Finite Group Databasebeta

← C2×#19147363 #25976378

Subgroups — C2×#19147363 #25976378

Order 11008.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583634C211yesmaximal, characteristic
2#19147363C2116yesmaximal, direct product factor
3C2×#14583265C211yesmaximal, characteristic
4C2×#14583261C211yesmaximal, characteristic, complemented
5C2×#14583256C211yesmaximal, characteristic, complemented
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583196C211yesmaximal, characteristic, complemented
8C2×#14583186C211yesmaximal, characteristic, complemented
9C2×#14583121C211yesmaximal, characteristic, complemented
10C2×#14583121C211yesmaximal, characteristic, complemented
11C2×#14583099C211yesmaximal, characteristic
12C2×#14583030C211yesmaximal, characteristic, complemented
13C2×#14583004C211yesmaximal, characteristic, complemented
14C2×#14582997C211yesmaximal, characteristic, complemented
15C2×C4×#10621884C211yesmaximal, characteristic, complemented
16C2×C43×#557C211yesmaximal, characteristic, complemented
17C22×#10621885C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621884C2211yescharacteristic
20#14583634—24no—
21#14583634C2218yes—
22C2×#13063322C2211yescharacteristic
23C2×#13063314—21no—
24C2×#13063313C2211yescharacteristic
25C2×#13063313C2211yescharacteristic
26C2×#13063310—21no—
27C2×#13063310—21no—
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×D172C2211yescharacteristic
30C2×C4×D172C2211yescharacteristic
31C2×#13063287—21no—
32#14583265C2218yes—
33#14583261C2218yescomplemented
34#14583256C2218yescomplemented
35#14583203C2218yescomplemented
36#14583196C2218yescomplemented
37#14583186C2218yescomplemented
38#14583121C2218yescomplemented
39#14583121C2218yescomplemented
40#14583099C2218yes—
41#14583030C2218yescomplemented
42#14583004C2218yescomplemented
43#14582997C2218yescomplemented
44C4×#10621884C2218yescomplemented
45C2×#13063258C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50C2×C4⋊(C43⋊C8)C2211yescharacteristic
51C2×#13063249C2211yescharacteristic
52C2×#13063248C2211yescharacteristic
53C2×#13063248C2211yescharacteristic
54C2×#13063248C2211yescharacteristic
55C2×#13063245C2211yescharacteristic
56C2×#13063245C2211yescharacteristic
57C2×#13063245C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×#13063236C2211yescharacteristic
62C2×#13063236C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#557—24no—
65C43×#557C2218yescomplemented
66C2×C4⋊Q8×C43—21no—
67C2×C4⋊Q8×C43C2211yescharacteristic
68C2×#125×C43—21no—
69C2×#125×C43—21no—
70C2×#125×C43C2211yescharacteristic
71C2×#125×C43C2211yescharacteristic
72C2×C4×Q8×C43—21no—
73C2×C4×Q8×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic
75C2×C4×Q8×C43C2211yescharacteristic
76C2×C4×Q8×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×D172—21no—
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C2×#10621885—24no—
85C2×#10621885C2314yes—
86C2×#10621884—24no—
87C2×#10621884—24no—
88C2×#10621884C2314yes—
89C2×#10621884C2314yes—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94#13063322—22no—
95#13063322C2314yes—
96#13063314—28no—
97#13063313—22no—
98#13063313—22no—
99#13063313C2314yes—
100#13063313C2314yes—
101#13063310—28no—
102#13063310—28no—
103C4×Dic86—22no—
104C4×Dic86C2314yes—
105C4×D172—22no—
106C4×D172—22no—
107C4×D172C2314yes—
108C4×D172C2314yes—
109#13063287—28no—
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×C4×Dic43—21no—
119#13063258C2314yes—
120#13063256C2314yes—
121#13063256C2314yes—
122C4⋊(C43⋊C8)C2314yes—
123C4⋊(C43⋊C8)C2314yes—
124C4⋊(C43⋊C8)C2314yes—
125#13063249C2314yes—
126#13063248C2314yes—
127#13063248C2314yes—
128#13063248C2314yes—
129#13063245C2314yes—
