Finite Group Databasebeta

← C2×#21454646 #30544105

Subgroups — C2×#21454646 #30544105

Order 15616.

2946 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519804C211yesmaximal, characteristic
2C2×#16840244C211yesmaximal, characteristic, complemented
3C2×#16840234C211yesmaximal, characteristic, complemented
4#21454646C2116yesmaximal, direct product factor
5C2×#16839873C211yesmaximal, characteristic, complemented
6C2×#16839872C211yesmaximal, characteristic, complemented
7C2×#16839863C211yesmaximal, characteristic, complemented
8C2×#16839860C211yesmaximal, characteristic, complemented
9C2×#16839847C211yesmaximal, characteristic, complemented
10C2×C4×D488C211yesmaximal, characteristic, complemented
11C2×#16839842C211yesmaximal, characteristic, complemented
12C2×#16839801C211yesmaximal, characteristic, complemented
13C2×#16839757C211yesmaximal, characteristic, complemented
14C2×#102×D61C211yesmaximal, characteristic, complemented
15C2×#16839716C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C2×#14519804C4116yescomplemented
20C2×#14519804C2218yes—
21C22×#11758201C2211yescharacteristic
22C22×D488C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840244—24no—
27#16840244C2218yescomplemented
28#16840234—24no—
29#16840234C2218yescomplemented
30C2×Q8×Dic61C2211yescharacteristic, complemented
31C2×C4×D244—21no—
32C2×C4×D244C2211yescharacteristic
33C2×C4×D244C2211yescharacteristic, complemented
34C2×D4×Dic61C2211yescharacteristic
35C2×#14519739—21no—
36C2×#14519739C2211yescharacteristic
37C2×#14519739C2211yescharacteristic, complemented
38C2×C4×C22⋊D61—21no—
39C2×#14519737—21no—
40C2×#14519735C2211yescharacteristic
41C2×#14519734—21no—
42C2×#14519734C2211yescharacteristic
43C2×C4⋊C4×D61—21no—
44C2×C4⋊C4×D61C2211yescharacteristic
45C22×#11758198—21no—
46C2×C22⋊C4×D61—21no—
47#16839873C2218yescomplemented
48#16839872C2218yescomplemented
49#16839863C2218yescomplemented
50#16839860C2218yescomplemented
51#16839847C2218yescomplemented
52C4×D488C2218yescomplemented
53#16839842C2218yescomplemented
54#16839801C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58#16839757C2218yescomplemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic, complemented
65#102×D61C2218yescomplemented
66#16839716C2218yescomplemented
67C2×#14519688C2211yescharacteristic, complemented
68C2×#14519687C2211yescharacteristic, complemented
69C2×C8×Dic61C2211yescharacteristic, complemented
70C22×SD16×C61C2211yescharacteristic
71C2×C4×Q8×C61C2211yescharacteristic, complemented
72C2×C4×D4×C61C2211yescharacteristic
73C4×SD16×C61C2218yescomplemented
74C2×#106×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×#102×C61C2211yescharacteristic
77C2×C4×C8×C61C2211yescharacteristic, complemented
78C24×D61—21no—
79C2×#11758226—22no—
80C2×#11758226—24no—
81C2×#11758226C2×C418yescomplemented
82C2×#11758226C2314yes—
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C2×D4×D61—22no—
88C2×D4×D61—24no—
89C2×D4×D61C2×C418yescomplemented
90C2×D4×D61C2314yes—
91C23×Dic61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61C2311yescharacteristic
99#14519804C2×C4164yescomplemented
100C2×#11758201C2×C418yescomplemented
101C2×#11758201C2314yes—
102C2×D488C2×C418yescomplemented
103C2×D488C2314yes—
104C2×#11758199C2×C418yescomplemented
105C2×#11758199C2314yes—
106C2×#11758189C2×C418yescomplemented
