Finite Group Databasebeta

← C2×#62189 #10579442

Subgroups — C2×#62189 #10579442

Order 512.

6196 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2C2×#3555C211yesmaximal, characteristic, complemented
3#62189C2132yesmaximal, direct product factor
4C2×#3386C211yesmaximal, characteristic, complemented
5C2×Q8×SD16C211yesmaximal, characteristic, complemented
6C2×#3369C211yesmaximal, characteristic, complemented
7C2×#3364C211yesmaximal, characteristic, complemented
8C2×#3356C212yesmaximal, complemented
9C2×#3353C211yesmaximal, characteristic, complemented
10C2×#3344C212yesmaximal, complemented
11C2×#3335C211yesmaximal, characteristic, complemented
12C2×#3331C211yesmaximal, characteristic, complemented
13C2×#3323C212yesmaximal, complemented
14C2×#3311C212yesmaximal, complemented
15C2×#3302C211yesmaximal, characteristic, complemented
16C2×#3258C212yesmaximal, complemented
17C2×#3255C211yesmaximal, characteristic, complemented
18C2×#3244C212yesmaximal, complemented
19C2×#3231C211yesmaximal, characteristic, complemented
20C2×#3120C212yesmaximal, complemented
21C2×#3101C211yesmaximal, characteristic, complemented
22C2×#3084C212yesmaximal, complemented
23C2×#3077C211yesmaximal, characteristic, complemented
24C2×#2993C211yesmaximal, characteristic, complemented
25#3555—28no—
26#3555C22116yescomplemented
27C2×#563—22no—
28#3520—28no—
29#3520C22116yes—
30C2×Q82C2211yescharacteristic, complemented
31C2×#557—21no—
32C2×#557C2211yescharacteristic, complemented
33C2×#556—21no—
34C2×#556C2211yescharacteristic
35C2×#556C2212yes—
36C2×#556C2211yescharacteristic, complemented
37C2×#554C2212yes—
38C2×#554C2211yescharacteristic, complemented
39C2×#552—21no—
40C2×#552C2212yes—
41C2×#551—22no—
42C2×D4×Q8C2211yescharacteristic
43C2×#548—21no—
44C2×#547C2211yescharacteristic
45C2×#547C2211yescharacteristic
46C2×#546C2212yes—
47C2×#544C2212yescomplemented
48C2×#542—21no—
49C2×#542C2212yes—
50C2×#541—22no—
51C2×#541—21no—
52C2×#541C2212yescomplemented
53C2×#539—22no—
54C2×#533C2211yescharacteristic
55C2×#533C2211yescharacteristic
56C2×#533C2211yescharacteristic
57C2×#529C2211yescharacteristic
58C2×#525—21no—
59C22×C22⋊Q8—21no—
60C2×#520C2212yes—
61C22×C4×D4C2211yescharacteristic
62#3386C22116yescomplemented
63Q8×SD16C22116yescomplemented
64#3369C22116yescomplemented
65#3364C22116yescomplemented
66#3356C22132yescomplemented
67#3353C22116yescomplemented
68#3344C22132yescomplemented
69#3335C22116yescomplemented
70#3331C22116yescomplemented
71#3323C22132yescomplemented
72#3311C22132yescomplemented
73#3302C22116yescomplemented
74#3258C22132yescomplemented
75#3255C22116yescomplemented
76#3244C22132yescomplemented
77#3231C22116yescomplemented
78C2×#501C2212yescomplemented
79C2×#500C2211yescharacteristic, complemented
80C2×#498C2211yescharacteristic, complemented
81C2×#498C2212yescomplemented
82C2×#489C2212yes—
83C2×#488C2212yes—
84C2×#487C2211yescharacteristic, complemented
85C2×#487C2211yescharacteristic, complemented
86#3120C22132yescomplemented
87#3101C22116yescomplemented
88C2×#484C2212yescomplemented
89C2×#481C2212yes—
90C2×#485C2212yes—
91C2×#485C2212yes—
92C2×#485C2212yescomplemented
93C2×#482C2212yes—
94C2×#483C2211yescharacteristic
95C2×#483C2211yescharacteristic
96C2×#483C2212yescomplemented
