteristic
422C2×D61—21no—
423C2×D61—22no—
424C2×D61—21no—
425C2×D61—21no—
426C2×D61—41no—
427C2×D61—41no—
428C2×D61—41no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—41no—
432C2×D61—41no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—41no—
436C2×D61D4211yescharacteristic
437C2×D61#54611yescharacteristic
438C2×D61C2×#13711yescharacteristic
439C2×D61#57511yescharacteristic
440C2×D61#57711yescharacteristic
441C2×D61#57711yescharacteristic
442#6923—22no—
443#6923—41no—
444#6923—41no—
445#6923—42no—
446#6923—41no—
447#6923—81no—
448#6923—81no—
449#6923—81no—
450C4×C61—21no—
451C4×C61—41no—
452C4×C61—41no—
453C4×C61—41no—
454C4×C61C2×C4×D411yescharacteristic
455C4×C61#51811yescharacteristic
456Dic61—21no—
457Dic61—41no—
458Dic61—41no—
459Dic61—41no—
460Dic61#54611yescharacteristic
461Dic61#55111yescharacteristic
462C2×#452—611no—
463C2×C4×SD16—611no—
464C2×#417—611no—
465#2360—611no—
466#2339—611no—
467#1971—611no—
468#1933—611no—
469#1927—611no—
470#1894—611no—
471#1878—611no—
472#1877—611no—
473#1864—611no—
474#1853—611no—
475#1762—611no—
476#1753—611no—
477C2×C61—41no—
478C2×C61—42no—
479C2×C61#235811yescharacteristic
480C2×C61C4×#13711yescharacteristic
481C2×C61#295211yescharacteristic
482D61—41no—
483D61—42no—
484D61#326611yescharacteristic
485D61#326711yescharacteristic
486D61#332311yescharacteristic
487D61#333111yescharacteristic
488C22×#41—611no—
489C22×Q16—611no—
490C22×SD16—611no—
491C22×M16—611no—
492C2×C22⋊Q8—611no—
493C2×C4×Q8—611no—
494C2×C4×D4—611no—
495C2×C4×D4—611no—
496C22×C4⋊C4—611no—
497#452—611no—
498#452—611no—
499#452—611no—
500#452—611no—
501#452—611no—
502#452—611no—
503#452—611no—
504#452#692311yescharacteristic, complemented
505C4×SD16—1224no—
506C2×#106—611no—
507C2×#106—611no—
508#417—1224no—
509C2×#103—611no—
510C2×#103—611no—
511C2×#103—611no—
512C2×#103—611no—
513C2×#103—611no—
514C2×#102—611no—
515C2×#102—611no—
516C2×#102—611no—
517C2×C22⋊C8—611no—
518C2×#97—611no—
519C2×C4×C8—611no—
520#391—611no—
521#391—611no—
522#391—611no—
523#389—611no—
524#389—1221no—
525#387—1221no—
526#386—1221no—
527#386—1221no—
528#385—1221no—
529#381—1221no—
530#380—611no—
531C4×C4⋊C4—611no—
532C4×C22⋊C4—611no—
533C4×C22⋊C4—1221no—
534C2×#95—1221no—
535#340—611no—
536#340—611no—
537#340—611no—
538#340—611no—
539#336—611no—
540#336—611no—
541C61#2288211yescharacteristic, complemented, Sylow
542C2×#41—611no—
543C2×#41—611no—
544C2×#41—611no—
545C2×#41—1221no—
546C2×#41—1221no—
547C2×#41—1222no—
548C2×#41—1222no—
549C2×#41—2441no—
550C2×#41—2441no—
551C2×#41C2×#692311yescharacteristic
552C22×Q8—611no—
553C22×Q8—611no—
554C22×D4—611no—
555C22×D4—1221no—
556C23×C4—611no—
557C23×C4—1221no—
558C23×C4—1221no—
559C23×C4—1221no—
560C23×C4—1221no—
561C2×Q16—611no—
562C2×Q16—611no—
563C2×Q16—611no—
564C2×Q16—2441no—
565C2×Q16—2441no—
566C2×Q16C2×#692311yescharacteristic, complemented
567C2×SD16—611no—
568C2×SD16—611no—
569C2×SD16—611no—
570C2×SD16—1222no—
571C2×SD16—1222no—
572C2×SD16C2×#692311yescharacteristic, complemented
573C2×M16—1222no—
574C2×M16—1221no—
575C2×M16—1221no—
576C2×M16—2441no—
577C22×C8—611no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—611no—
581C22⋊Q8—611no—
582C22⋊Q8—611no—
583C22⋊Q8—611no—
584C22⋊Q8—1221no—
585C22⋊Q8—1221no—
586C22⋊Q8C2×#692311yescharacteristic, complemented
