Finite Group Databasebeta

← C2×#21456930 #30551410

Subgroups — C2×#21456930 #30551410

Order 15616.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840383C211yesmaximal, characteristic, complemented
2C2×#16840338C211yesmaximal, characteristic, complemented
3#21456930C2116yesmaximal, direct product factor
4C2×#16840156C211yesmaximal, characteristic, complemented
5C2×#16840146C211yesmaximal, characteristic, complemented
6C2×#16840122C211yesmaximal, characteristic, complemented
7C2×#16840113C211yesmaximal, characteristic, complemented
8C2×#16839985C211yesmaximal, characteristic, complemented
9C2×#16839973C211yesmaximal, characteristic, complemented
10C2×#16839978C211yesmaximal, characteristic, complemented
11C2×#16839968C211yesmaximal, characteristic, complemented
12C2×#16839926C211yesmaximal, characteristic, complemented
13C2×#16839909C211yesmaximal, characteristic
14C2×#16839920C211yesmaximal, characteristic, complemented
15C2×#16839903C211yesmaximal, characteristic, complemented
16C2×C61×#433C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×Dic122C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×Dic244C2211yescharacteristic
22C22×#11758190C2211yescharacteristic
23C22×#11758190C2211yescharacteristic
24C22×#11758190C2211yescharacteristic
25C22×#11758190C2211yescharacteristic
26C22×D488C2211yescharacteristic
27#16840383—24no—
28#16840383C2218yescomplemented
29#16840338—24no—
30#16840338C2218yescomplemented
31C2×#14519777C2211yescharacteristic
32C2×#14519777C2211yescharacteristic
33C2×#14519777C2211yescharacteristic
34C2×#14519772—21no—
35C2×#14519765C2211yescharacteristic
36C2×#14519765C2211yescharacteristic
37C2×#14519765C2211yescharacteristic
38C2×#14519763—21no—
39C2×#14519761—21no—
40C2×#14519761—21no—
41C2×#14519759—21no—
42C2×#14519757—21no—
43C2×#14519757—21no—
44C2×#14519756C2211yescharacteristic
45C2×#14519755—21no—
46C2×#14519751C2211yescharacteristic
47C2×C4×Dic122C2211yescharacteristic
48C2×C4×D244C2211yescharacteristic
49#16840156C2218yescomplemented
50#16840146C2218yescomplemented
51#16840122C2218yescomplemented
52#16840113C2218yescomplemented
53#16839985C2218yescomplemented
54#16839978C2218yescomplemented
55#16839973C2218yescomplemented
56#16839968C2218yescomplemented
57#16839926C2218yescomplemented
58#16839920C2218yescomplemented
59#16839909C2218yes—
60#16839903C2218yescomplemented
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519702C2211yescharacteristic
65C2×#14519702C2211yescharacteristic
66C2×#14519702C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C2×#117×C61C2211yescharacteristic
70C61×#433C2218yescomplemented
71C2×C4⋊C8×C61C2211yescharacteristic
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122—22no—
83C22×Dic122—21no—
84C22×Dic122—42no—
85C22×Dic122—42no—
86C22×Dic122C2311yescharacteristic
87C22×Dic122C2311yescharacteristic
88C22×Dic122C2311yescharacteristic
89C22×Dic122C2311yescharacteristic
90C22×Dic122C2314yes—
91C22×D244C2311yescharacteristic
92C22×D244C2311yescharacteristic
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C23×Dic61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C2×Dic244—42no—
99C2×Dic244—42no—
100C2×Dic244—42no—
101C2×Dic244C2314yes—
102C2×Dic244C2314yes—
