Finite Group Databasebeta

← C2×#21456928 #30551408

Subgroups — C2×#21456928 #30551408

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
2#21456928C2116yesmaximal, direct product factor
3C2×#16840154C211yesmaximal, characteristic, complemented
4C2×#16840144C211yesmaximal, characteristic, complemented
5C2×#16840121C211yesmaximal, characteristic, complemented
6C2×#16840112C211yesmaximal, characteristic, complemented
7C2×#16839981C211yesmaximal, characteristic, complemented
8C2×#16839969C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839964C211yesmaximal, characteristic, complemented
11C2×#16839924C211yesmaximal, characteristic, complemented
12C2×#16839907C211yesmaximal, characteristic
13C2×#16839918C211yesmaximal, characteristic, complemented
14C2×#16839901C211yesmaximal, characteristic, complemented
15C2×#16839823C211yesmaximal, characteristic, complemented
16C2×C61×#536C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758199C2211yescharacteristic
25#16840383—24no—
26#16840383C2218yescomplemented
27C2×#14519777C2211yescharacteristic
28C2×#14519772—21no—
29C2×#14519765C2211yescharacteristic
30C2×#14519763—21no—
31C2×#14519759—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519755—21no—
34C2×#14519751C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37#16840154C2218yescomplemented
38#16840144C2218yescomplemented
39#16840121C2218yescomplemented
40#16840112C2218yescomplemented
41#16839981C2218yescomplemented
42#16839974C2218yescomplemented
43#16839969C2218yescomplemented
44#16839964C2218yescomplemented
45#16839924C2218yescomplemented
46#16839918C2218yescomplemented
47#16839907C2218yes—
48#16839901C2218yescomplemented
49#16839823C2218yescomplemented
50C2×C4⋊#92418C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519701C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519701C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C22×#41×C61C2211yescharacteristic
65C23×Q8×C61C2211yescharacteristic
66C61×#536—24no—
67C61×#536C2218yescomplemented
68C2×C4⋊Q8×C61C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×#124×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×#123×C61—21no—
73C2×#123×C61—21no—
74C2×C22⋊Q8×C61—21no—
75C2×C22⋊Q8×C61—21no—
76C2×#117×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C4×D61—21no—
82C2×#11758202—42no—
83C2×#11758202—42no—
84C2×#11758202—42no—
85C2×#11758202C2314yes—
86C2×#11758202C2314yes—
87C2×#11758202C2314yes—
88C2×#11758200—42no—
89C2×#11758200C2314yes—
90C2×#11758201—42no—
91C2×#11758201—42no—
92C2×#11758201—42no—
93C2×#11758201C2314yes—
94C2×#11758201C2314yes—
95C2×#11758201C2314yes—
96C2×#11758199—42no—
97C2×#11758199C2314yes—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519777—22no—
103#14519777C2314yes—
104#14519772—28no—
105#14519765—22no—
106#14519765C2314yes—
107#14519763—28no—
108#14519759—28no—
109#14519756—22no—
110#14519756C2314yes—
111#14519755—28no—
112#14519751—22no—
113#14519751C2314yes—
114C4×Dic122—22no—
115C4×Dic122C2314yes—
116C4×D244—22no—
117C4×D244C2314yes—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×#11758196—21no—
122C2×#11758196—21no—
123C2×C22⋊Dic61—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×C4×Dic61—21no—
129C4⋊#92418C2314yes—
130C4⋊#92418C2314yes—
131#14519701C2314yes—
132#14519701C2314yes—
133#14519701C2314yes—
134#14519701C2314yes—
135#14519701C2314yes—
136#14519701C2314yes—
137#14519698C2314yes—
138#14519698C2314yes—
139C22⋊#92418C2314yes—
140C22⋊#92418C2314yes—
141#14519688C2314yes—
142C4×#92418C2314yes—
143C2×#41×C61—22no—
144C2×#41×C61—42no—
145C2×#41×C61—42no—
146C2×#41×C61C2314yes—
147C22×Q8×C61—22no—
148C22×Q8×C61—21no—
149C22×Q8×C61—42no—
150C22×Q8×C61—42no—
