Finite Group Databasebeta

← C2×#19145675 #25967977

Subgroups — C2×#19145675 #25967977

Order 11008.

2022 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583507C211yesmaximal, characteristic, complemented
2C2×#14583469C211yesmaximal, characteristic
3#19145675C2116yesmaximal, direct product factor
4C2×#14583290C211yesmaximal, characteristic, complemented
5C2×#14583277C211yesmaximal, characteristic, complemented
6C2×#14583266C211yesmaximal, characteristic, complemented
7C2×#14583252C211yesmaximal, characteristic, complemented
8C2×#14583118C211yesmaximal, characteristic, complemented
9C2×#14583110C211yesmaximal, characteristic, complemented
10C2×#14583109C211yesmaximal, characteristic, complemented
11C2×#14583062C211yesmaximal, characteristic
12C2×#14583058C211yesmaximal, characteristic
13C2×#14583056C211yesmaximal, characteristic, complemented
14C2×#14583053C211yesmaximal, characteristic, complemented
15C2×#14582959C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×Dic172C2211yescharacteristic
21C22×#10621885C2211yescharacteristic
22C22×#10621885C2211yescharacteristic
23C22×#10621885C2211yescharacteristic
24C22×#10621883C2211yescharacteristic
25#14583507—24no—
26#14583507C2218yescomplemented
27#14583469—24no—
28#14583469C2218yes—
29C2×#13063325C2211yescharacteristic
30C2×#13063323C2211yescharacteristic
31C2×#13063323C2211yescharacteristic
32C2×#13063320—21no—
33C2×#13063319—21no—
34C2×#13063317—21no—
35C2×#13063316C2211yescharacteristic
36C2×#13063315—21no—
37C2×#13063312C2211yescharacteristic
38C2×#13063307—21no—
39C2×#13063307—21no—
40C2×#13063305C2211yescharacteristic
41C2×#13063302—21no—
42C2×#13063302—21no—
43C2×#13063301C2211yescharacteristic
44C2×C4×Dic86C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583290C2218yescomplemented
47#14583277C2218yescomplemented
48#14583266C2218yescomplemented
49#14583252C2218yescomplemented
50#14583118C2218yescomplemented
51#14583110C2218yescomplemented
52#14583109C2218yescomplemented
53#14583062C2218yes—
54#14583058C2218yes—
55#14583056C2218yescomplemented
56#14583053C2218yescomplemented
57#14582959C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—42no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2311yescharacteristic
85C2×Q8×D43—22no—
86C2×Q8×D43—42no—
87C2×Q8×D43—42no—
88C2×Q8×D43C2314yes—
89C22×C22⋊D43—21no—
90C23×Dic43—21no—
91C22×C4×D43—21no—
92C22×C4×D43C2311yescharacteristic
93C2×Dic172—42no—
94C2×Dic172—42no—
95C2×Dic172C2314yes—
96C2×Dic172C2314yes—
97C2×#10621885—42no—
98C2×#10621885—42no—
99C2×#10621885—42no—
100C2×#10621885C2314yes—
101C2×#10621885C2314yes—
102C2×#10621885C2314yes—
103C2×#10621883—42no—
104C2×#10621883C2314yes—
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107#13063325—22no—
108#13063325C2314yes—
109#13063323—22no—
110#13063323—22no—
111#13063323C2314yes—
112#13063323C2314yes—
113#13063320—28no—
114#13063319—28no—
115#13063317—28no—
116#13063316—22no—
117#13063316C2314yes—
118#13063315—28no—
119#13063312—22no—
120#13063312C2314yes—
121#13063307—28no—
122#13063307—28no—
123#13063305—22no—
124#13063305C2314yes—
125#13063302—28no—
126#13063302—28no—
127#13063301—22no—
128#13063301C2314yes—
129C4×Dic86—22no—
130C4×Dic86C2314yes—
131#13063282D414yes—
132#13063282C2314yes—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43—21no—
135C2×C4⋊Dic43—21no—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊C4—21no—
145C2×Dic43⋊C4D411yescharacteristic
146C2×Dic43⋊C4D411yescharacteristic
147C2×C22⋊Dic43—21no—
148C2×C22⋊Dic43—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4D411yescharacteristic
152C2×(C2×D43)⋊C4D411yescharacteristic
153C2×C4×Dic43—21no—
154C2×C4×Dic43C2311yescharacteristic
155C4⋊(C43⋊C8)C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063249C2314yes—
159#13063248C2314yes—