103C2×Dic244C2314yes—
104C2×#11758190—42no—
105C2×#11758190—42no—
106C2×#11758190—42no—
107C2×#11758190—42no—
108C2×#11758190C2314yes—
109C2×#11758190C2314yes—
110C2×#11758190C2314yes—
111C2×#11758190C2314yes—
112C2×D488—42no—
113C2×D488C2314yes—
114#14519777—22no—
115#14519777—22no—
116#14519777—22no—
117#14519777C2314yes—
118#14519777C2314yes—
119#14519777C2314yes—
120#14519772—28no—
121#14519765—22no—
122#14519765—22no—
123#14519765—22no—
124#14519765C2314yes—
125#14519765C2314yes—
126#14519765C2314yes—
127#14519763—28no—
128#14519761—28no—
129#14519761—28no—
130#14519759—28no—
131#14519757—28no—
132#14519757—28no—
133#14519756—22no—
134#14519756C2314yes—
135#14519755—28no—
136#14519751—22no—
137#14519751C2314yes—
138C4×Dic122—22no—
139C4×Dic122C2314yes—
140C4×D244—22no—
141C4×D244C2314yes—
142C2×C4⋊Dic61—21no—
143C2×C4⋊Dic61—21no—
144C2×C4⋊Dic61—21no—
145C2×C4⋊Dic61—21no—
146C2×C4⋊Dic61—21no—
147C2×C4⋊Dic61C2311yescharacteristic
148C2×C4⋊Dic61C2311yescharacteristic
149C2×#11758196—21no—
150C2×#11758196—21no—
151C2×C22⋊Dic61—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198—21no—
157C2×#11758198—21no—
158C2×#11758198—21no—
159C2×#11758198—21no—
160C2×C4×Dic61—21no—
161#14519702C2314yes—
162#14519702C2314yes—
163#14519702C2314yes—
164#14519702C2314yes—
165#14519702C2314yes—
166#14519702C2314yes—
167#14519699C2314yes—
168#14519699C2314yes—
169C23×C4×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#117×C61D414yes—
175#117×C61C2314yes—
176C2×C4⋊C4×C61D411yescharacteristic
177C2×C4⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183C4⋊C8×C61C2314yes—
184C22⋊C8×C61C2314yes—
185C22⋊C8×C61C2314yes—
186#97×C61C2314yes—
187C4×C8×C61C2314yes—
188C24×C61C2×D411yescharacteristic
189C23×D61—21no—
190C23×D61—21no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2412yes—
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—44no—
204C2×C22⋊D61—82no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—24no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—44no—
213#11758222—44no—
214#11758222—44no—
215#11758222—48no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244C2412yes—
223C2×D244C2412yes—
224C2×C4×D61—24no—
225C2×C4×D61—24no—
226C2×C4×D61—44no—
227C2×C4×D61—82no—
228C2×Dic122—22no—
229C2×Dic122—22no—
230C2×Dic122—22no—
231C2×Dic122—22no—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—24no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—24no—
242C2×Dic122—44no—
243C2×Dic122—44no—
244C2×Dic122—44no—
245C2×Dic122—48no—
246C2×Dic122—82no—
247C2×Dic122C2412yes—
248C2×Dic122C2412yes—
249C2×Dic122C2412yes—
250C2×Dic122C2412yes—
251C2×C8×C61—22no—
252C2×C8×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61C2412yes—
256C2×C8×C61C2412yes—
257C2×C8×C61C2412yes—
258C2×C8×C61C2412yes—
259C4⋊C4×C61C2×D414yes—
260C4⋊C4×C61C2×D414yes—
261C22⋊C4×C61C2×D414yes—
262C22⋊C4×C61C2×D414yes—
263C42×C61C2×D412yes—
264C42×C61C2×D412yes—
265C42×C61C2412yes—
266C42×C61C2412yes—
267C22⋊Dic61—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276C4⋊Dic61—24no—
277C4⋊Dic61—24no—
278C4⋊Dic61—24no—
279C4⋊Dic61—24no—
280C4⋊Dic61—24no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C2412yes—
284C4⋊Dic61C2412yes—
285#11758196—24no—
