Finite Group Databasebeta

← C2×#19145674 #25967976

Subgroups — C2×#19145674 #25967976

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×#14583509C211yesmaximal, characteristic, complemented
2C2×#14583473C211yesmaximal, characteristic
3#19145674C2116yesmaximal, direct product factor
4C2×#14583292C211yesmaximal, characteristic, complemented
5C2×#14583277C211yesmaximal, characteristic, complemented
6C2×#14583266C211yesmaximal, characteristic, complemented
7C2×#14583255C211yesmaximal, characteristic, complemented
8C2×#14583124C211yesmaximal, characteristic, complemented
9C2×#14583123C211yesmaximal, characteristic, complemented
10C2×#14583108C211yesmaximal, characteristic, complemented
11C2×#14583107C211yesmaximal, characteristic, complemented
12C2×#14583063C211yesmaximal, characteristic
13C2×#14583059C211yesmaximal, characteristic
14C2×#14583055C211yesmaximal, characteristic, complemented
15C2×#14582957C211yesmaximal, characteristic, complemented
16C2×C43×#451C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621884C2211yescharacteristic
24#14583509—24no—
25#14583509C2218yescomplemented
26#14583473—24no—
27#14583473C2218yes—
28C2×#13063323C2211yescharacteristic
29C2×#13063323C2211yescharacteristic
30C2×#13063323C2211yescharacteristic
31C2×#13063318—21no—
32C2×#13063318—21no—
33C2×#13063316—21no—
34C2×#13063316C2211yescharacteristic
35C2×#13063315—21no—
36C2×#13063314C2211yescharacteristic
37C2×#13063314C2211yescharacteristic
38C2×#13063308—21no—
39C2×#13063308—21no—
40C2×#13063304C2211yescharacteristic
41C2×#13063301—21no—
42C2×#13063301—21no—
43C2×Q8×Dic43C2211yescharacteristic
44C2×#13063290C2211yescharacteristic
45C2×#13063284C2211yescharacteristic
46#14583292C2218yescomplemented
47#14583277C2218yescomplemented
48#14583266C2218yescomplemented
49#14583255C2218yescomplemented
50#14583124C2218yescomplemented
51#14583123C2218yescomplemented
52#14583108C2218yescomplemented
53#14583107C2218yescomplemented
54#14583063C2218yes—
55#14583059C2218yes—
56#14583055C2218yescomplemented
57#14582957C2218yescomplemented
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C23×Q8×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×Q16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#451C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—42no—
79C2×#10621898—42no—
80C2×#10621898C2314yes—
81C22×Dic86C2311yescharacteristic
82C22×Dic86C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×C22⋊D43—21no—
85C22×C4×D43—21no—
86C2×Dic172—42no—
87C2×Dic172C2314yes—
88C2×#10621885—42no—
89C2×#10621885—42no—
90C2×#10621885—42no—
91C2×#10621885C2314yes—
92C2×#10621885C2314yes—
93C2×#10621885C2314yes—
94C2×#10621873—42no—
95C2×#10621873C2314yes—
96C2×#10621884—42no—
97C2×#10621884C2314yes—
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100#13063323—22no—
101#13063323—22no—
102#13063323—22no—
103#13063323C2314yes—
104#13063323C2314yes—
105#13063323C2314yes—
106#13063318—28no—
107#13063318—28no—
108#13063316—28no—
109#13063316—22no—
110#13063316C2314yes—
111#13063315—28no—
112#13063314—22no—
113#13063314—22no—
114#13063314C2314yes—
115#13063314C2314yes—
116#13063308—28no—
117#13063308—28no—
118#13063304—22no—
119#13063304C2314yes—
120#13063301—28no—
121#13063301—28no—
122Q8×Dic43—22no—
123Q8×Dic43C2314yes—
124#13063290—22no—
125#13063290C2314yes—
126#13063284D414yes—
127#13063284C2314yes—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43D411yescharacteristic