97C2×#483C2212yescomplemented
98#3084C22132yescomplemented
99#3077C22116yescomplemented
100C2×#479C2212yescomplemented
101C2×#479C2212yescomplemented
102C2×#479C2212yescomplemented
103C2×#477C2212yescomplemented
104C2×#475C2211yescharacteristic, complemented
105C2×#475C2212yescomplemented
106C2×#475C2211yescharacteristic, complemented
107C2×#475C2212yescomplemented
108C2×#475C2212yescomplemented
109C2×#478C2212yes—
110C2×#478C2212yes—
111C2×#478C2212yes—
112C2×#476C2211yescharacteristic
113C2×#476C2211yescharacteristic
114C2×#476C2211yescharacteristic
115C2×#476C2212yes—
116C2×#476C2211yescharacteristic
117C2×#474C2211yescharacteristic
118C2×#474C2211yescharacteristic
119C2×#470C2212yes—
120C2×#470C2212yes—
121C2×#470C2212yescomplemented
122C2×#468C2212yes—
123C2×#467C2212yescomplemented
124C2×#465C2212yes—
125C2×#464C2212yes—
126C2×#464C2212yes—
127C2×#462C2211yescharacteristic, complemented
128C2×#462C2211yescharacteristic, complemented
129C2×#462C2212yescomplemented
130C2×#461C2211yescharacteristic
131C2×#461C2211yescharacteristic
132C2×#452C2212yes—
133C2×#452C2212yes—
134C2×#450C2211yescharacteristic
135C2×#450C2211yescharacteristic
136#2993C22116yescomplemented
137C2×#446C2211yescharacteristic, complemented
138C2×C8×Q8C2211yescharacteristic, complemented
139C2×#441C2212yescomplemented
140C2×#440C2212yes—
141C2×C4×Q16C2212yescomplemented
142C2×C4×SD16C2211yescharacteristic
143C2×C4×SD16C2211yescharacteristic
144C2×C4×SD16C2211yescharacteristic
145C2×C4×SD16C2211yescharacteristic
146C2×C4×SD16C2212yes—
147C2×#436C2212yes—
148C2×#436C2211yescharacteristic, complemented
149C2×#435C2212yes—
150C2×C8×D4C2211yescharacteristic, complemented
151C2×#433C2212yescomplemented
152C2×#431C2211yescharacteristic
153C2×#428C2212yes—
154C2×#428C2212yescomplemented
155C22×#106C2212yescomplemented
156C2×#424C2212yescomplemented
157C2×#423C2211yescharacteristic
158C2×#417C2212yes—
159C2×#418C2212yes—
160C2×#416C2212yes—
161C22×#41—21no—
162C22×#41C2312yes—
163C23×Q8—21no—
164C23×D4C2311yescharacteristic
165C24×C4—21no—
166C22×Q16C2312yes—
167C22×Q16C2312yes—
168C22×SD16C2311yescharacteristic
169C22×SD16C2311yescharacteristic
170C22×SD16C2311yescharacteristic
171C22×SD16C2311yescharacteristic
172C22×M16C2312yes—
173C22×M16C2312yes—
174C23×C8C2312yes—
175#563—232no—
176Q82—24no—
177Q82C2318yescomplemented
178#557—216no—
179#557—24no—
180#557C2318yescomplemented
181#556—216no—
182#556—24no—
183#556—28no—
184#556—24no—
185#556C2318yes—
186#556C23116yes—
187#556C2318yescomplemented
188#554—28no—
189#554—24no—
190#554C23116yes—
191#554C2318yescomplemented
192#552—216no—
193#552—28no—
194#552C23116yes—
195#551—232no—
196D4×Q8—24no—
197D4×Q8C2318yes—
198#548—216no—
199#547—24no—
200#547—24no—
201#547C2318yes—
202#547C2318yes—
203#546—28no—
204#546C23116yes—
205#544—28no—
206#544C23116yescomplemented
207#542—216no—
208#542—28no—
209#542C23116yes—
210#541—232no—
211#541—216no—
212#541—28no—
213#541C23116yescomplemented
214#539—232no—
215#533—24no—
216#533—24no—
217#533—24no—
218#533C2318yes—
219#533C2318yes—
220#533C2318yes—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—22no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8—22no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233#529D418yes—