107C2×#11758189C2314yes—
108C22×#92418C2311yescharacteristic
109C22×#92418C2311yescharacteristic
110C2×C8×D61—24no—
111C2×C8×D61C2314yes—
112Q8×Dic61—22no—
113Q8×Dic61C2314yescomplemented
114C4×D244—22no—
115C4×D244—22no—
116C4×D244—28no—
117C4×D244C2314yes—
118C4×D244C2314yescomplemented
119D4×Dic61—22no—
120D4×Dic61C2314yes—
121#14519739—28no—
122#14519739—22no—
123#14519739—22no—
124#14519739C2314yes—
125#14519739C2314yescomplemented
126C4×C22⋊D61—28no—
127#14519737—28no—
128#14519735—22no—
129#14519735C2314yes—
130#14519734—28no—
131#14519734D414yes—
132#14519734C2314yes—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196—21no—
137C2×#11758196D411yescharacteristic
138C2×#11758196D411yescharacteristic
139C4⋊C4×D61—22no—
140C4⋊C4×D61—28no—
141C4⋊C4×D61C2314yes—
142C2×C22⋊Dic61—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—28no—
149C2×#11758198D411yescharacteristic
150C2×#11758198D411yescharacteristic
151C22⋊C4×D61—28no—
152C2×C4×Dic61—21no—
153C2×C4×Dic61—21no—
154C2×C4×Dic61C2311yescharacteristic
155#14519711C2314yescomplemented
156#14519710C2314yescomplemented
157#14519708C2314yescomplemented
158#14519701C2314yescomplemented
159#14519699C2314yes—
160#14519699C2314yescomplemented
161#14519698C2314yes—
162#14519697C2314yes—
163#14519697C2314yescomplemented
164#14519688C2314yescomplemented
165#14519687C2314yescomplemented
166C8×Dic61C2314yescomplemented
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C23×C4×C61—21no—
170C2×SD16×C61C2×C418yescomplemented
171C2×SD16×C61C2314yes—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C4×Q8×C61—22no—
175C4×Q8×C61C2314yescomplemented
176C4×D4×C61—22no—
177C4×D4×C61C2314yes—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C42×C61—21no—
183C2×C42×C61C2311yescharacteristic
184#106×C61C2314yescomplemented
185#103×C61C2314yescomplemented
186#102×C61C2314yes—
187C4×C8×C61C2314yescomplemented
188C24×C61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—28no—
192C23×D61—24no—
193C23×D61—82no—
194C23×D61—82no—
195C23×D61C2×D411yescharacteristic
196C2×Q8×C61—21no—
197C2×Q8×C61—22no—
198C2×Q8×C61C22×C414yes—
199C2×Q8×C61C2412yes—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61C22×C414yes—
203C2×D4×C61C2412yes—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—82no—
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—28no—
213C2×C22⋊D61—24no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—24no—
217C22×Dic61—82no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758226—216no—
222#11758226—28no—
223#11758226C22×C4116yescomplemented
224D4×D61—216no—
225D4×D61—28no—
226D4×D61C22×C4116yescomplemented
227C2×D244—28no—
228C2×D244—24no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244C22×C414yes—
234C2×D244C22×C414yes—
235C2×D244C2412yes—
236C2×D244C2412yes—
237C2×C4×D61—28no—
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—24no—
241C2×C4×D61—24no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—82no—
245C2×C4×D61—82no—
246C2×C4×D61—82no—
247C2×C4×D61—82no—
248C2×C4×D61—82no—
249C2×C4×D61C22×C414yes—
250C2×C4×D61C2×D412yes—
251C2×C4×D61#4114yes—
252C2×C4×D61C2412yes—
253SD16×C61C22×C4116yescomplemented
254C2×C8×C61—22no—
255C2×C8×C61C22×C414yes—
256C2×C8×C61C2412yes—
257C2×C8×C61C2412yes—
258C4⋊C4×C61—24no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C2412yes—