160#13063248C2314yes—
161#13063246C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164#13063235C2314yes—
165C8×Dic43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C2×Q16×C43—42no—
170C2×Q16×C43C2314yes—
171C2×SD16×C43—42no—
172C2×SD16×C43C2314yes—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175#124×C43—22no—
176#124×C43C2314yes—
177C4×Q8×C43—22no—
178C4×Q8×C43C2314yes—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C4⋊C8×C43C2314yes—
186#103×C43C2314yes—
187#102×C43C2314yes—
188C24×C43—21no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43C2412yes—
197C2×Q8×C43C2412yes—
198C2×D4×C43—21no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43C2412yes—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—44no—
210C22×Dic43—24no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—44no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219Q8×D43—44no—
220Q8×D43—44no—
221Q8×D43—48no—
222#10621900—44no—
223#10621900—44no—
224#10621900—48no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—24no—
228C2×C4×D43—44no—
229C2×C4×D43C2×D412yes—
230C2×C4×D43C2412yes—
231C2×Dic86—22no—
232C2×Dic86—22no—
233C2×Dic86—22no—
234C2×Dic86—22no—
235C2×Dic86—22no—
236C2×Dic86—22no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—24no—
241C2×Dic86—44no—
242C2×Dic86C2412yes—
243C2×Dic86C2412yes—
244C2×Dic86C2412yes—
245Q16×C43—44no—
246SD16×C43—44no—
247C2×C8×C43—22no—
248C2×C8×C43—22no—
249C2×C8×C43C2412yes—
250C2×C8×C43C2412yes—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43C2412yes—
254C22⋊C4×C43—24no—
255C22⋊C4×C43—24no—
256C42×C43—24no—
257C42×C43C2×D412yes—
258C42×C43C2412yes—
259C22⋊Dic43—24no—
260C22⋊Dic43—24no—
261#10621885—44no—
262#10621885—44no—
263#10621885—44no—
264#10621883—44no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4C2×D414yes—
268(C2×D43)⋊C4C2×D414yes—
269C4⋊Dic43—24no—
270C4⋊Dic43—24no—
271C4⋊Dic43—21no—
272C4⋊Dic43—24no—
273C4⋊Dic43—24no—
274C4⋊Dic43C2412yes—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4C2×D414yes—
283Dic43⋊C4C2×D414yes—
284C4×Dic43—24no—
285C4×Dic43C2×D412yes—
286C4×Dic43C2412yes—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291Dic172—44no—
292Dic172—44no—
293C23×C43—22no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43C22×D412yes—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—42no—
307Q8×C43—42no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—42no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43C22×D412yes—
320C2×C4×C43C22×D412yes—
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43H(5,𝔽2)12yes—
323C2×C4×C43H(5,𝔽2)12yes—
324C2×C4×C43C2511yescharacteristic
325C22⋊D43—48no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—48no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43C22×D412yes—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341C4×D43—24no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—48no—
345Dic86—22no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349Dic86—22no—
350Dic86—22no—
351Dic86—48no—
352Dic86—42no—
353Dic86—42no—
354Dic86—42no—
355C8×C43—22no—
356C8×C43—22no—
357C43⋊C8—22no—
358C43⋊C8—22no—
359C2×#3223—431nomaximal, Sylow
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—84no—
364C22×C43#53512yes—
365C22×C43#57812yes—
366C22×C43#57812yes—
367C22×C43C23×D411yescharacteristic
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—44no—
372C4×C43—22no—
373C4×C43—22no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43—42no—
377C4×C43#53512yes—
378C4×C43C2×H(5,𝔽2)11yescharacteristic
379C4×C43C2×H(5,𝔽2)11yescharacteristic
380Dic43—22no—
381Dic43—22no—
382Dic43—22no—
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387C2×#541—431no—
388C2×#536—431no—
389#3223—4316no—
390C2×#497—431no—
391C2×#494—431no—
392C2×#491—431no—
393C2×#488—431no—