234#529C2318yes—
235C2×#126—22no—
236C2×#126—22no—
237C2×#126—22no—
238C2×#126—22no—
239C2×#126—22no—
240C2×#126—22no—
241C2×#126—22no—
242C2×#126—22no—
243C2×#126D412yes—
244C2×#125—22no—
245C2×#125—22no—
246C2×#125—22no—
247C2×#125—22no—
248C2×#125—21no—
249C2×#125—22no—
250C2×#125—22no—
251C2×#125—21no—
252C2×#125—21no—
253C2×#125D411yescharacteristic
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#124—21no—
257C2×#124—22no—
258C2×#124—22no—
259C2×#124D411yescharacteristic
260C2×#124C2312yes—
261#525—216no—
262C2×#123—22no—
263C2×#123—22no—
264C2×#123—22no—
265C2×#123—22no—
266C2×#123—22no—
267C2×#123D412yes—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—21no—
272C2×C22⋊Q8—21no—
273C2×C22⋊Q8—216no—
274C2×C22⋊Q8—22no—
275C2×C22⋊Q8—21no—
276C2×C22⋊Q8—21no—
277C2×C22⋊Q8—22no—
278C2×C22⋊Q8—22no—
279C2×C22⋊Q8—22no—
280C2×C22⋊Q8—22no—
281C2×C22⋊Q8—22no—
282C2×C22⋊Q8—22no—
283C2×C22⋊Q8D411yescharacteristic
284C2×C22⋊Q8C2311yescharacteristic
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×#121—21no—
291C2×#121—22no—
292C2×#121D411yescharacteristic
293C2×#121C2312yes—
294C2×#120—22no—
295#520—28no—
296#520C23116yes—
297C2×C4×Q8—21no—
298C2×C4×Q8—22no—
299C2×C4×Q8—21no—
300C2×C4×Q8—21no—
301C2×C4×Q8—21no—
302C2×C4×Q8—21no—
303C2×C4×Q8—21no—
304C2×C4×Q8—21no—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×D4—22no—
313C2×C4×D4—21no—
314C2×C4×D4—22no—
315C2×C4×D4—22no—
316C2×C4×D4—21no—
317C2×C4×D4—21no—
318C2×C4×D4—24no—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2318yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×#117—21no—
328C2×#117—21no—
329C2×#117—22no—
330C2×#117—21no—
331C2×#117—22no—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C22×C4⋊C4—22no—
336C22×C4⋊C4—21no—
337C22×C4⋊C4C2311yescharacteristic
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C22⋊C4—21no—
341C22×C22⋊C4—22no—
342C22×C42C2311yescharacteristic
343#501C23116yescomplemented
344#500C2318yescomplemented
345#498C2318yescomplemented
346#498C23116yescomplemented
347#489C23116yes—
348#488C23116yes—
349#487C2318yescomplemented
350#487C2318yescomplemented
351#485C23116yes—
352#485C23116yes—
353#485C23116yescomplemented
354#484C23116yescomplemented
355#483C2318yes—
356#483C2318yes—
357#483C23116yescomplemented
358#483C23116yescomplemented
359#482C23116yes—
360#481C23116yes—
361#479C23116yescomplemented
362#479C23116yescomplemented
363#479C23116yescomplemented
364#478C23116yes—
365#478C23116yes—
366#478C23116yes—
367#477C23116yescomplemented
368#476C2318yes—
369#476C2318yes—
370#476C2318yes—
371#476C23116yes—
372#476C2318yes—
373#475C2318yescomplemented
374#475C23116yescomplemented
375#475C23116yescomplemented
376#475C23116yescomplemented
377#475C2318yescomplemented
378#474C2318yes—
379#474C2318yes—
380#470C23116yes—
381#470C23116yes—
382#470C23116yescomplemented
383#468C23116yes—
384#467C23116yescomplemented
385#465C23116yes—
386#464C23116yes—
387#464C23116yes—
388#462C2318yescomplemented
389#462C2318yescomplemented
390#462C23116yescomplemented
391#461C2318yes—
392#461C2318yes—
393#452C23116yes—
394#452C23116yes—
395#450C2318yes—
396#450C2318yes—
397#446C2318yescomplemented
398C8×Q8C2318yescomplemented
399#441C23116yescomplemented
400#440C23116yes—
401C4×Q16C23116yescomplemented