286#11758196—24no—
287C4×Dic61—24no—
288Dic244—44no—
289Dic244—44no—
290Dic244—44no—
291D488—44no—
292#11758190—44no—
293#11758190—44no—
294#11758190—44no—
295#11758190—44no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61C22×D412yes—
300C23×C61C22×D411yescharacteristic
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—24no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D412yes—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61H(5,𝔽2)12yes—
324C2×C4×C61H(5,𝔽2)12yes—
325C2×C4×C61C2511yescharacteristic
326C22⋊D61—48no—
327C22⋊D61—84no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—48no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—22no—
345D244—42no—
346D244—42no—
347C4×D61—48no—
348C4×D61—84no—
349Dic122—22no—
350Dic122—22no—
351Dic122—22no—
352Dic122—22no—
353Dic122—22no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—48no—
358Dic122—42no—
359Dic122—42no—
360Dic122—42no—
361Dic122—42no—
362Dic122—84no—
363C8×C61—22no—
364C8×C61—22no—
365C8×C61—22no—
366C8×C61—22no—
367C2×#3225—611nomaximal, Sylow
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—44no—
372C22×C61#53512yes—
373C22×C61#57712yes—
374C22×C61#57812yes—
375C22×C61C23×D411yescharacteristic
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—84no—
383C2×D61—84no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61#53512yes—
390C4×C61C2×H(5,𝔽2)11yescharacteristic
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392Dic61—42no—
393Dic61—42no—
394Dic61—42no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#542—611no—
399C2×#536—611no—
400#3225—6116no—
401C2×#497—611no—
402C2×#495—611no—
403C2×#489—611no—
404C2×#487—611no—
405C2×#464—611no—
406C2×#462—611no—
407C2×#463—611no—
408C2×#461—611no—
409C2×#452—611no—
410C2×#449—611no—
411C2×#451—611no—
412C2×#448—611no—
413C2×#433D6111yescharacteristic, complemented
414C2×C61—42no—
415C2×C61#322514yescomplemented
416C2×C61C2×#53511yescharacteristic
417C2×C61C2×#57711yescharacteristic
418C2×C61C2×#57811yescharacteristic
419D61—82no—
420D61—82no—
421C22×#41—611no—
422C23×Q8—611no—
423C22×Q16—611no—
424C22×Q16—611no—
425C22×Q16—611no—
426C22×SD16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×SD16—611no—
430C22×D8—611no—
431#542—618no—
432#542—1224no—
433#536—618no—
434#536—1224no—
435C2×C4⋊Q8—611no—
436C2×C4⋊Q8—611no—
437C2×C4⋊Q8—611no—
438C2×#126—1221no—
439C2×#124—611no—
440C2×#124—611no—
441C2×#124—611no—
442C2×#124—1221no—
443C2×#123—1221no—
444C2×#123—1221no—
445C2×#123—1221no—
446C2×C22⋊Q8—611no—
447C2×C22⋊Q8—1221no—
448C2×C22⋊Q8—1221no—
449C2×C22⋊Q8—1221no—
450C2×#121—611no—
451C2×C4×Q8—611no—
452C2×C4×D4—611no—
453C2×#117C2×D6111yescharacteristic
454#497—618no—
455#495—618no—
456#489—618no—
457#487—618no—
458#464—618no—
459#463—618no—
460#462—618no—
461#461—618no—
462#452—618no—
463#451—618no—
464#449—618no—
465#448—618no—
466#433C2×D6118yescomplemented
467C2×C4⋊C8C2×D6111yescharacteristic
468C2×C4⋊C8C2×D6111yescharacteristic
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×C22⋊C8C2×D6111yescharacteristic
478C2×C22⋊C8C2×D6111yescharacteristic
479C2×#97C2×D6111yescharacteristic
480C2×C4×C8C2×D6111yescharacteristic
481C61C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—614no—