262C4⋊C4×C61C2412yes—
263C22⋊C4×C61—24no—
264C42×C61—24no—
265C42×C61C2×D412yes—
266C42×C61C2412yes—
267C22⋊Dic61—24no—
268#11758201C22×C4116yescomplemented
269#11758199C22×C4116yescomplemented
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198C2×D414yes—
276#11758198C2×D414yes—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—24no—
280C4⋊Dic61C2412yes—
281C4⋊Dic61C2412yes—
282#11758196—24no—
283#11758196C2×D414yes—
284#11758196C2×D414yes—
285C4×Dic61—24no—
286C4×Dic61—24no—
287C4×Dic61C2×D412yes—
288C4×Dic61C2412yes—
289C2×#92418—22no—
290C2×#92418C22×C414yes—
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293D488C22×C4116yescomplemented
294#11758189C22×C4116yescomplemented
295C8×D61—28no—
296C23×C61—24no—
297C23×C61—22no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61C22×D411yescharacteristic
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—24no—
304C22×D61—24no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—216no—
308C22×D61—42no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—816no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61C4×D414yes—
316C22×D61C22×D412yes—
317Q8×C61—24no—
318Q8×C61—22no—
319Q8×C61C23×C414yes—
320D4×C61—24no—
321D4×C61—22no—
322D4×C61C23×C414yes—
323C2×C4×C61—24no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—42no—
330C2×C4×C61—42no—
331C2×C4×C61—84no—
332C2×C4×C61C23×C412yes—
333C2×C4×C61C22×D412yes—
334C2×C4×C61C22×D412yes—
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4112yes—
337C2×C4×C61C2511yescharacteristic
338C22⋊D61—216no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—84no—
346C2×Dic61C4×D414yes—
347C2×Dic61C22×D412yes—
348C2×Dic61C22×D412yes—
349C2×Dic61C22×D412yes—
350D244—216no—
351D244—24no—
352D244—24no—
353D244—22no—
354D244—22no—
355D244C23×C414yes—
356D244C23×C414yes—
357C4×D61—216no—
358C4×D61—84no—
359C4×D61—84no—
360C4×D61—84no—
361C4×D61—84no—
362C4×D61—84no—
363C4×D61C4×D418yes—
364C4×D61C23×C414yes—
365C4×D61C2×#4114yes—
366C8×C61—22no—
367C8×C61C23×C414yes—
368#92418—22no—
369#92418C23×C414yes—
370C2×#2946—611nomaximal, Sylow
371C22×C61—24no—
372C22×C61—48no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61C2×C4×D412yes—
376C22×C61#57612yes—
377C22×C61#57712yes—
378C22×C61C23×D411yescharacteristic
379C2×D61—28no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—48no—
385C2×D61—48no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—816no—
391C2×D61C2×C4×D414yes—
392C4×C61—24no—
393C4×C61—22no—
394C4×C61—22no—
395C4×C61—42no—
396C4×C61—42no—
397C4×C61C2×C4×D412yes—
398C4×C61C24×C411yescharacteristic
399C4×C61C22×#4111yescharacteristic
400Dic61—22no—
401Dic61—22no—
402Dic61—42no—
403Dic61—42no—
404Dic61C2×C4×D414yes—
405C22×AGL(1,ℤ/8)—611no—
406C2×#520—611no—
407C2×#518—611no—
408#2946—6116no—
409C2×#442—611no—
410C2×#442—611no—
411C2×#440—611no—
412C2×#440—611no—
413C2×C4×SD16—611no—
414C2×C4×SD16D6111yescharacteristic, complemented
415C2×C4×D8—611no—
416C2×C4×D8—611no—
417C2×#428—611no—
418C2×#416—611no—
419C22×#102—611no—
420C2×#405—611no—
421C2×C61—44no—
422C2×C61#294614yescomplemented
423C2×C61C22×C4×D411yescharacteristic
424C2×C61C2×#57611yescharacteristic
425C2×C61C2×#57711yescharacteristic
426D61—24no—
427D61—44no—
428D61—44no—
429C22×#41—611no—
430C23×D4—611no—
431C2×AGL(1,ℤ/8)—6116no—
432C2×AGL(1,ℤ/8)—618no—
433C22×SD16—611no—