402C4×SD16C2318yes—
403C4×SD16C2318yes—
404C4×SD16C2318yes—
405C4×SD16C2318yes—
406C4×SD16C23116yes—
407#436C23116yes—
408#436C2318yescomplemented
409#435C23116yes—
410C8×D4C2318yescomplemented
411#433C23116yescomplemented
412#431C2318yes—
413#428C23116yes—
414#428C23116yescomplemented
415C2×#107C2312yes—
416C2×#107C2312yes—
417C2×#107C2312yes—
418C2×#107C2312yes—
419C2×#106C2312yes—
420C2×#106C2312yes—
421C2×#106C2312yes—
422C2×#106C2311yescharacteristic
423C2×#106C2312yes—
424C2×#106C2312yes—
425C2×#106C2311yescharacteristic
426C2×#106C2312yes—
427C2×#106C2311yescharacteristic
428C2×#106C2311yescharacteristic
429C2×#106C23116yescomplemented
430#424C23116yescomplemented
431#423C2318yes—
432C2×C4⋊C8C2312yes—
433C2×C4⋊C8C2312yes—
434C2×C4⋊C8C2312yes—
435C2×C4⋊C8C2311yescharacteristic
436C2×C4⋊C8C2311yescharacteristic
437C2×C4⋊C8C2311yescharacteristic
438C2×C4⋊C8C2311yescharacteristic
439#418C23116yes—
440#417C23116yes—
441#416C23116yes—
442C2×#103C2311yescharacteristic
443C2×#103C2312yes—
444C2×#103C2312yes—
445C2×#103C2312yes—
446C2×#103C2312yes—
447C2×#103C2312yes—
448C2×#103C2311yescharacteristic
449C2×#103C2312yes—
450C2×#103C2312yes—
451C2×#103C2312yes—
452C2×#103C2311yescharacteristic
453C2×#103C2311yescharacteristic
454C2×#102C2312yes—
455C2×#102C2311yescharacteristic
456C2×#102C2312yes—
457C2×#102C2312yes—
458C2×#102C2312yes—
459C2×#102C2311yescharacteristic
460C2×#102C2311yescharacteristic
461C2×#102C2311yescharacteristic
462C2×C22⋊C8C2311yescharacteristic
463C2×C22⋊C8C2311yescharacteristic
464C2×C22⋊C8C2312yes—
465C2×C22⋊C8C2312yes—
466C2×#97C2312yes—
467C2×C4×C8C2311yescharacteristic
468C2×C4×C8C2311yescharacteristic
469C2×C4×C8C2312yes—
470C25—21no—
471C2×#41—28no—
472C2×#41—24no—
473C2×#41—28no—
474C2×#41—44no—
475C2×#41—84no—
476C2×#41C2418yes—
477C22×Q8—28no—
478C22×Q8—21no—
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—84no—
485C22×Q8C2×D411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×Q8C2412yes—
489C22×D4—24no—
490C22×D4—22no—
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—22no—
494C22×D4—42no—
495C22×D4C2×D411yescharacteristic
496C22×D4C2×D412yes—
497C22×D4C2411yescharacteristic
498C22×D4C2414yes—
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—22no—
502C23×C4—22no—
503C23×C4—22no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—22no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—28no—
510C23×C4—84no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2412yes—
514C23×C4C2411yescharacteristic
515C2×Q16—44no—
516C2×Q16—44no—
517C2×Q16C2418yes—
518C2×Q16C2418yes—
519C2×SD16—24no—
520C2×SD16—24no—
521C2×SD16—42no—
522C2×SD16—42no—
523C2×SD16C2414yes—
524C2×SD16C2414yes—
525C2×SD16C2414yes—
526C2×SD16C2414yes—
527C2×M16—44no—
528C2×M16—44no—
529C2×M16C2418yes—
530C2×M16C2418yes—
531C22×C8—44no—
532C22×C8C2411yescharacteristic
533C22×C8C2412yes—
534C22×C8C2411yescharacteristic
535C22×C8C2412yes—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2418yes—
539C4⋊Q8—28no—
540C4⋊Q8—216no—
541C4⋊Q8—28no—
542C4⋊Q8—216no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8—22no—
546C4⋊Q8—22no—
547C4⋊Q8—22no—
548C4⋊Q8—22no—
549C4⋊Q8—24no—
550C4⋊Q8—24no—
551C4⋊Q8C2414yes—
552C4⋊Q8C2414yes—
553C4⋊Q8C2414yes—
554C4⋊Q8C2414yes—