483C2×#41—1222no—
484C2×#41—2442no—
485C2×#41—2442no—
486C22×Q8—611no—
487C22×Q8—611no—
488C22×Q8—611no—
489C22×Q8—611no—
490C22×Q8—614no—
491C22×Q8—1221no—
492C22×Q8—1221no—
493C22×Q8—1222no—
494C22×Q8—2442no—
495C22×Q8—2442no—
496C22×D4—611no—
497C22×D4—611no—
498C22×D4—1221no—
499C22×D4—1221no—
500C23×C4—1221no—
501C23×C4—1221no—
502C23×C4—1221no—
503C23×C4C22×D6111yescharacteristic
504C2×Q16—614no—
505C2×Q16—614no—
506C2×Q16—614no—
507C2×Q16—2442no—
508C2×Q16—2442no—
509C2×Q16—2442no—
510C2×SD16—614no—
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16—614no—
514C2×SD16—2442no—
515C2×SD16—2442no—
516C2×SD16—2442no—
517C2×SD16—2442no—
518C2×D8—614no—
519C2×D8—2442no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522C22×C8C22×D6111yescharacteristic
523C22×C8C22×D6111yescharacteristic
524C4⋊Q8—614no—
525C4⋊Q8—614no—
526C4⋊Q8—614no—
527C4⋊Q8—1222no—
528C4⋊Q8—1222no—
529C4⋊Q8—1222no—
530#126—1228no—
531#124—614no—
532#124—614no—
533#124—614no—
534#124—1228no—
535#124—1222no—
536#124—1222no—
537#124—1222no—
538#123—1228no—
539#123—1228no—
540#123—1228no—
541C22⋊Q8—614no—
542C22⋊Q8—1222no—
543C22⋊Q8—1228no—
544C22⋊Q8—1228no—
545C22⋊Q8—1228no—
546#121—614no—
547#121—1222no—
548C4×Q8—614no—
549C4×Q8—1222no—
550C4×D4—614no—
551C4×D4—1222no—
552#117D24414yes—
553#117C22×D6114yes—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4D24411yescharacteristic
564C2×C4⋊C4D24411yescharacteristic
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4D24411yescharacteristic
575C2×C22⋊C4D24411yescharacteristic
576C2×C42—1221no—
577C2×C42C22×D6111yescharacteristic
578C2×C42C22×D6111yescharacteristic
579C4⋊C8C22×D6114yes—
580C4⋊C8C22×D6114yes—
581#103—614no—
582#103—614no—
583#103—614no—
584#103—614no—
585#103—614no—
586#103—614no—
587#102—614no—
588#102—614no—
589C22⋊C8C22×D6114yes—
590C22⋊C8C22×D6114yes—
591#97C22×D6114yes—
592C4×C8C22×D6114yes—
593C24—1221no—
594C24—1221no—
595C24C2×D24411yescharacteristic
596#41—2444no—
597#41—2444no—
598#41—2448no—
599C2×Q8—612no—
600C2×Q8—612no—
601C2×Q8—612no—
602C2×Q8—612no—
603C2×Q8—1224no—
604C2×Q8—1221no—
605C2×Q8—1224no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1222no—
610C2×Q8—1222no—
611C2×Q8—1222no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×Q8—1222no—
615C2×Q8—1222no—
616C2×Q8—1222no—
617C2×Q8—4882no—
618C2×Q8—2444no—
619C2×Q8—2444no—
620C2×Q8—2444no—
621C2×Q8—2448no—
622C2×D4—612no—
623C2×D4—612no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—4882no—
633C2×D4—2444no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—1224no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—4882no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4C2×D24412yes—
649C22×C4C2×D24411yescharacteristic
650C22×C4C2×D24411yescharacteristic
651C22×C4C2×D24411yescharacteristic
652C22×C4C2×D24411yescharacteristic
653C22×C4C2×D24411yescharacteristic
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657Q16—2444no—
658Q16—2444no—
659SD16—2444no—
660SD16—2444no—
661SD16—2444no—
662SD16—2444no—
663D8—2444no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8C23×D6112yes—
669C2×C8C23×D6112yes—
670C2×C8C23×D6112yes—
671C2×C8C23×D6112yes—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1224no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4C2×D24414yes—