131C2×C4⋊Dic43D411yescharacteristic
132C2×C4⋊Dic43C2311yescharacteristic
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×C22⋊Dic43—21no—
143C2×C22⋊Dic43D411yescharacteristic
144C2×C22⋊Dic43D411yescharacteristic
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153Dic43⋊C8C2314yes—
154Dic43⋊C8C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063247C2314yes—
160#13063245C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162#13063235C2314yes—
163C8×Dic43C2314yes—
164C22×Q8×C43—21no—
165C22×Q8×C43—22no—
166C22×Q8×C43—42no—
167C22×Q8×C43—42no—
168C22×Q8×C43C2311yescharacteristic
169C22×Q8×C43C2311yescharacteristic
170C22×Q8×C43C2311yescharacteristic
171C22×Q8×C43C2314yes—
172C23×C4×C43—21no—
173C23×C4×C43C2311yescharacteristic
174C2×Q16×C43—42no—
175C2×Q16×C43—42no—
176C2×Q16×C43C2314yes—
177C2×Q16×C43C2314yes—
178C22×C8×C43C2311yescharacteristic
179C22×C8×C43C2311yescharacteristic
180C22⋊Q8×C43—22no—
181C22⋊Q8×C43C2314yes—
182C2×C4⋊C4×C43—21no—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#103×C43C2314yes—
186#103×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43C2×D411yescharacteristic
189C23×D43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—24no—
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43—44no—
201C2×Q8×C43—44no—
202C2×Q8×C43—44no—
203C2×Q8×C43—48no—
204C2×Q8×C43C2412yes—
205C2×Q8×C43C2412yes—
206C2×Q8×C43C2412yes—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—24no—
214C22×C4×C43—44no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—24no—
220C2×C22⋊D43—44no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228#10621898—44no—
229#10621898—44no—
230#10621898—48no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172C2412yes—
235C2×C4×D43—24no—
236C2×C4×D43—44no—
237C2×Dic86—22no—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86C2412yes—
244C2×Dic86C2412yes—
245Q16×C43—44no—
246Q16×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⋊Dic43—24no—
256C22⋊Dic43C2×D414yes—
257C22⋊Dic43C2×D414yes—
258#10621885—44no—
259#10621885—44no—
260#10621885—44no—
261#10621884—44no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43—24no—
269C4⋊Dic43C2×D414yes—
270C4⋊Dic43C2×D414yes—
271C4⋊Dic43C2412yes—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C4×Dic43C2×D412yes—
284C4×Dic43C2×D412yes—
285C4×Dic43C2412yes—
286C4×Dic43C2412yes—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291Dic172—44no—
292#10621873—44no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43C22×D412yes—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—42no—
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—22no—
308Q8×C43—48no—
309Q8×C43—42no—
310Q8×C43—42no—
311Q8×C43—42no—
312C2×C4×C43—22no—
313C2×C4×C43—24no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—48no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43C22×D412yes—
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43H(5,𝔽2)12yes—
328C2×C4×C43H(5,𝔽2)12yes—
329C2×C4×C43C2511yescharacteristic
330C22⋊D43—48no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43C22×D412yes—
342C2×Dic43C22×D412yes—
343C2×Dic43C22×D412yes—
344C2×Dic43C22×D412yes—
345D172—22no—
346D172—22no—
347D172—42no—
348C4×D43—48no—
349Dic86—22no—
350Dic86—22no—
351Dic86—22no—
352Dic86—22no—
353Dic86—42no—
354Dic86—42no—
355C8×C43—22no—
356C8×C43—22no—
357C43⋊C8—22no—
358C43⋊C8—22no—