151C22×Q8×C61C2311yescharacteristic
152C22×Q8×C61C2311yescharacteristic
153C22×Q8×C61C2311yescharacteristic
154C22×Q8×C61C2314yes—
155C22×D4×C61—21no—
156C22×D4×C61C2311yescharacteristic
157C23×C4×C61—21no—
158C23×C4×C61—21no—
159C23×C4×C61C2311yescharacteristic
160C4⋊Q8×C61—22no—
161C4⋊Q8×C61—22no—
162C4⋊Q8×C61C2314yes—
163C4⋊Q8×C61C2314yes—
164#124×C61—22no—
165#124×C61—22no—
166#124×C61C2314yes—
167#124×C61C2314yes—
168#123×C61—28no—
169#123×C61—28no—
170C22⋊Q8×C61—28no—
171C22⋊Q8×C61—28no—
172#117×C61D414yes—
173#117×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61D411yescharacteristic
179C2×C4⋊C4×C61D411yescharacteristic
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61D411yescharacteristic
185C2×C22⋊C4×C61D411yescharacteristic
186C2×C42×C61C2311yescharacteristic
187C2×C42×C61C2311yescharacteristic
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190C23×D61—21no—
191#41×C61—44no—
192#41×C61—44no—
193#41×C61—48no—
194C2×Q8×C61—24no—
195C2×Q8×C61—21no—
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×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61—44no—
205C2×Q8×C61—44no—
206C2×Q8×C61—44no—
207C2×Q8×C61—48no—
208C2×Q8×C61C2412yes—
209C2×Q8×C61C2412yes—
210C2×Q8×C61C2412yes—
211C2×D4×C61—24no—
212C2×D4×C61—21no—
213C2×D4×C61—22no—
214C2×D4×C61—22no—
215C2×D4×C61—44no—
216C2×D4×C61C2412yes—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—24no—
223C22×C4×C61—24no—
224C22×C4×C61—44no—
225C22×C4×C61—44no—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2412yes—
233C22×C4×C61C2411yescharacteristic
234C2×C22⋊D61—24no—
235C2×C22⋊D61—82no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—21no—
242C2×D244C2412yes—
243C2×C4×D61—24no—
244C2×C4×D61—82no—
245C2×Dic122—22no—
246C2×Dic122—22no—
247C2×Dic122—21no—
248C2×Dic122—24no—
249C2×Dic122—82no—
250C2×Dic122C2412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—24no—
254C4⋊C4×C61—24no—
255C4⋊C4×C61C2×D414yes—
256C4⋊C4×C61C2×D414yes—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61C2×D414yes—
262C22⋊C4×C61C2×D414yes—
263C42×C61C2×D412yes—
264C42×C61C2×D412yes—
265C42×C61C2412yes—
266C42×C61C2412yes—
267C22⋊Dic61—24no—
268#11758202—44no—
269#11758202—44no—
270#11758202—44no—
271#11758201—44no—
272#11758201—44no—
273#11758201—44no—
274#11758200—44no—
275#11758199—44no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198—24no—
280C4⋊Dic61—24no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61C2412yes—
284C4⋊Dic61C2412yes—
285#11758196—24no—
286#11758196—24no—
287C4×Dic61—24no—
288C2×#92418—22no—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294C2×#92418C2412yes—
295C2×#92418C2412yes—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61C22×D412yes—
304C23×C61C22×D411yescharacteristic
305C22×D61—22no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61—42no—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—22no—
315Q8×C61—48no—
316Q8×C61—42no—
317Q8×C61—42no—
318Q8×C61—42no—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—48no—
322D4×C61—42no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—24no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—48no—
335C2×C4×C61—48no—
336C2×C4×C61—42no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61C22×D412yes—
340C2×C4×C61C22×D412yes—
341C2×C4×C61C22×D412yes—
342C2×C4×C61C22×D412yes—
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61H(5,𝔽2)12yes—
346C2×C4×C61H(5,𝔽2)12yes—
347C2×C4×C61C2511yescharacteristic
348C22⋊D61—84no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355D244—22no—
356D244—22no—
357D244—42no—
358C4×D61—84no—
359Dic122—22no—
360Dic122—22no—
361Dic122—42no—
362Dic122—84no—
363#92418—22no—
364#92418—22no—
