Finite Group Databasebeta

← C2×#21456888 #30551353

Subgroups — C2×#21456888 #30551353

Order 15616.

2214 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840370C211yesmaximal, characteristic, complemented
2C2×#16840330C211yesmaximal, characteristic
3#21456888C2116yesmaximal, direct product factor
4C2×#16840155C211yesmaximal, characteristic, complemented
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16840125C211yesmaximal, characteristic, complemented
7C2×#16840118C211yesmaximal, characteristic, complemented
8C2×#16839981C211yesmaximal, characteristic, complemented
9C2×#16839963C211yesmaximal, characteristic, complemented
10C2×#16839962C211yesmaximal, characteristic, complemented
11C2×#16839927C211yesmaximal, characteristic, complemented
12C2×#16839923C211yesmaximal, characteristic, complemented
13C2×#16839914C211yesmaximal, characteristic, complemented
14C2×#16839911C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic, complemented
20C22×#11758190C2211yescharacteristic
21C22×#11758190C2211yescharacteristic, complemented
22C22×#11758200C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758201C2211yescharacteristic, complemented
25#16840370—24no—
26#16840370C2218yescomplemented
27#16840330—24no—
28#16840330C2218yes—
29C2×#14519775C2211yescharacteristic, complemented
30C2×#14519774C2211yescharacteristic
31C2×#14519773C2211yescharacteristic
32C2×#14519772—21no—
33C2×#14519771—21no—
34C2×#14519769—21no—
35C2×#14519768C2211yescharacteristic, complemented
36C2×#14519767—21no—
37C2×#14519766C2211yescharacteristic
38C2×#14519757C2211yescharacteristic
39C2×#14519753C2211yescharacteristic
40C2×#14519750—21no—
41C2×#14519750—21no—
42C2×#14519747—21no—
43C2×#14519747—21no—
44C2×C4×Dic122C2211yescharacteristic, complemented
45C2×#14519734C2211yescharacteristic
46#16840155C2218yescomplemented
47#16840133C2218yescomplemented
48#16840125C2218yescomplemented
49#16840118C2218yescomplemented
50#16839981C2218yescomplemented
51#16839963C2218yescomplemented
52#16839962C2218yescomplemented
53#16839927C2218yescomplemented
54#16839923C2218yescomplemented
55#16839914C2218yescomplemented
56#16839911C2218yescomplemented
57#16839822C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic, complemented
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C22×Q16×C61C2211yescharacteristic, complemented
70C22×SD16×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic, complemented
73C61×#464C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic, complemented
75C2×#103×C61C2211yescharacteristic, complemented
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C2×#11758226—22no—
79C2×#11758226—42no—
80C2×#11758226—42no—
81C2×#11758226C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244—21no—
85C22×D244—21no—
86C22×D244C2311yescharacteristic
87C22×D244C2311yescharacteristic
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C2×D4×D61—22no—
92C2×D4×D61—42no—
93C2×D4×D61—42no—
94C2×D4×D61C2314yes—
95C22×C4×D61—21no—
96C22×C4×D61C2311yescharacteristic
97C2×#11758202—42no—
98C2×#11758202C2314yescomplemented
99C2×#11758190—42no—
100C2×#11758190—42no—
101C2×#11758190C2314yes—
102C2×#11758190C2314yescomplemented
103C2×#11758200—42no—
104C2×#11758200C2314yes—
105C2×#11758201—42no—
106C2×#11758201—42no—
107C2×#11758201C2314yes—
108C2×#11758201C2314yescomplemented
109C22×#92418C2311yescharacteristic
110C22×#92418C2311yescharacteristic
111#14519775—22no—
112#14519775C2314yescomplemented
113#14519774—22no—
114#14519774C2314yes—
115#14519773—22no—
116#14519773C2314yes—
117#14519772—28no—
118#14519771—28no—
119#14519769—28no—
120#14519768—22no—
121#14519768C2314yescomplemented
122#14519767—28no—
123#14519766—22no—