587C4×Q8—1222no—
588C4×Q8—2441no—
589C4×D4—1222no—
590C4×D4—1222no—
591C4×D4—2441no—
592C4×D4—2441no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1222no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—2441no—
604C2×C22⋊C4—611no—
605C2×C22⋊C4—611no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—1221no—
613C2×C42—1221no—
614#106—1222no—
615#106—2441no—
616#103—611no—
617#103—611no—
618#103—611no—
619#103—1222no—
620#103—1222no—
621#103—1222no—
622#103—2441no—
623#103C2×#692311yescharacteristic, complemented
624#102—614no—
625#102—611no—
626#102—611no—
627#102—611no—
628#102—1222no—
629#102C2×#692311yescharacteristic, complemented
630C22⋊C8—611no—
631C22⋊C8—611no—
632C22⋊C8—611no—
633C22⋊C8C2×#692311yescharacteristic, complemented
634#97—2441no—
635C4×C8—1222no—
636#95—611no—
637#95—611no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641#95—1221no—
642#95—1221no—
643#95—1221no—
644#95—1221no—
645#95—1221no—
646#95—1221no—
647C24—611no—
648C24—1221no—
649#41—22no—
650#41—41no—
651#41—1222no—
652#41—1222no—
653#41—1222no—
654#41—2441no—
655#41—2442no—
656#41—2442no—
657#41—2441no—
658#41—2442no—
659#41—2442no—
660#41—2441no—
661C2×Q8—611no—
662C2×Q8—611no—
663C2×Q8—1221no—
664C2×Q8—1221no—
665C2×Q8—1221no—
666C2×Q8—1221no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—1221no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×Q8C22×#692311yescharacteristic
674C2×Q8C22×#692311yescharacteristic
675C2×D4—21no—
676C2×D4—612no—
677C2×D4—612no—
678C2×D4—611no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—2442no—
686C2×D4—2442no—
687C2×D4C22×#692311yescharacteristic
688C22×C4—21no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—4881no—
713C22×C4—4881no—
714C22×C4—4881no—
715C22×C4—2442no—
716C22×C4—2442no—
717C22×C4—2442no—
718C22×C4—2442no—
719C22×C4—2442no—
720C22×C4—2442no—
721C22×C4—2442no—
722C22×C4—2442no—
723C22×C4C22×#692311yescharacteristic
724Q16—41no—
725Q16—2441no—
726Q16—2441no—
727Q16—2441no—
728SD16—22no—
729SD16—1222no—
730SD16—1222no—
731SD16—1222no—
732M16—2442no—
733M16—2442no—
734C2×C8—612no—
735C2×C8—611no—
736C2×C8—611no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8C22×#692311yescharacteristic
747C2×C8C22×#692311yescharacteristic
748C4⋊C4—21no—
749C4⋊C4—612no—
750C4⋊C4—611no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—4881no—
763C4⋊C4—2442no—
764C4⋊C4—2442no—
765C4⋊C4C22×#692311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1222no—
770C22⋊C4—1221no—
771C22⋊C4—4881no—
772C22⋊C4—2441no—
773C22⋊C4—2442no—
774C22⋊C4—2442no—
775C42—1221no—
776C42—1221no—
777C42—1221no—
778C42—1221no—
779C42—4881no—
780C42—2442no—
781C23—21no—
782C23—611no—
783C23—611no—
784C23—1221no—
785C23—1221no—
786C23—1222no—
787C23—1222no—
788C23—1221no—
789C23—1221no—
790C23—1221no—
791C23—1221no—
792C23—1221no—
793C23—2441no—
794C23—2441no—
795C23—2441no—
796C23—2441no—
797C23D4×#692311yescharacteristic
798Q8—21no—
799Q8—21no—
800Q8—21no—
801Q8—21no—
802Q8—1221no—
803Q8—1221no—
804Q8—1221no—
805Q8—1221no—
806Q8—2441no—
807Q8—2441no—
808Q8—2441no—
809Q8—2441no—
810D4—21no—
811D4—42no—
812D4—612no—
813D4—1222no—
814D4—1222no—
815D4—1221no—
816D4—2442no—
817D4—2442no—
818D4—2442no—
819D4D4×#692312yes—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—42no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—612no—