365#92418—22no—
366#92418—22no—
367C2×#3225—611nomaximal, Sylow
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—44no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—84no—
376C22×C61#53512yes—
377C22×C61#57712yes—
378C22×C61#57812yes—
379C22×C61C23×D411yescharacteristic
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—84no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—22no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61#53512yes—
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394C4×C61C2×H(5,𝔽2)11yescharacteristic
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#542—611no—
399C2×#536D6111yescharacteristic, complemented
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×#433—611no—
414C2×C61—42no—
415C2×C61—82no—
416C2×C61#322514yescomplemented
417C2×C61C2×#53511yescharacteristic
418C2×C61C2×#57711yescharacteristic
419C2×C61C2×#57811yescharacteristic
420D61—82no—
421C22×#41C2×D6111yescharacteristic
422C23×Q8C2×D6111yescharacteristic
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—24no—
434#536C2×D6118yescomplemented
435C2×C4⋊Q8—611no—
436C2×C4⋊Q8C2×D6111yescharacteristic
437C2×C4⋊Q8C2×D6111yescharacteristic
438C2×#126—1221no—
439C2×#124—611no—
440C2×#124—1221no—
441C2×#124C2×D6111yescharacteristic
442C2×#124C2×D6111yescharacteristic
443C2×#123—21no—
444C2×#123—21no—
445C2×#123—1221no—
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—611no—
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#433—618no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8—611no—
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⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×#97—611no—
480C2×C4×C8—611no—
481C61C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—22no—
483C2×#41—42no—
484C2×#41—42no—
485C2×#41C22×D6114yes—
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—42no—
489C22×Q8—42no—
490C22×Q8—611no—
491C22×Q8—1221no—
492C22×Q8C22×D6111yescharacteristic
493C22×Q8C22×D6111yescharacteristic
494C22×Q8C22×D6111yescharacteristic
495C22×Q8C22×D6114yes—
496C22×D4—21no—
497C22×D4—611no—
498C22×D4—1221no—
499C22×D4C22×D6111yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
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×C8—611no—
521C22×C8—611no—
522C22×C8—611no—
523C22×C8—611no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—614no—
527C4⋊Q8—1222no—
528C4⋊Q8C22×D6114yes—
529C4⋊Q8C22×D6114yes—
530#126—1228no—
531#124—22no—
532#124—22no—
533#124—614no—
534#124—1228no—
535#124—1222no—
536#124C22×D6114yes—
537#124C22×D6114yes—
538#123—28no—
539#123—28no—
540#123—1228no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543C22⋊Q8—614no—
544C22⋊Q8—1222no—
545C22⋊Q8—1228no—
546#121—614no—
547#121—1222no—
548C4×Q8—614no—
549C4×Q8—1222no—
550C4×D4—614no—
551C4×D4—1222no—
552#117C22⋊D6114yes—
553#117C22×D6114yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4C22⋊D6111yescharacteristic
564C2×C4⋊C4C22⋊D6111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4C22⋊D6111yescharacteristic
575C2×C22⋊C4C22⋊D6111yescharacteristic
576C2×C42—1221no—
577C2×C42C22×D6111yescharacteristic
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—614no—
580C4⋊C8—614no—
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⋊C8—614no—
590C22⋊C8—614no—
591#97—614no—
592C4×C8—614no—
593C24—21no—
594C24—1221no—
595C24C2×C22⋊D6111yescharacteristic
596#41—44no—
597#41—44no—
598#41—48no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—48no—
613C2×Q8—612no—
614C2×Q8—1224no—
615C2×Q8—1221no—
616C2×Q8—1222no—
617C2×Q8—1222no—
618C2×Q8—4882no—
619C2×Q8C23×D6112yes—
620C2×Q8C23×D6112yes—
621C2×Q8C23×D6112yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—612no—