124#14519766C2314yes—
125#14519757—22no—
126#14519757C2314yes—
127#14519753—22no—
128#14519753C2314yes—
129#14519750—28no—
130#14519750—28no—
131#14519747—28no—
132#14519747—28no—
133C4×Dic122—22no—
134C4×Dic122C2314yescomplemented
135#14519734D414yes—
136#14519734C2314yes—
137C2×C4⋊Dic61—21no—
138C2×C4⋊Dic61—21no—
139C2×C4⋊Dic61C2311yescharacteristic
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758196—21no—
144C2×#11758196—21no—
145C2×#11758196D411yescharacteristic
146C2×#11758196D411yescharacteristic
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198D411yescharacteristic
152C2×#11758198D411yescharacteristic
153C2×C4×Dic61—21no—
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yescomplemented
156#14519701C2314yescomplemented
157#14519699C2314yes—
158#14519699C2314yescomplemented
159#14519698C2314yes—
160#14519697C2314yes—
161#14519697C2314yescomplemented
162#14519689C2314yes—
163#14519689C2314yes—
164#14519687C2314yescomplemented
165C8×Dic61C2314yescomplemented
166C22×Q8×C61C2311yescharacteristic
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C2×Q16×C61—42no—
170C2×Q16×C61C2314yescomplemented
171C2×SD16×C61—42no—
172C2×SD16×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175#124×C61—22no—
176#124×C61C2314yes—
177C4×Q8×C61—22no—
178C4×Q8×C61C2314yescomplemented
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C4⋊C8×C61C2314yescomplemented
186#103×C61C2314yescomplemented
187#102×C61C2314yes—
188C24×C61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—24no—
192C23×D61—44no—
193C23×D61—82no—
194C23×D61—82no—
195C23×D61C2×D411yescharacteristic
196C2×Q8×C61—21no—
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61—22no—
202C2×Q8×C61C2412yes—
203C2×Q8×C61C2412yes—
204C2×D4×C61—21no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61C2412yes—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214C2×C22⋊D61—24no—
215C2×C22⋊D61—24no—
216C2×C22⋊D61—24no—
217C2×C22⋊D61—44no—
218C2×C22⋊D61—82no—
219C2×C22⋊D61—82no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758226—44no—
226#11758226—44no—
227#11758226—48no—
228D4×D61—44no—
229D4×D61—44no—
230D4×D61—48no—
231C2×D244—22no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—22no—
235C2×D244—24no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—24no—
239C2×D244—24no—
240C2×D244—44no—
241C2×D244—82no—
242C2×D244—82no—
243C2×D244C2412yes—
244C2×D244C2412yes—
245C2×C4×D61—22no—
246C2×C4×D61—22no—
247C2×C4×D61—24no—
248C2×C4×D61—44no—
249C2×C4×D61C2×D412yes—
250C2×C4×D61C2412yes—
251C2×Dic122—22no—
252C2×Dic122—22no—
253C2×Dic122—21no—
254C2×Dic122C2412yes—
255Q16×C61—44no—
256SD16×C61—44no—
257C2×C8×C61—22no—
258C2×C8×C61—22no—
259C2×C8×C61C2412yes—
260C2×C8×C61C2412yes—
261C4⋊C4×C61—24no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C2412yes—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—24no—
266C42×C61—24no—
267C42×C61C2×D412yes—
268C42×C61C2412yes—
269#11758202—44no—
270#11758201—44no—
271#11758201—44no—
272#11758200—44no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198C2×D414yes—
278#11758198C2×D414yes—
279C4⋊Dic61—21no—
280C4⋊Dic61—24no—
281C4⋊Dic61—24no—
282C4⋊Dic61C2412yes—
283#11758196—24no—
284#11758196—24no—
285#11758196—24no—
286#11758196—24no—
287#11758196—24no—
288#11758196C2×D414yes—
289#11758196C2×D414yes—
290C4×Dic61—24no—
291C4×Dic61C2×D412yes—
292C4×Dic61C2412yes—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418C2412yes—
296C2×#92418C2412yes—
297#11758190—44no—
298#11758190—44no—
299C23×C61—22no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—48no—
310C22×D61—42no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—84no—
317C22×D61—84no—
318C22×D61—816no—