555C4⋊Q8C2414yes—
556C4⋊Q8C2414yes—
557C4⋊Q8C2418yes—
558C4⋊Q8C2418yes—
559#126—216no—
560#126—216no—
561#126—216no—
562#126—216no—
563#126—216no—
564#126—216no—
565#126—216no—
566#126—216no—
567#126C2×D4116yes—
568#125—216no—
569#125—216no—
570#125—216no—
571#125—216no—
572#125—28no—
573#125—216no—
574#125—216no—
575#125—28no—
576#125—28no—
577#125—24no—
578#125—24no—
579#125C2×D418yes—
580#125C2418yes—
581#125C2418yes—
582#124—28no—
583#124—216no—
584#124—216no—
585#124—24no—
586#124C2×D418yes—
587#124C2418yes—
588#123—216no—
589#123—216no—
590#123—216no—
591#123—216no—
592#123—216no—
593#123C2×D4116yes—
594C22⋊Q8—28no—
595C22⋊Q8—28no—
596C22⋊Q8—28no—
597C22⋊Q8—28no—
598C22⋊Q8—28no—
599C22⋊Q8—24no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—24no—
603C22⋊Q8—24no—
604C22⋊Q8—24no—
605C22⋊Q8—216no—
606C22⋊Q8—28no—
607C22⋊Q8—28no—
608C22⋊Q8—216no—
609C22⋊Q8—216no—
610C22⋊Q8—216no—
611C22⋊Q8—216no—
612C22⋊Q8—216no—
613C22⋊Q8—216no—
614C22⋊Q8C2×D418yes—
615C22⋊Q8C2418yes—
616C22⋊Q8C2414yes—
617C22⋊Q8C2414yes—
618C22⋊Q8C2418yes—
619C22⋊Q8C2418yes—
620C22⋊Q8C2418yes—
621#121—28no—
622#121—24no—
623#121—216no—
624#121C2×D418yes—
625#121C2418yes—
626#120—216no—
627C4×Q8—28no—
628C4×Q8—216no—
629C4×Q8—28no—
630C4×Q8—28no—
631C4×Q8—28no—
632C4×Q8—28no—
633C4×Q8—28no—
634C4×Q8—28no—
635C4×Q8—24no—
636C4×Q8—24no—
637C4×Q8—22no—
638C4×Q8—22no—
639C4×Q8—24no—
640C4×Q8—24no—
641C4×Q8C2×D414yes—
642C4×Q8C2418yes—
643C4×Q8C2418yes—
644C4×Q8C2414yes—
645C4×Q8C2414yes—
646C4×Q8C2418yes—
647C4×Q8C2418yes—
648C4×Q8C2414yes—
649C4×D4—216no—
650C4×D4—28no—
651C4×D4—216no—
652C4×D4—216no—
653C4×D4—22no—
654C4×D4—28no—
655C4×D4—22no—
656C4×D4—22no—
657C4×D4—22no—
658C4×D4—28no—
659C4×D4—24no—
660C4×D4C2×D418yes—
661C4×D4C2×D414yes—
662C4×D4C2414yes—
663C4×D4C2414yes—
664C4×D4C2414yes—
665C4×D4C2414yes—
666C4×D4C2418yes—
667C4×D4C2418yes—
668C4×D4C2414yes—
669#117—28no—
670#117—28no—
671#117—24no—
672#117—24no—
673#117—216no—
674#117—28no—
675#117—216no—
676#117C2×D418yes—
677#117C2418yes—
678#117C2418yes—
679#117C2418yes—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—24no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—24no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4—21no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—216no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4C2×D412yes—
715C2×C4⋊C4C2×D411yescharacteristic
716C2×C4⋊C4C2×D412yes—
717C2×C4⋊C4C2×D411yescharacteristic
718C2×C4⋊C4C2×D412yes—
719C2×C4⋊C4C2×D412yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2418yes—
727C2×C4⋊C4C2418yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C22⋊C4—22no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—28no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—216no—
748C2×C22⋊C4C2×D412yes—
749C2×C22⋊C4C2×D412yes—
750C2×C22⋊C4C2×D412yes—
751C2×C22⋊C4C2×D412yes—
752C2×C22⋊C4C2×D412yes—
753C2×C42—22no—
754C2×C42—22no—
755C2×C42—22no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—22no—
759C2×C42—22no—
760C2×C42—22no—
761C2×C42C2×D411yescharacteristic
762C2×C42C2×D411yescharacteristic
763C2×C42C2×D414yes—
764C2×C42C2411yescharacteristic
765C2×C42C2412yes—
766C2×C42C2411yescharacteristic
767C2×C42C2414yes—
768#107C2418yes—
769#107C2418yes—
770#107C2418yes—