434C22×SD16C2×D6111yescharacteristic
435C22×D8—611no—
436C22×D8—611no—
437C22×M16—611no—
438C23×C8—611no—
439#520—618no—
440#520—1224no—
441#518—618no—
442#518—1224no—
443C2×C4×Q8—611no—
444C2×C4×Q8C2×D6111yescharacteristic, complemented
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×C4×D4—611no—
450C2×C4×D4—1221no—
451C2×C4×D4—1221no—
452C2×C4×D4—1221no—
453C2×C4×D4—1221no—
454C2×C4×D4C2×D6111yescharacteristic
455C2×#117—611no—
456C2×#117—611no—
457C2×#117—1221no—
458C22×C4⋊C4—611no—
459C22×C4⋊C4—1221no—
460C22×C22⋊C4—1221no—
461C22×C22⋊C4—1221no—
462#442—618no—
463#442—618no—
464#440—618no—
465#440—618no—
466C4×SD16—618no—
467C4×SD16C2×D6118yescomplemented
468C4×D8—618no—
469C4×D8—618no—
470#428—618no—
471C2×#107—611no—
472C2×#107—611no—
473C2×#106—611no—
474C2×#106C2×D6111yescharacteristic, complemented
475#416—618no—
476C2×#103—611no—
477C2×#103C2×D6111yescharacteristic, complemented
478C2×#102—611no—
479C2×#102—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—618no—
484C2×#102C2×D6111yescharacteristic
485#405—618no—
486C2×#97—611no—
487C2×#97—611no—
488C2×C4×C8—611no—
489C2×C4×C8C2×D6111yescharacteristic, complemented
490C61C2×#294611yescharacteristic, complemented, Sylow
491C25—1221no—
492C2×#41—618no—
493C2×#41—614no—
494C2×#41—1222no—
495C2×#41—1224no—
496C22×Q8C22×D6111yescharacteristic
497C22×D4—618no—
498C22×D4—614no—
499C22×D4—611no—
500C22×D4—611no—
501C22×D4—1221no—
502C22×D4—1222no—
503C22×D4—1224no—
504C22×D4—1221no—
505C22×D4C22×D6111yescharacteristic
506C23×C4—21no—
507C23×C4—611no—
508C23×C4—1221no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4—1221no—
512C23×C4—1221no—
513C23×C4—1221no—
514C23×C4—1221no—
515AGL(1,ℤ/8)—6164no—
516C2×SD16—618no—
517C2×SD16—614no—
518C2×SD16C4×D6118yescomplemented
519C2×SD16C22×D6114yes—
520C2×D8—618no—
521C2×D8—614no—
522C2×D8—618no—
523C2×D8—614no—
524C2×M16—618no—
525C2×M16—614no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—614no—
529C22×C8—1224no—
530C22×C8C22×D6111yescharacteristic
531C22×C8C22×D6111yescharacteristic
532C4×Q8—22no—
533C4×Q8—614no—
534C4×Q8—1222no—
535C4×Q8C22×D6114yescomplemented
536C4×D4—22no—
537C4×D4—614no—
538C4×D4—614no—
539C4×D4—614no—
540C4×D4—614no—
541C4×D4—614no—
542C4×D4—1228no—
543C4×D4—1222no—
544C4×D4—1222no—
545C4×D4—1222no—
546C4×D4—1228no—
547C4×D4—1228no—
548C4×D4—1228no—
549C4×D4—1222no—
550C4×D4—1222no—
551C4×D4C22×D6114yes—
552#117—614no—
553#117—614no—
554#117—614no—
555#117—1228no—
556#117—1222no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—614no—
563C2×C4⋊C4—1228no—
564C2×C4⋊C4—1222no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—1228no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C42—21no—
581C2×C42—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C2×C42C22×D6111yescharacteristic
585#107—614no—
586#107—614no—
587#106—614no—
588#106C22×D6114yescomplemented
589#103—614no—
590#103C22×D6114yescomplemented
591#102—614no—
592#102—614no—
593#102—614no—
594#102—614no—
595#102—614no—
596#102C22×D6114yes—
597#97—614no—
598#97—614no—
599C4×C8—614no—
600C4×C8C22×D6114yescomplemented
601C24—21no—
602C24—611no—
603C24—1224no—
604C24—1228no—
605C24—1221no—
606C24—1221no—
607C24—4882no—
608C24—4882no—
609#41—6116no—
610#41—12216no—
611#41—1228no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8C2×C4×D6114yes—