319C22×D61C22×D412yes—
320Q8×C61—22no—
321Q8×C61—22no—
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—42no—
325Q8×C61—42no—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—42no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—42no—
335C2×C4×C61—42no—
336C2×C4×C61—42no—
337C2×C4×C61C22×D412yes—
338C2×C4×C61C22×D412yes—
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61H(5,𝔽2)12yes—
341C2×C4×C61H(5,𝔽2)12yes—
342C2×C4×C61C2511yescharacteristic
343C22⋊D61—48no—
344C22⋊D61—84no—
345C22⋊D61—84no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—42no—
352C2×Dic61—42no—
353C2×Dic61C22×D412yes—
354C2×Dic61C22×D412yes—
355C2×Dic61C22×D412yes—
356D244—22no—
357D244—22no—
358D244—22no—
359D244—22no—
360D244—48no—
361D244—42no—
362D244—42no—
363D244—84no—
364D244—84no—
365C4×D61—24no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—48no—
369Dic122—22no—
370Dic122—22no—
371Dic122—42no—
372C8×C61—22no—
373C8×C61—22no—
374#92418—22no—
375#92418—22no—
376C2×#3222—611nomaximal, Sylow
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—84no—
381C22×C61#53512yes—
382C22×C61#57712yes—
383C22×C61#57712yes—
384C22×C61C23×D411yescharacteristic
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—44no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—816no—
396C2×D61—84no—
397C2×D61—84no—
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61#53512yes—
404C4×C61C2×H(5,𝔽2)11yescharacteristic
405C4×C61C2×H(5,𝔽2)11yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—22no—
409Dic61—42no—
410Dic61—42no—
411C2×#541—611no—
412C2×#535—611no—
413#3222—6116no—
414C2×#497—611no—
415C2×#492—611no—
416C2×#490—611no—
417C2×#488—611no—
418C2×#464—611no—
419C2×#464D6111yescharacteristic, complemented
420C2×#460—611no—
421C2×#460—611no—
422C2×#452—611no—
423C2×#452—611no—
424C2×#450—611no—
425C2×#450—611no—
426C2×#433—611no—
427C2×C61—82no—
428C2×C61#322214yescomplemented
429C2×C61C2×#53511yescharacteristic
430C2×C61C2×#57711yescharacteristic
431C2×C61C2×#57711yescharacteristic
432D61—42no—
433D61—82no—
434D61—82no—
435C22×#41—611no—
436C23×D4—611no—
437C22×Q16—611no—
438C22×Q16C2×D6111yescharacteristic, complemented
439C22×SD16—611no—
440C22×SD16—611no—
441C22×SD16—611no—
442C22×SD16—611no—
443C22×SD16—611no—
444C22×SD16C2×D6111yescharacteristic
445#541—618no—
446#541—1224no—
447#535—618no—
448#535—1224no—
449C2×C4⋊Q8—611no—
450C2×#127—611no—
451C2×#127—611no—
452C2×#126—1221no—
453C2×#126—1221no—
454C2×#125—611no—
455C2×#125—1221no—
456C2×#125—1221no—
457C2×#124—611no—
458C2×#124C2×D6111yescharacteristic
459C2×C22⋊Q8—611no—
460C2×C22⋊Q8—611no—
461C2×#121—1221no—
462C2×#121—1221no—
463C2×#120—1221no—
464C2×#120—1221no—
465C2×C4×Q8—611no—
466C2×C4×Q8C2×D6111yescharacteristic, complemented
467C2×#117—611no—
468#497—618no—
469#492—618no—
470#490—618no—
471#488—618no—
472#464—618no—
473#464C2×D6118yescomplemented
474#460—618no—
475#460—618no—
476#452—618no—
477#452—618no—
478#450—618no—
479#450—618no—
480#433—618no—
481C2×C4⋊C8—611no—
482C2×C4⋊C8C2×D6111yescharacteristic, complemented
483C2×#103—611no—
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102C2×D6111yescharacteristic
491C2×C22⋊C8—611no—
492C2×C22⋊C8—611no—
493C2×#97—611no—
494C2×C4×C8—611no—
495C61C2×#322211yescharacteristic, complemented, Sylow
496C25—1221no—
497C2×#41—614no—
498C2×#41—1222no—
499C2×#41—2442no—
500C2×#41—2442no—
501C22×Q8—611no—
502C22×Q8C22×D6111yescharacteristic
503C22×Q8C22×D6111yescharacteristic
504C22×D4—614no—
505C22×D4—611no—
506C22×D4—611no—
507C22×D4—1221no—
508C22×D4—1222no—
509C22×D4—1221no—
510C22×D4—1221no—
511C22×D4—1221no—
512C22×D4—1221no—
513C22×D4—1221no—
514C22×D4—2442no—
515C22×D4—2442no—