771#107C2418yes—
772#106C2414yes—
773#106C2418yes—
774#106C2418yes—
775#106C2418yes—
776#106C2418yes—
777#106C2414yes—
778#106C2418yes—
779#106C2414yes—
780#106C2414yes—
781#106C2418yes—
782C4⋊C8C2418yes—
783C4⋊C8C2414yes—
784C4⋊C8C2414yes—
785C4⋊C8C2414yes—
786C4⋊C8C2418yes—
787C4⋊C8C2418yes—
788C4⋊C8C2414yes—
789#103C2418yes—
790#103C2418yes—
791#103C2418yes—
792#103C2418yes—
793#103C2414yes—
794#103C2414yes—
795#103C2414yes—
796#103C2414yes—
797#103C2418yes—
798#103C2418yes—
799#103C2418yes—
800#103C2418yes—
801#102C2414yes—
802#102C2418yes—
803#102C2414yes—
804#102C2418yes—
805#102C2418yes—
806#102C2418yes—
807#102C2414yes—
808#102C2414yes—
809C22⋊C8C2414yes—
810C22⋊C8C2414yes—
811C22⋊C8C2418yes—
812C22⋊C8C2418yes—
813#97C2418yes—
814C4×C8C2414yes—
815C4×C8C2414yes—
816C4×C8C2418yes—
817C24—21no—
818C24—21no—
819C24—24no—
820C24—44no—
821C24—44no—
822C24—82no—
823C24C22×D411yescharacteristic
824C24C22×D412yes—
825#41—216no—
826#41—48no—
827#41—416no—
828#41—816no—
829C2×Q8—24no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—24no—
833C2×Q8—22no—
834C2×Q8—24no—
835C2×Q8—24no—
836C2×Q8—24no—
837C2×Q8—28no—
838C2×Q8—28no—
839C2×Q8—22no—
840C2×Q8—22no—
841C2×Q8—24no—
842C2×Q8—22no—
843C2×Q8—22no—
844C2×Q8—24no—
845C2×Q8—44no—
846C2×Q8—44no—
847C2×Q8—82no—
848C2×Q8—82no—
849C2×Q8—84no—
850C2×Q8—84no—
851C2×Q8—816no—
852C2×Q8C22×D414yes—
853C2×Q8C2514yes—
854C2×Q8C2512yes—
855C2×Q8C2512yes—
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—24no—
860C2×D4—21no—
861C2×D4—24no—
862C2×D4—21no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—44no—
867C2×D4—48no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—48no—
871C2×D4—84no—
872C2×D4C22×D414yes—
873C2×D4C22×D418yes—
874C2×D42−1+414yes—
875C2×D4C2512yes—
876C2×D4C2512yes—
877C22×C4—24no—
878C22×C4—22no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—22no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—21no—
889C22×C4—22no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—24no—
893C22×C4—28no—
894C22×C4—28no—
895C22×C4—28no—
896C22×C4—24no—
897C22×C4—24no—
898C22×C4—28no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—42no—
902C22×C4—48no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—816no—
906C22×C4—82no—
907C22×C4—82no—
908C22×C4—84no—
909C22×C4—84no—
910C22×C4—82no—
911C22×C4—84no—
912C22×C4C22×D412yes—
913C22×C4C22×D414yes—
914C22×C4C22×D414yes—
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D414yes—
923C22×C4C22×D411yescharacteristic
924C22×C4C2512yes—
925C22×C4C2514yes—
926C22×C4C2511yescharacteristic
927Q16—48no—
928Q16—48no—
929SD16—28no—
930SD16—28no—
931SD16—44no—
932SD16—44no—
933M16—48no—
934M16—48no—
935C2×C8—22no—
936C2×C8—22no—
937C2×C8—22no—
938C2×C8—24no—
939C2×C8—22no—
940C2×C8—24no—
941C2×C8—48no—
942C2×C8C2512yes—
943C2×C8C2512yes—
944C2×C8C2514yes—
945C2×C8C2512yes—
946C2×C8C2512yes—
947C2×C8C2514yes—
948C4⋊C4—21no—
949C4⋊C4—28no—
950C4⋊C4—21no—
951C4⋊C4—24no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—22no—
956C4⋊C4—24no—
957C4⋊C4—21no—
958C4⋊C4—22no—
959C4⋊C4—28no—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—28no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—28no—
968C4⋊C4—24no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—22no—
983C4⋊C4—21no—