615C2×Q8C23×D6112yes—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—6116no—
619C2×D4—614no—
620C2×D4—614no—
621C2×D4—612no—
622C2×D4—612no—
623C2×D4—1224no—
624C2×D4—1228no—
625C2×D4—12216no—
626C2×D4—1228no—
627C2×D4—1224no—
628C2×D4—1228no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1222no—
632C2×D4—1222no—
633C2×D4C2×C4×D6114yes—
634C2×D4C23×D6112yes—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—82no—
640C22×C4—611no—
641C22×C4—614no—
642C22×C4—612no—
643C22×C4—614no—
644C22×C4—612no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—1224no—
648C22×C4—1228no—
649C22×C4—1224no—
650C22×C4—1224no—
651C22×C4—1224no—
652C22×C4—1224no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1224no—
656C22×C4—1224no—
657C22×C4—4882no—
658C22×C4—4882no—
659C22×C4—4882no—
660C22×C4—4882no—
661C22×C4—4882no—
662C22×C4—4882no—
663C22×C4D4×D6111yescharacteristic
664C22×C4D4×D6111yescharacteristic
665C22×C4C23×D6111yescharacteristic
666SD16—6116no—
667SD16C2×C4×D61116yescomplemented
668D8—6116no—
669D8—6116no—
670M16—6116no—
671C2×C8—22no—
672C2×C8—614no—
673C2×C8—612no—
674C2×C8—612no—
675C2×C8—1228no—
676C2×C8—1222no—
677C2×C8C2×C4×D6114yes—
678C2×C8C23×D6112yes—
679C2×C8C23×D6112yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—614no—
684C4⋊C4—614no—
685C4⋊C4—612no—
686C4⋊C4—612no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4C23×D6112yes—
692C4⋊C4C23×D6112yes—
693C22⋊C4—24no—
694C22⋊C4—614no—
695C22⋊C4—614no—
696C22⋊C4—1224no—
697C22⋊C4—1224no—
698C22⋊C4—1224no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—1224no—
702C42—24no—
703C42—612no—
704C42—612no—
705C42—1224no—
706C42—1224no—
707C42D4×D6112yes—
708C42C23×D6112yes—
709C23—24no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—614no—
714C23—612no—
715C23—12216no—
716C23—1222no—
717C23—1222no—
718C23—1224no—
719C23—1224no—
720C23—1222no—
721C23—1222no—
722C23—48816no—
723C23—4884no—
724C23—4884no—
725C23—2442no—
726C23—2442no—
727C23—2442no—
728C23—2442no—
729C23C2×D4×D6111yescharacteristic
730Q8—24no—
731Q8—22no—
732Q8C22×C4×D6114yes—
733D4—24no—
734D4—22no—
735D4—614no—
736D4—614no—
737D4—12216no—
738D4—12216no—
739D4—1224no—
740D4—1224no—
741D4—1222no—
742D4—1222no—
743D4C22×C4×D6114yes—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—84no—
753C2×C4—614no—
754C2×C4—612no—
755C2×C4—618no—
756C2×C4—614no—
757C2×C4—614no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—12216no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—4884no—
766C2×C4—4884no—
767C2×C4—4884no—
768C2×C4—4884no—
769C2×C4—4884no—
770C2×C4—4884no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4C22×C4×D6112yes—
774C2×C4C2×D4×D6112yes—
775C2×C4C2×D4×D6112yes—
776C2×C4C2×D4×D6111yescharacteristic
777C2×C4#41×D6112yes—
778C2×C4C24×D6111yescharacteristic
779C8—22no—
780C8—614no—
781C8—1222no—
782C8C22×C4×D6114yes—
783C22—24no—
784C22—48no—
785C22—42no—
786C22—42no—
787C22—614no—
788C22—1228no—
789C22—1222no—
790C22—1222no—
791C22—1224no—
792C22—1224no—
793C22—48816no—
794C22—2448no—
795C22—2448no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22C4×D4×D6112yes—
801C22#1684056412yes—
802C22#1684056812yes—
803C22C22×D4×D6111yescharacteristic
804C4—24no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—42no—
809C4—614no—
810C4—1222no—
811C4—1222no—
812C4—2442no—
813C4—2442no—