394C2×#464—431no—
395C2×#464D4311yescharacteristic, complemented
396C2×#462—431no—
397C2×#462—431no—
398C2×#452—431no—
399C2×#452—431no—
400C2×#451—431no—
401C2×#451—431no—
402C2×#433—431no—
403C2×C43—82no—
404C2×C43#322314yescomplemented
405C2×C43C2×#53511yescharacteristic
406C2×C43C2×#57811yescharacteristic
407C2×C43C2×#57811yescharacteristic
408D43—42no—
409C22×#41—431no—
410C23×Q8—431no—
411C22×Q16—431no—
412C22×Q16—431no—
413C22×Q16—431no—
414C22×Q16—431no—
415C22×Q16—431no—
416C22×Q16C2×D4311yescharacteristic
417C22×SD16—431no—
418C22×SD16C2×D4311yescharacteristic
419#541—438no—
420#541—864no—
421#536—438no—
422#536—864no—
423C2×C4⋊Q8—431no—
424C2×C4⋊Q8—431no—
425C2×C4⋊Q8—431no—
426C2×#126—861no—
427C2×#126—861no—
428C2×#125—431no—
429C2×#125—861no—
430C2×#125—861no—
431C2×#124—431no—
432C2×#124C2×D4311yescharacteristic
433C2×#123—861no—
434C2×#123—861no—
435C2×C22⋊Q8—431no—
436C2×C22⋊Q8—431no—
437C2×C22⋊Q8—861no—
438C2×C22⋊Q8—861no—
439C2×C4×Q8—431no—
440C2×C4×Q8C2×D4311yescharacteristic
441C2×#117—431no—
442#497—438no—
443#494—438no—
444#491—438no—
445#488—438no—
446#464—438no—
447#464C2×D4318yescomplemented
448#462—438no—
449#462—438no—
450#452—438no—
451#452—438no—
452#451—438no—
453#451—438no—
454#433—438no—
455C2×C4⋊C8—431no—
456C2×C4⋊C8C2×D4311yescharacteristic
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103C2×D4311yescharacteristic
463C2×#102—431no—
464C2×#102C2×D4311yescharacteristic
465C2×C22⋊C8—431no—
466C2×C22⋊C8—431no—
467C2×#97—431no—
468C2×C4×C8—431no—
469C43C2×#322311yescharacteristic, complemented, Sylow
470C2×#41—434no—
471C2×#41—862no—
472C2×#41—1722no—
473C2×#41—1722no—
474C22×Q8—434no—
475C22×Q8—431no—
476C22×Q8—431no—
477C22×Q8—431no—
478C22×Q8—861no—
479C22×Q8—862no—
480C22×Q8—1722no—
481C22×Q8—1722no—
482C22×Q8C22×D4311yescharacteristic
483C22×Q8C22×D4311yescharacteristic
484C22×D4—861no—
485C22×D4C22×D4311yescharacteristic
486C23×C4—431no—
487C23×C4—861no—
488C23×C4—861no—
489C2×Q16—42no—
490C2×Q16—434no—
491C2×Q16—434no—
492C2×Q16—434no—
493C2×Q16—434no—
494C2×Q16—434no—
495C2×Q16—1722no—
496C2×Q16—1722no—
497C2×Q16—1722no—
498C2×Q16—1722no—
499C2×Q16—1722no—
500C2×Q16C22×D4314yes—
501C2×SD16—42no—
502C2×SD16—434no—
503C2×SD16—1722no—
504C2×SD16C22×D4314yes—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8C22×D4311yescharacteristic
508C22×C8C22×D4311yescharacteristic
509C4⋊Q8—434no—
510C4⋊Q8—434no—
511C4⋊Q8—434no—
512C4⋊Q8—862no—
513C4⋊Q8—862no—
514C4⋊Q8—862no—
515#126—868no—
516#126—868no—
517#125—434no—
518#125—868no—
519#125—862no—
520#125—868no—
521#124—22no—
522#124—434no—
523#124—862no—
524#124C22×D4314yes—
525#123—868no—
526#123—868no—
527C22⋊Q8—434no—
528C22⋊Q8—434no—
529C22⋊Q8—868no—
530C22⋊Q8—868no—
531C22⋊Q8—862no—
532C22⋊Q8—862no—
533C4×Q8—22no—
534C4×Q8—434no—
535C4×Q8—862no—
536C4×Q8C22×D4314yes—
537#117—434no—
538#117—434no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—861no—
544C2×C4⋊C4—861no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—431no—
558C2×C22⋊C4—431no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C42—21no—
564C2×C42—431no—
565C2×C42—861no—
566C2×C42C22×D4311yescharacteristic
567C4⋊C8—434no—
568C4⋊C8C22×D4314yes—
569#103—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#103—434no—
574#103C22×D4314yes—
575#102—434no—
576#102C22×D4314yes—
577C22⋊C8—434no—
578C22⋊C8—434no—
579#97—434no—
580C4×C8—434no—
581C24—21no—
582C24—431no—
583#41—1724no—
584#41—1724no—
585#41—1728no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—432no—
593C2×Q8—432no—
594C2×Q8—432no—
595C2×Q8—864no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8—862no—
600C2×Q8—862no—
601C2×Q8—862no—
602C2×Q8—862no—
603C2×Q8—862no—
604C2×Q8—862no—
605C2×Q8—1724no—
606C2×Q8—1724no—
607C2×Q8—1724no—
608C2×Q8—1728no—
609C2×Q8C23×D4312yes—