359C2×#3223—431nomaximal, Sylow
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—44no—
364C22×C43#53512yes—
365C22×C43#57812yes—
366C22×C43#57812yes—
367C22×C43C23×D411yescharacteristic
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—84no—
372C4×C43—22no—
373C4×C43—42no—
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—22no—
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×#464—431no—
396C2×#462—431no—
397C2×#462—431no—
398C2×#452—431no—
399C2×#452—431no—
400C2×#451—431no—
401C2×#451D4311yescharacteristic, complemented
402C2×#433—431no—
403C2×C43—42no—
404C2×C43#322314yescomplemented
405C2×C43C2×#53511yescharacteristic
406C2×C43C2×#57811yescharacteristic
407C2×C43C2×#57811yescharacteristic
408D43—82no—
409C22×#41—431no—
410C23×Q8C2×D4311yescharacteristic
411C22×Q16—431no—
412C22×Q16—431no—
413C22×Q16—431no—
414C22×Q16—431no—
415C22×Q16C2×D4311yescharacteristic
416C22×Q16C2×D4311yescharacteristic
417C22×SD16—431no—
418C22×SD16—431no—
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×#124—431no—
433C2×#123—861no—
434C2×#123—861no—
435C2×C22⋊Q8—431no—
436C2×C22⋊Q8—861no—
437C2×C22⋊Q8—861no—
438C2×C22⋊Q8C2×D4311yescharacteristic
439C2×C4×Q8—431no—
440C2×C4×Q8—431no—
441C2×#117—431no—
442#497—438no—
443#494—438no—
444#491—438no—
445#488—438no—
446#464—438no—
447#464—438no—
448#462—438no—
449#462—438no—
450#452—438no—
451#452—438no—
452#451—438no—
453#451C2×D4318yescomplemented
454#433—438no—
455C2×C4⋊C8—431no—
456C2×C4⋊C8—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103—431no—
461C2×#103C2×D4311yescharacteristic
462C2×#103C2×D4311yescharacteristic
463C2×#102—431no—
464C2×#102—431no—
465C2×C22⋊C8—431no—
466C2×C22⋊C8C2×D4311yescharacteristic
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—21no—
475C22×Q8—22no—
476C22×Q8—42no—
477C22×Q8—42no—
478C22×Q8—431no—
479C22×Q8—431no—
480C22×Q8C22×D4311yescharacteristic
481C22×Q8C22×D4311yescharacteristic
482C22×Q8C22×D4311yescharacteristic
483C22×Q8C22×D4314yes—
484C22×D4—431no—
485C22×D4—861no—
486C23×C4—21no—
487C23×C4—861no—
488C23×C4C22×D4311yescharacteristic
489C2×Q16—42no—
490C2×Q16—42no—
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×Q16C22×D4314yes—
500C2×Q16C22×D4314yes—
501C2×SD16—434no—
502C2×SD16—434no—
503C2×SD16—1722no—
504C2×SD16—1722no—
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—862no—
519#125—868no—
520#125—868no—
521#124—434no—
522#124—434no—
523#124—862no—
524#124—862no—
525#123—868no—
526#123—868no—
527C22⋊Q8—22no—
528C22⋊Q8—434no—
529C22⋊Q8—868no—
530C22⋊Q8—868no—
531C22⋊Q8—862no—
532C22⋊Q8C22×D4314yes—
533C4×Q8—434no—
534C4×Q8—434no—
535C4×Q8—862no—
536C4×Q8—862no—
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—431no—
557C2×C22⋊C4—431no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—861no—
566C2×C42—861no—
567C4⋊C8—434no—
568C4⋊C8—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#103C22×D4314yes—
574#103C22×D4314yes—
575#102—434no—
576#102—434no—
577C22⋊C8—434no—
578C22⋊C8C22×D4314yes—
579#97—434no—
580C4×C8—434no—
581C24—861no—
582C24D4×D4311yescharacteristic
583#41—1724no—
584#41—1724no—
585#41—1728no—
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—44no—
597C2×Q8—44no—
598C2×Q8—44no—
599C2×Q8—48no—
600C2×Q8—432no—
601C2×Q8—432no—
602C2×Q8—861no—
603C2×Q8—861no—
604C2×Q8—862no—
605C2×Q8—862no—
606C2×Q8—862no—
607C2×Q8—862no—
608C2×Q8C23×D4312yes—
609C2×Q8C23×D4312yes—