814C4C4×D4×D6112yes—
815C4C23×C4×D6111yescharacteristic
816C4C2×#41×D6111yescharacteristic
817C2—44no—
818C2—1224no—
819C2—2444no—
820C2—2444no—
821C2#2145464614yesdirect product factor
822C2C2×C4×D4×D6111yescharacteristic
823C2C2×#1684056411yescharacteristic
824C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC22×#14519804C2
cosocleC2×C4×C61C25
hypercenterC2×C4×SD16D61
hypocenterC61C2×#2946
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#16840244C2semidirect
3. C2×#16840234C2semidirect
4. #21454646C2direct (N × H)
5. C2×#16839873C2semidirect
6. C2×#16839872C2semidirect
7. C2×#16839863C2semidirect
8. C2×#16839860C2semidirect
9. C2×#16839847C2semidirect
10. C2×C4×D488C2semidirect
11. C2×#16839842C2semidirect
12. C2×#16839801C2semidirect
13. C2×#16839757C2semidirect
14. C2×#102×D61C2semidirect
15. C2×#16839716C2semidirect
16. C2×C4×SD16×C61C2semidirect
19. C2×#14519804C4semidirect
27. #16840244C22semidirect
29. #16840234C22semidirect
30. C2×Q8×Dic61C22semidirect
33. C2×C4×D244C22semidirect
37. C2×#14519739C22semidirect
47. #16839873C22semidirect
48. #16839872C22semidirect
49. #16839863C22semidirect
50. #16839860C22semidirect
51. #16839847C22semidirect
52. C4×D488C22semidirect
53. #16839842C22semidirect
54. #16839801C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519708C22semidirect
58. #16839757C22semidirect
59. C2×#14519701C22semidirect
61. C2×#14519699C22semidirect
64. C2×#14519697C22semidirect
65. #102×D61C22semidirect
66. #16839716C22semidirect
67. C2×#14519688C22semidirect
68. C2×#14519687C22semidirect
69. C2×C8×Dic61C22semidirect
71. C2×C4×Q8×C61C22semidirect
73. C4×SD16×C61C22semidirect
74. C2×#106×C61C22semidirect
75. C2×#103×C61C22semidirect
77. C2×C4×C8×C61C22semidirect
81. C2×#11758226C2×C4semidirect
89. C2×D4×D61C2×C4semidirect
99. #14519804C2×C4semidirect
100. C2×#11758201C2×C4semidirect
102. C2×D488C2×C4semidirect
104. C2×#11758199C2×C4semidirect
106. C2×#11758189C2×C4semidirect
113. Q8×Dic61C23semidirect
118. C4×D244C23semidirect
125. #14519739C23semidirect
155. #14519711C23semidirect
156. #14519710C23semidirect
157. #14519708C23semidirect
158. #14519701C23semidirect
160. #14519699C23semidirect
163. #14519697C23semidirect
164. #14519688C23semidirect
165. #14519687C23semidirect
166. C8×Dic61C23semidirect
170. C2×SD16×C61C2×C4semidirect
175. C4×Q8×C61C23semidirect
184. #106×C61C23semidirect
185. #103×C61C23semidirect
187. C4×C8×C61C23semidirect
223. #11758226C22×C4semidirect
226. D4×D61C22×C4semidirect
253. SD16×C61C22×C4semidirect
268. #11758201C22×C4semidirect
269. #11758199C22×C4semidirect
293. D488C22×C4semidirect
294. #11758189C22×C4semidirect
414. C2×C4×SD16D61semidirect
422. C2×C61#2946semidirect
444. C2×C4×Q8C2×D61semidirect
467. C4×SD16C2×D61semidirect
474. C2×#106C2×D61semidirect
477. C2×#103C2×D61semidirect
489. C2×C4×C8C2×D61semidirect
490. C61C2×#2946semidirect
518. C2×SD16C4×D61semidirect
535. C4×Q8C22×D61semidirect
588. #106C22×D61semidirect
590. #103C22×D61semidirect
600. C4×C8C22×D61semidirect
667. SD16C2×C4×D61semidirect
821. C2#21454646direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198042
C2×#168402442
C2×#168402342
#214546462
C2×#168398732
C2×#168398722
C2×#168398632
C2×#168398602
C2×#168398472
C2×C4×D4882
C2×#168398422
C2×#168398012
C2×#168397572
C2×#102×D612
C2×#168397162
C2×C4×SD16×C612
C2×#294661