516C22×D4C22×D6111yescharacteristic
517C23×C4—611no—
518C23×C4—1221no—
519C2×Q16—42no—
520C2×Q16—614no—
521C2×Q16—2442no—
522C2×Q16C22×D6114yescomplemented
523C2×SD16—42no—
524C2×SD16—614no—
525C2×SD16—614no—
526C2×SD16—614no—
527C2×SD16—614no—
528C2×SD16—614no—
529C2×SD16—2442no—
530C2×SD16—2442no—
531C2×SD16—2442no—
532C2×SD16—2442no—
533C2×SD16—2442no—
534C2×SD16C22×D6114yes—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8C22×D6111yescharacteristic
538C22×C8C22×D6111yescharacteristic
539C4⋊Q8—614no—
540C4⋊Q8—1222no—
541#127—614no—
542#127—614no—
543#127—1222no—
544#127—1222no—
545#126—1228no—
546#126—1228no—
547#125—614no—
548#125—1228no—
549#125—1222no—
550#125—1228no—
551#124—22no—
552#124—614no—
553#124—1222no—
554#124C22×D6114yes—
555C22⋊Q8—614no—
556C22⋊Q8—614no—
557C22⋊Q8—1222no—
558C22⋊Q8—1222no—
559#121—1228no—
560#121—1228no—
561#120—1228no—
562#120—1228no—
563C4×Q8—22no—
564C4×Q8—614no—
565C4×Q8—1222no—
566C4×Q8C22×D6114yescomplemented
567#117—614no—
568#117—614no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—611no—
584C2×C22⋊C4—611no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C42—21no—
590C2×C42—611no—
591C2×C42—1221no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—614no—
594C4⋊C8C22×D6114yescomplemented
595#103—614no—
596#103C22×D6114yescomplemented
597#102—614no—
598#102—614no—
599#102—614no—
600#102—614no—
601#102—614no—
602#102C22×D6114yes—
603C22⋊C8—614no—
604C22⋊C8—614no—
605#97—614no—
606C4×C8—614no—
607C24—21no—
608C24—611no—
609C24—1224no—
610C24—1221no—
611C24—1221no—
612C24—4882no—
613C24—4882no—
614C24—2444no—
615#41—2444no—
616#41—2444no—
617#41—2448no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—612no—
625C2×Q8—1221no—
626C2×Q8—1222no—
627C2×Q8—1222no—
628C2×Q8C23×D6112yes—
629C2×Q8C23×D6112yes—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—612no—
634C2×D4—612no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1222no—
644C2×D4—1222no—
645C2×D4—1222no—
646C2×D4—1222no—
647C2×D4—4882no—
648C2×D4—4882no—
649C2×D4—4882no—
650C2×D4—4882no—
651C2×D4—2444no—
652C2×D4—2444no—
653C2×D4—2444no—
654C2×D4—2448no—
655C2×D4—2444no—
656C2×D4C23×D6112yes—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—1224no—
666C22×C4—1222no—
667C22×C4—1222no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—2444no—
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—44no—
675Q16—2444no—
676SD16—44no—
677SD16—2444no—
678SD16—2444no—
679SD16—2444no—
680SD16—2444no—
681SD16—2444no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—612no—
685C2×C8—612no—
686C2×C8—1222no—
687C2×C8—1222no—
688C2×C8C23×D6112yes—
689C2×C8C23×D6112yes—
690C4⋊C4—24no—
691C4⋊C4—21no—
692C4⋊C4—614no—
693C4⋊C4—614no—
694C4⋊C4—612no—
695C4⋊C4—1224no—
696C4⋊C4—1224no—
697C4⋊C4—1224no—
698C4⋊C4—1224no—
699C4⋊C4—1224no—
700C4⋊C4—1224no—
701C4⋊C4—1221no—
702C4⋊C4—1224no—
703C4⋊C4C23×D6112yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—614no—
707C22⋊C4—614no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C42—24no—
713C42—612no—
714C42—612no—
715C42—1224no—
716C42D4×D6112yes—
717C42C23×D6112yes—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—612no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23—4884no—
729C23—4884no—
730C23—48816no—
731C23—2448no—
732C23—2442no—
733C23—2442no—
734C23—2442no—
735C23—2442no—
736C23—2442no—
737C23—2442no—
738C23C2×D4×D6111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—1222no—
746Q8—1222no—
747Q8—2442no—
748D4—22no—
749D4—22no—
750D4—42no—
751D4—1222no—
752D4—1222no—
753D4—1222no—
754D4—1222no—
755D4—4884no—
756D4—4884no—
757D4—4884no—
758D4—4884no—
759D4—2448no—
760D4—2448no—
761D4—2442no—
762D4—2442no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—612no—