610C2×Q8C23×D4312yes—
611C2×D4—432no—
612C2×D4—864no—
613C2×D4—861no—
614C2×D4—862no—
615C2×D4—862no—
616C2×D4—1724no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—44no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—864no—
633C22×C4—1724no—
634C22×C4D4×D4312yes—
635C22×C4D4×D4311yescharacteristic
636C22×C4C23×D4312yes—
637C22×C4C23×D4311yescharacteristic
638Q16—44no—
639Q16—44no—
640Q16—1724no—
641Q16—1724no—
642Q16—1724no—
643Q16—1724no—
644SD16—1724no—
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—864no—
668C4⋊C4—864no—
669C4⋊C4—861no—
670C4⋊C4—864no—
671C4⋊C4C23×D4312yes—
672C22⋊C4—24no—
673C22⋊C4—434no—
674C22⋊C4—434no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C42—432no—
681C42—432no—
682C42—432no—
683C42—432no—
684C42—864no—
685C42—864no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—862no—
690C23—1722no—
691C23—1722no—
692C23—1722no—
693C23C2×D4×D4312yes—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—48no—
702Q8—42no—
703Q8—42no—
704Q8—42no—
705Q8—862no—
706Q8—862no—
707Q8—862no—
708Q8—862no—
709Q8—1722no—
710Q8—1722no—
711D4—862no—
712D4—862no—
713D4—1728no—
714D4—1722no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—48no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—432no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—1728no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4C2×D4×D4312yes—
744C2×C4C2×D4×D4311yescharacteristic
745C2×C4#1306337012yes—
746C2×C4#1306337012yes—
747C2×C4C24×D4311yescharacteristic
748C8—22no—
749C8—22no—
750C8—862no—
751C8—862no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—44no—
756C22—3444no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22#1458346412yes—
761C22#1458371212yes—
762C22#1458371512yes—
763C22C22×D4×D4311yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—862no—
770C4—862no—
771C4—862no—
772C4—862no—
773C4—1722no—
774C4—1722no—
775C4—1722no—
776C4#1458346412yes—
777C4C2×#1306337011yescharacteristic
778C4C2×#1306337011yescharacteristic
779C2—42no—
780C2—3442no—
781C2#1914567414yesdirect product factor
782C2C2×#1458346411yescharacteristic
783C2C2×#1458371211yescharacteristic
784C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC2×#451D43
hypocenterC43C2×#3223
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#14583509C2semidirect
3. #19145674C2direct (N × H)
4. C2×#14583292C2semidirect
5. C2×#14583277C2semidirect
6. C2×#14583266C2semidirect
7. C2×#14583255C2semidirect
8. C2×#14583124C2semidirect
9. C2×#14583123C2semidirect
10. C2×#14583108C2semidirect
11. C2×#14583107C2semidirect
14. C2×#14583055C2semidirect
15. C2×#14582957C2semidirect
16. C2×C43×#451C2semidirect
25. #14583509C22semidirect
46. #14583292C22semidirect
47. #14583277C22semidirect
48. #14583266C22semidirect
49. #14583255C22semidirect
50. #14583124C22semidirect
51. #14583123C22semidirect
52. #14583108C22semidirect
53. #14583107C22semidirect
56. #14583055C22semidirect
57. #14582957C22semidirect
73. C43×#451C22semidirect
401. C2×#451D43semidirect
404. C2×C43#3223semidirect
453. #451C2×D43semidirect
469. C43C2×#3223semidirect
781. C2#19145674direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835092
C2×#145834732
#191456742
C2×#145832922
C2×#145832772
C2×#145832662
C2×#145832552
C2×#145831242
C2×#145831232
C2×#145831082
C2×#145831072
C2×#145830632
C2×#145830592
C2×#145830552
C2×#145829572
C2×C43×#4512
C2×#322343