832C2×C4—611no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1222no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—4884no—
857C2×C4—4884no—
858C2×C4—4884no—
859C2×C4—2442no—
860C2×C4—2442no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2442no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4D4×#692311yescharacteristic
880C2×C4C23×#692311yescharacteristic
881C8—21no—
882C8—21no—
883C8—1222no—
884C8—1221no—
885C8—1221no—
886C8—2441no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—22no—
891C22—41no—
892C22—41no—
893C22—611no—
894C22—611no—
895C22—611no—
896C22—611no—
897C22—611no—
898C22—611no—
899C22—1221no—
900C22—1221no—
901C22—1221no—
902C22—1222no—
903C22—2441no—
904C22—2442no—
905C22—2442no—
906C22—2441no—
907C22—2441no—
908C22—2441no—
909C22—2442no—
910C22—2442no—
911C22—2441no—
912C22—2441no—
913C22C2×D4×#692311yescharacteristic
914C4—21no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—611no—
919C4—611no—
920C4—1222no—
921C4—1221no—
922C4—4881no—
923C4—4881no—
924C4—4881no—
925C4—2441no—
926C4—2441no—
927C4—2441no—
928C4—2442no—
929C4—2441no—
930C4—2441no—
931C4—2441no—
932C4C2×D4×#692311yescharacteristic
933C4#1684082911yescharacteristic
934C2—41no—
935C2—42no—
936C2—611no—
937C2—611no—
938C2—611no—
939C2—611no—
940C2—2441no—
941C2—2442no—
942C2#2146234111yescharacteristic
943C2#137×#692311yescharacteristic
944C2#2146258211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#452C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#452#6923
hypocenterC61#22882
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
3. #21462343C2semidirect
5. #21461967C2semidirect
6. #21461908C2semidirect
7. #21461898C2semidirect
8. #21461834C2semidirect
9. #21461813C2semidirect
10. #21461812C2semidirect
11. #21461784C2semidirect
12. #21461769C2semidirect
13. #21461590C2semidirect
14. #21461562C2semidirect
58. #16839927C4semidirect
59. #16839926C4semidirect
60. #16839925C4semidirect
61. #16839924C4semidirect
62. #16839923C4semidirect
63. #16839922C4semidirect
64. #16839921C4semidirect
68. C61×#452C4semidirect
138. C2×Dic244C2×C4semidirect
139. C2×#11758202C2×C4semidirect
140. C2×#11758202C2×C4semidirect
143. C2×#11758190C2×C4semidirect
144. C2×#11758200C2×C4semidirect
145. C2×#11758201C2×C4semidirect
150. #14519757C2×C4semidirect
151. #14519756C2×C4semidirect
154. #14519753C2×C4semidirect
158. #14519702C2×C4semidirect
159. #14519701C2×C4semidirect
160. #14519700C2×C4semidirect
161. #14519699C2×C4semidirect
162. #14519698C2×C4semidirect
163. #14519697C2×C4semidirect
164. C22⋊#92418C2×C4semidirect
165. #14519689C2×C4semidirect
166. #14519689C2×C4semidirect
168. C2×Q16×C61C2×C4semidirect
169. C2×SD16×C61C2×C4semidirect
170. C22⋊Q8×C61C2×C4semidirect
171. #103×C61C2×C4semidirect
172. #102×C61C2×C4semidirect
173. C22⋊C8×C61C2×C4semidirect
504. #452#6923semidirect
541. C61#22882semidirect
566. C2×Q16C2×#6923semidirect
572. C2×SD16C2×#6923semidirect
586. C22⋊Q8C2×#6923semidirect
623. #103C2×#6923semidirect
629. #102C2×#6923semidirect
633. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C2×#168407532
#214623432
#214623222
#214619672
#214619082
#214618982
#214618342
#214618132
#214618122
#214617842
#214617692
#214615902
#214615622
#452×D612
#2288261