628C2×D4—1224no—
629C2×D4—1221no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—4882no—
633C2×D4C23×D6112yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1224no—
647C22×C4—4882no—
648C22×C4C2×C22⋊D6112yes—
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—2444no—
657Q16—2444no—
658Q16—2444no—
659SD16—2444no—
660SD16—2444no—
661SD16—2444no—
662SD16—2444no—
663D8—2444no—
664C2×C8—612no—
665C2×C8—612no—
666C2×C8—612no—
667C2×C8—612no—
668C2×C8—1222no—
669C2×C8—1222no—
670C2×C8—1222no—
671C2×C8—1222no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—612no—
677C4⋊C4—612no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4C2×C22⋊D6114yes—
684C4⋊C4C2×C22⋊D6114yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4C2×C22⋊D6114yes—
695C22⋊C4C2×C22⋊D6114yes—
696C42—1224no—
697C42C2×C22⋊D6112yes—
698C42C2×C22⋊D6112yes—
699C42C23×D6112yes—
700C42C23×D6112yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—1222no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23C22×C22⋊D6112yes—
713C23C22×C22⋊D6111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—48no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—1222no—
725Q8—1222no—
726Q8—4884no—
727Q8—2442no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—1222no—
733D4—1222no—
734D4—4884no—
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—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—4884no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4C22×C22⋊D6112yes—
760C2×C4C22×C22⋊D6112yes—
761C2×C4C22×C22⋊D6112yes—
762C2×C4C22×C22⋊D6112yes—
763C2×C4C22×C22⋊D6112yes—
764C2×C4C22×C22⋊D6111yescharacteristic
765C2×C4#1451982212yes—
766C2×C4#1451982212yes—
767C2×C4C24×D6111yescharacteristic
768C8—1222no—
769C8—1222no—
770C8—1222no—
771C8—1222no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—4884no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22#1684032912yes—
785C22#1684057012yes—
786C22#1684057712yes—
787C22C23×C22⋊D6111yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4#1684032912yes—
800C4C2×#1451982211yescharacteristic
801C4C2×#1451982211yescharacteristic
802C2—42no—
803C2—82no—
804C2—4882no—
805C2#2145692814yesdirect product factor
806C2C2×#1684032911yescharacteristic
807C2C2×#1684057011yescharacteristic
808C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#536C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
hypercenterC2×#536D61
hypocenterC61C2×#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#16840383C2semidirect
2. #21456928C2direct (N × H)
3. C2×#16840154C2semidirect
4. C2×#16840144C2semidirect
5. C2×#16840121C2semidirect
6. C2×#16840112C2semidirect
7. C2×#16839981C2semidirect
8. C2×#16839969C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839964C2semidirect
11. C2×#16839924C2semidirect
13. C2×#16839918C2semidirect
14. C2×#16839901C2semidirect
15. C2×#16839823C2semidirect
16. C2×C61×#536C2semidirect
26. #16840383C22semidirect
37. #16840154C22semidirect
38. #16840144C22semidirect
39. #16840121C22semidirect
40. #16840112C22semidirect
41. #16839981C22semidirect
42. #16839974C22semidirect
43. #16839969C22semidirect
44. #16839964C22semidirect
45. #16839924C22semidirect
46. #16839918C22semidirect
48. #16839901C22semidirect
49. #16839823C22semidirect
67. C61×#536C22semidirect
399. C2×#536D61semidirect
416. C2×C61#3225semidirect
434. #536C2×D61semidirect
481. C61C2×#3225semidirect
805. C2#21456928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
#214569282
C2×#168401542
C2×#168401442
C2×#168401212
C2×#168401122
C2×#168399812
C2×#168399692
C2×#168399742
C2×#168399642
C2×#168399242
C2×#168399072
C2×#168399182
C2×#168399012
C2×#168398232
C2×C61×#5362
C2×#322561