984C4⋊C4C22×D418yes—
985C4⋊C4C22×D414yes—
986C4⋊C4C22×D418yes—
987C4⋊C4C22×D414yes—
988C4⋊C4C22×D418yes—
989C4⋊C4C22×D418yes—
990C4⋊C4C2512yes—
991C4⋊C4C2514yes—
992C4⋊C4C2512yes—
993C4⋊C4C2514yes—
994C4⋊C4C2512yes—
995C4⋊C4C2512yes—
996C4⋊C4C2514yes—
997C22⋊C4—28no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—24no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4C22×D418yes—
1014C22⋊C4C22×D418yes—
1015C22⋊C4C22×D418yes—
1016C22⋊C4C22×D418yes—
1017C22⋊C4C22×D418yes—
1018C42—28no—
1019C42—28no—
1020C42—28no—
1021C42—24no—
1022C42—24no—
1023C42—28no—
1024C42—28no—
1025C42—28no—
1026C42C22×D412yes—
1027C42C22×D412yes—
1028C42C22×D414yes—
1029C42C22×D414yes—
1030C42C22×D414yes—
1031C42C2512yes—
1032C42C2514yes—
1033C42C2512yes—
1034C23—22no—
1035C23—24no—
1036C23—22no—
1037C23—24no—
1038C23—22no—
1039C23—24no—
1040C23—22no—
1041C23—24no—
1042C23—22no—
1043C23—48no—
1044C23—48no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—84no—
1051C23—816no—
1052C23C23×D412yes—
1053C23C23×D414yes—
1054C23C23×D411yescharacteristic
1055Q8—28no—
1056Q8—22no—
1057Q8—22no—
1058Q8—24no—
1059Q8—22no—
1060Q8—22no—
1061Q8—24no—
1062Q8—42no—
1063Q8—42no—
1064Q8—44no—
1065Q8—48no—
1066Q8—48no—
1067Q8—84no—
1068Q8—84no—
1069Q8—88no—
1070Q8—88no—
1071D4—22no—
1072D4—22no—
1073D4—22no—
1074D4—24no—
1075D4—28no—
1076D4—48no—
1077D4—48no—
1078D4—416no—
1079D4—42no—
1080D4—88no—
1081D4C2×2−1+414yes—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—28no—
1095C2×C4—28no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—44no—
1107C2×C4—416no—
1108C2×C4—42no—
1109C2×C4—44no—
1110C2×C4—42no—
1111C2×C4—44no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—44no—
1117C2×C4—44no—
1118C2×C4—48no—
1119C2×C4—48no—
1120C2×C4—84no—
1121C2×C4—84no—
1122C2×C4—88no—
1123C2×C4—88no—
1124C2×C4—84no—
1125C2×C4—88no—
1126C2×C4#57714yes—
1127C2×C4C23×D412yes—
1128C2×C4C23×D412yes—
1129C2×C4C23×D414yes—
1130C2×C4C23×D414yes—
1131C2×C4C23×D414yes—
1132C2×C4C23×D412yes—
1133C2×C4C23×D412yes—
1134C2×C4C23×D411yescharacteristic
1135C2×C4C23×D412yes—
1136C2×C4C2×2−1+412yes—
1137C2×C4#58512yes—
1138C2×C4C2611yescharacteristic
1139C8—22no—
1140C8—22no—
1141C8—22no—
1142C8—24no—
1143C8—22no—
1144C8—24no—
1145C22—24no—
1146C22—22no—
1147C22—24no—
1148C22—22no—
1149C22—24no—
1150C22—22no—
1151C22—24no—
1152C22—42no—
1153C22—42no—
1154C22—48no—
1155C22—44no—
1156C22—48no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—816no—
1161C22—84no—
1162C22#348912yes—
1163C22C2×#57712yes—
1164C22#358612yes—
1165C22C24×D411yescharacteristic
1166C4—24no—
1167C4—22no—
1168C4—22no—
1169C4—24no—
1170C4—22no—
1171C4—22no—
1172C4—24no—
1173C4—44no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—44no—
1179C4—44no—
1180C4—42no—
1181C4—44no—
1182C4—42no—
1183C4#348912yes—
1184C4C2×#57714yes—
1185C4C22×2−1+411yescharacteristic
1186C4C2×#58511yescharacteristic
1187C2—44no—
1188C2—42no—
1189C2—44no—
1190C2—82no—
1191C2#6218914yesdirect product factor
1192C2C2×#348911yescharacteristic
1193C2C22×#57711yescharacteristic
1194C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC2×#3520C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3555C2semidirect
3. #62189C2direct (N × H)
4. C2×#3386C2semidirect
5. C2×Q8×SD16C2semidirect