610C2×Q8C23×D4312yes—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—864no—
615C2×D4—1724no—
616C2×D4C23×D4312yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—432no—
624C22×C4—432no—
625C22×C4—864no—
626C22×C4—864no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—1724no—
634C22×C4—1724no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638Q16—44no—
639Q16—1724no—
640Q16—1724no—
641Q16—1724no—
642Q16—1724no—
643Q16—1724no—
644SD16—44no—
645SD16—1724no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—432no—
649C2×C8—432no—
650C2×C8—862no—
651C2×C8—862no—
652C2×C8C23×D4312yes—
653C2×C8C23×D4312yes—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—434no—
657C4⋊C4—434no—
658C4⋊C4—432no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—864no—
663C4⋊C4—864no—
664C4⋊C4—864no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—861no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4C23×D4312yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—434no—
675C22⋊C4—434no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C42—24no—
681C42—432no—
682C42—432no—
683C42—864no—
684C42D4×D4312yes—
685C42C23×D4312yes—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—432no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—862no—
702Q8—862no—
703Q8—862no—
704Q8—862no—
705Q8—862no—
706Q8—862no—
707Q8—1728no—
708Q8—1722no—
709Q8—1722no—
710Q8—1722no—
711D4—22no—
712D4—22no—
713D4—42no—
714D4—1728no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—432no—
724C2×C4—432no—
725C2×C4—432no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—864no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—1728no—
737C2×C4—1728no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4C2×D4×D4312yes—
743C2×C4C2×D4×D4312yes—
744C2×C4C2×D4×D4311yescharacteristic
745C2×C4#1306337012yes—
746C2×C4#1306337112yes—
747C2×C4C24×D4311yescharacteristic
748C8—22no—
749C8—22no—
750C8—862no—
751C8—862no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—862no—
757C22—862no—
758C22—862no—
759C22—1724no—
760C22#1458346512yes—
761C22#1458371312yes—
762C22#1458371512yes—
763C22C22×D4×D4311yescharacteristic
764C4—22no—
765C4—22no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—862no—
770C4—862no—
771C4—862no—
772C4—1722no—
773C4—1722no—
774C4—1722no—
775C4—1722no—
776C4#1458346512yes—
777C4C2×#1306337011yescharacteristic
778C4C2×#1306337111yescharacteristic
779C2—82no—
780C2—1722no—
781C2#1914567514yesdirect product factor
782C2C2×#1458346511yescharacteristic
783C2C2×#1458371311yescharacteristic
784C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
hypercenterC2×#464D43
hypocenterC43C2×#3223
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#14583507C2semidirect
3. #19145675C2direct (N × H)
4. C2×#14583290C2semidirect
5. C2×#14583277C2semidirect
6. C2×#14583266C2semidirect
7. C2×#14583252C2semidirect
8. C2×#14583118C2semidirect
9. C2×#14583110C2semidirect
10. C2×#14583109C2semidirect
13. C2×#14583056C2semidirect
14. C2×#14583053C2semidirect
15. C2×#14582959C2semidirect
16. C2×C43×#464C2semidirect
26. #14583507C22semidirect
46. #14583290C22semidirect
47. #14583277C22semidirect
48. #14583266C22semidirect
49. #14583252C22semidirect
50. #14583118C22semidirect
51. #14583110C22semidirect
52. #14583109C22semidirect
55. #14583056C22semidirect
56. #14583053C22semidirect
57. #14582959C22semidirect
73. C43×#464C22semidirect
395. C2×#464D43semidirect
404. C2×C43#3223semidirect
447. #464C2×D43semidirect
469. C43C2×#3223semidirect
781. C2#19145675direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835072
C2×#145834692
#191456752
C2×#145832902
C2×#145832772
C2×#145832662
C2×#145832522
C2×#145831182
C2×#145831102
C2×#145831092
C2×#145830622
C2×#145830582
C2×#145830562
C2×#145830532
C2×#145829592
C2×C43×#4642
C2×#322343