684C4⋊C4C2×D24414yes—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4C2×D24414yes—
695C22⋊C4C2×D24414yes—
696C42—1224no—
697C42C2×D24412yes—
698C42C2×D24412yes—
699C42C23×D6112yes—
700C42C23×D6112yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—1222no—
705C23—1222no—
706C23—2442no—
707C23—2442no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23C22×D24412yes—
713C23C22×D24411yescharacteristic
714Q8—1222no—
715Q8—1222no—
716Q8—1222no—
717Q8—1222no—
718Q8—1222no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—4884no—
723Q8—2448no—
724Q8—2442no—
725Q8—2442no—
726Q8—2442no—
727Q8—2442no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—1222no—
732D4—4884no—
733D4—2448no—
734D4—2442no—
735D4—2442no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—4884no—
751C2×C4—2448no—
752C2×C4—2448no—
753C2×C4—2442no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4C22×D24412yes—
760C2×C4C22×D24412yes—
761C2×C4C22×D24412yes—
762C2×C4C22×D24412yes—
763C2×C4C22×D24412yes—
764C2×C4C22×D24411yescharacteristic
765C2×C4#1451982312yes—
766C2×C4#1451982312yes—
767C2×C4C24×D6111yescharacteristic
768C8—22no—
769C8—22no—
770C8—22no—
771C8—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—4884no—
777C22—4884no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22#1684033112yes—
785C22#1684057412yes—
786C22#1684057912yes—
787C22C23×D24411yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—2442no—
794C4—2442no—
795C4—2442no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4#1684033112yes—
800C4C2×#1451982311yescharacteristic
801C4C2×#1451982311yescharacteristic
802C2—42no—
803C2—4882no—
804C2—4882no—
805C2#2145693014yesdirect product factor
806C2C2×#1684033111yescharacteristic
807C2C2×#1684057411yescharacteristic
808C2C2×#1684057911yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
prime radicalC2×#16839909C2
hypercenterC2×#433D61
hypocenterC61C2×#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16840383C2semidirect
2. C2×#16840338C2semidirect
3. #21456930C2direct (N × H)
4. C2×#16840156C2semidirect
5. C2×#16840146C2semidirect
6. C2×#16840122C2semidirect
7. C2×#16840113C2semidirect
8. C2×#16839985C2semidirect
9. C2×#16839973C2semidirect
10. C2×#16839978C2semidirect
11. C2×#16839968C2semidirect
12. C2×#16839926C2semidirect
14. C2×#16839920C2semidirect
15. C2×#16839903C2semidirect
16. C2×C61×#433C2semidirect
28. #16840383C22semidirect
30. #16840338C22semidirect
49. #16840156C22semidirect
50. #16840146C22semidirect
51. #16840122C22semidirect
52. #16840113C22semidirect
53. #16839985C22semidirect
54. #16839978C22semidirect
55. #16839973C22semidirect
56. #16839968C22semidirect
57. #16839926C22semidirect
58. #16839920C22semidirect
60. #16839903C22semidirect
70. C61×#433C22semidirect
413. C2×#433D61semidirect
415. C2×C61#3225semidirect
466. #433C2×D61semidirect
481. C61C2×#3225semidirect
805. C2#21456930direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
C2×#168403382
#214569302
C2×#168401562
C2×#168401462
C2×#168401222
C2×#168401132
C2×#168399852
C2×#168399732
C2×#168399782
C2×#168399682
C2×#168399262
C2×#168399092
C2×#168399202
C2×#168399032
C2×C61×#4332
C2×#322561