6. C2×#3369C2semidirect
7. C2×#3364C2semidirect
8. C2×#3356C2semidirect
9. C2×#3353C2semidirect
10. C2×#3344C2semidirect
11. C2×#3335C2semidirect
12. C2×#3331C2semidirect
13. C2×#3323C2semidirect
14. C2×#3311C2semidirect
15. C2×#3302C2semidirect
16. C2×#3258C2semidirect
17. C2×#3255C2semidirect
18. C2×#3244C2semidirect
19. C2×#3231C2semidirect
20. C2×#3120C2semidirect
21. C2×#3101C2semidirect
22. C2×#3084C2semidirect
23. C2×#3077C2semidirect
24. C2×#2993C2semidirect
26. #3555C22semidirect
30. C2×Q82C22semidirect
32. C2×#557C22semidirect
36. C2×#556C22semidirect
38. C2×#554C22semidirect
47. C2×#544C22semidirect
52. C2×#541C22semidirect
62. #3386C22semidirect
63. Q8×SD16C22semidirect
64. #3369C22semidirect
65. #3364C22semidirect
66. #3356C22semidirect
67. #3353C22semidirect
68. #3344C22semidirect
69. #3335C22semidirect
70. #3331C22semidirect
71. #3323C22semidirect
72. #3311C22semidirect
73. #3302C22semidirect
74. #3258C22semidirect
75. #3255C22semidirect
76. #3244C22semidirect
77. #3231C22semidirect
78. C2×#501C22semidirect
79. C2×#500C22semidirect
80. C2×#498C22semidirect
81. C2×#498C22semidirect
84. C2×#487C22semidirect
85. C2×#487C22semidirect
86. #3120C22semidirect
87. #3101C22semidirect
88. C2×#484C22semidirect
92. C2×#485C22semidirect
96. C2×#483C22semidirect
97. C2×#483C22semidirect
98. #3084C22semidirect
99. #3077C22semidirect
100. C2×#479C22semidirect
101. C2×#479C22semidirect
102. C2×#479C22semidirect
103. C2×#477C22semidirect
104. C2×#475C22semidirect
105. C2×#475C22semidirect
106. C2×#475C22semidirect
107. C2×#475C22semidirect
108. C2×#475C22semidirect
121. C2×#470C22semidirect
123. C2×#467C22semidirect
127. C2×#462C22semidirect
128. C2×#462C22semidirect
129. C2×#462C22semidirect
136. #2993C22semidirect
137. C2×#446C22semidirect
138. C2×C8×Q8C22semidirect
139. C2×#441C22semidirect
141. C2×C4×Q16C22semidirect
148. C2×#436C22semidirect
150. C2×C8×D4C22semidirect
151. C2×#433C22semidirect
154. C2×#428C22semidirect
155. C22×#106C22semidirect
156. C2×#424C22semidirect
177. Q82C23semidirect
180. #557C23semidirect
187. #556C23semidirect
191. #554C23semidirect
206. #544C23semidirect
213. #541C23semidirect
343. #501C23semidirect
344. #500C23semidirect
345. #498C23semidirect
346. #498C23semidirect
349. #487C23semidirect
350. #487C23semidirect
353. #485C23semidirect
354. #484C23semidirect
357. #483C23semidirect
358. #483C23semidirect
361. #479C23semidirect
362. #479C23semidirect
363. #479C23semidirect
367. #477C23semidirect
373. #475C23semidirect
374. #475C23semidirect
375. #475C23semidirect
376. #475C23semidirect
377. #475C23semidirect
382. #470C23semidirect
384. #467C23semidirect
388. #462C23semidirect
389. #462C23semidirect
390. #462C23semidirect
397. #446C23semidirect
398. C8×Q8C23semidirect
399. #441C23semidirect
401. C4×Q16C23semidirect
408. #436C23semidirect
410. C8×D4C23semidirect
411. #433C23semidirect
414. #428C23semidirect
429. C2×#106C23semidirect
430. #424C23semidirect
1191. C2#62189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35202
C2×#35552
#621892
C2×#33862
C2×Q8×SD162
C2×#33692
C2×#33642
C2×#33562
C2×#33532
C2×#33442
C2×#33352
C2×#33312
C2×#33232
C2×#33112
C2×#33022
C2×#32582
C2×#32552
C2×#32442
C2×#32312
C2×#31202
C2×#31012
C2×#30842
C2×#30772
C2×#29932