772C2×C4—612no—
773C2×C4—612no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1224no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—2448no—
783C2×C4—2442no—
784C2×C4—2442no—
785C2×C4C2×D4×D6112yes—
786C2×C4C2×D4×D6112yes—
787C2×C4C2×D4×D6111yescharacteristic
788C2×C4#1451982212yes—
789C2×C4#1451982312yes—
790C2×C4C24×D6111yescharacteristic
791C8—22no—
792C8—22no—
793C8—1222no—
794C8—1222no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—84no—
799C22—1222no—
800C22—1222no—
801C22—1222no—
802C22—48816no—
803C22—4884no—
804C22—4884no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—2442no—
810C22—2442no—
811C22—2444no—
812C22#1684032812yes—
813C22#1684056912yes—
814C22#1684057112yes—
815C22C22×D4×D6111yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—1222no—
822C4—1222no—
823C4—1222no—
824C4—2442no—
825C4—2442no—
826C4#1684032812yes—
827C4C2×#1451982211yescharacteristic
828C4C2×#1451982311yescharacteristic
829C2—82no—
830C2—4882no—
831C2—4882no—
832C2—2442no—
833C2#2145688814yesdirect product factor
834C2C2×#1684032811yescharacteristic
835C2C2×#1684056911yescharacteristic
836C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC2×#16840330C2
hypercenterC2×#464D61
hypocenterC61C2×#3222
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16840370C2semidirect
3. #21456888C2direct (N × H)
4. C2×#16840155C2semidirect
5. C2×#16840133C2semidirect
6. C2×#16840125C2semidirect
7. C2×#16840118C2semidirect
8. C2×#16839981C2semidirect
9. C2×#16839963C2semidirect
10. C2×#16839962C2semidirect
11. C2×#16839927C2semidirect
12. C2×#16839923C2semidirect
13. C2×#16839914C2semidirect
14. C2×#16839911C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#464C2semidirect
19. C22×#11758202C22semidirect
21. C22×#11758190C22semidirect
24. C22×#11758201C22semidirect
26. #16840370C22semidirect
29. C2×#14519775C22semidirect
35. C2×#14519768C22semidirect
44. C2×C4×Dic122C22semidirect
46. #16840155C22semidirect
47. #16840133C22semidirect
48. #16840125C22semidirect
49. #16840118C22semidirect
50. #16839981C22semidirect
51. #16839963C22semidirect
52. #16839962C22semidirect
53. #16839927C22semidirect
54. #16839923C22semidirect
55. #16839914C22semidirect
56. #16839911C22semidirect
57. #16839822C22semidirect
58. C2×C4⋊#92418C22semidirect
59. C2×#14519701C22semidirect
61. C2×#14519699C22semidirect
64. C2×#14519697C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
69. C22×Q16×C61C22semidirect
72. C2×C4×Q8×C61C22semidirect
73. C61×#464C22semidirect
74. C2×C4⋊C8×C61C22semidirect
75. C2×#103×C61C22semidirect
98. C2×#11758202C23semidirect
102. C2×#11758190C23semidirect
108. C2×#11758201C23semidirect
112. #14519775C23semidirect
121. #14519768C23semidirect
134. C4×Dic122C23semidirect
155. C4⋊#92418C23semidirect
156. #14519701C23semidirect
158. #14519699C23semidirect
161. #14519697C23semidirect
164. #14519687C23semidirect
165. C8×Dic61C23semidirect
170. C2×Q16×C61C23semidirect
178. C4×Q8×C61C23semidirect
185. C4⋊C8×C61C23semidirect
186. #103×C61C23semidirect
419. C2×#464D61semidirect
428. C2×C61#3222semidirect
438. C22×Q16C2×D61semidirect
466. C2×C4×Q8C2×D61semidirect
473. #464C2×D61semidirect
482. C2×C4⋊C8C2×D61semidirect
484. C2×#103C2×D61semidirect
495. C61C2×#3222semidirect
522. C2×Q16C22×D61semidirect
566. C4×Q8C22×D61semidirect
594. C4⋊C8C22×D61semidirect
596. #103C22×D61semidirect
833. C2#21456888direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403702
C2×#168403302
#214568882
C2×#168401552
C2×#168401332
C2×#168401252
C2×#168401182
C2×#168399812
C2×#168399632
C2×#168399622
C2×#168399272
C2×#168399232
C2×#168399142
C2×#168399112
C2×#168398222
C2×C61×#4642
C2×#322261