130#13063245C2314yes—
131#13063245C2314yes—
132#13063245C2314yes—
133#13063245C2314yes—
134#13063245C2314yes—
135#13063236C2314yes—
136#13063236C2314yes—
137C4×C43⋊C8C2314yes—
138C22×Q8×C43—21no—
139C22×Q8×C43D411yescharacteristic
140C22×Q8×C43C2311yescharacteristic
141C4⋊Q8×C43—28no—
142C4⋊Q8×C43—22no—
143C4⋊Q8×C43C2314yes—
144#125×C43—28no—
145#125×C43—28no—
146#125×C43—22no—
147#125×C43—22no—
148#125×C43C2314yes—
149#125×C43C2314yes—
150C4×Q8×C43—28no—
151C4×Q8×C43—22no—
152C4×Q8×C43—22no—
153C4×Q8×C43—22no—
154C4×Q8×C43D414yes—
155C4×Q8×C43C2314yes—
156C4×Q8×C43C2314yes—
157C4×Q8×C43C2314yes—
158C4×Q8×C43C2314yes—
159C2×C4⋊C4×C43—21no—
160C2×C4⋊C4×C43—21no—
161C2×C4⋊C4×C43—21no—
162C2×C4⋊C4×C43—21no—
163C2×C4⋊C4×C43—21no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43D411yescharacteristic
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43D411yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C42×C43—21no—
174C2×C42×C43—21no—
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177C2×C42×C43C2311yescharacteristic
178C2×C42×C43C2311yescharacteristic
179C23×D43—21no—
180C23×D43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—24no—
183C2×Q8×C43—22no—
184C2×Q8×C43—42no—
185C2×Q8×C43—44no—
186C2×Q8×C43C2×D414yes—
187C2×Q8×C43#4114yes—
188C2×Q8×C43C2412yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C22×Dic43—21no—
201C22×Dic43—21no—
202C2×D172—24no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—24no—
206C2×D172—22no—
207C2×D172—22no—
208C2×D172—22no—
209C2×D172—22no—
210C2×D172—44no—
211C2×D172—82no—
212C2×D172C2412yes—
213C2×D172C2412yes—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—82no—
217C2×C4×D43—82no—
218C2×Dic86—22no—
219C2×Dic86—22no—
220C2×Dic86—21no—
221C2×Dic86C2412yes—
222C4⋊C4×C43—24no—
223C4⋊C4×C43—24no—
224C4⋊C4×C43—24no—
225C4⋊C4×C43—24no—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C2×D414yes—
234C4⋊C4×C43C2×D414yes—
235C4⋊C4×C43C2×D414yes—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C42×C43—24no—
240C42×C43—24no—
241C42×C43—24no—
242C42×C43C2×D412yes—
243C42×C43C2×D412yes—
244C42×C43C2×D412yes—
245C42×C43C2412yes—
246C42×C43C2412yes—
247C42×C43C2412yes—
248#10621885—28no—
249#10621884—28no—
250#10621884—28no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260C4×Dic43—24no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269C23×C43C22×D411yescharacteristic
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—42no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278Q8×C43—24no—
279Q8×C43—22no—
280Q8×C43—44no—
281Q8×C43—48no—
282Q8×C43C2×#4114yes—
283C2×C4×C43—24no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D412yes—
300C2×C4×C43C22×D412yes—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D412yes—
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4112yes—
305C2×C4×C432−1+412yes—
306C2×C4×C43C2511yescharacteristic
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311D172—22no—
312D172—22no—
313D172—22no—
314D172—22no—
315D172—48no—
316D172—42no—
317D172—42no—
318D172—84no—
319C4×D43—84no—
320C4×D43—84no—
321Dic86—22no—
322Dic86—22no—
323Dic86—42no—
324C43⋊C8—22no—
325C43⋊C8—22no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328C2×#3371—431nomaximal, Sylow
329C22×C43#54812yes—
330C22×C43#57512yes—
331C22×C43#57712yes—
332C22×C43C23×D411yescharacteristic
333C2×D43—42no—
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—84no—
340C2×D43—84no—
341C4×C43—24no—
342C4×C43—22no—
343C4×C43—22no—
344C4×C43—22no—
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43#54812yes—
352C4×C43C22×#4111yescharacteristic
353C4×C43C2×2−1+411yescharacteristic
354Dic43—42no—
355Dic43—42no—
356C2×#559—431no—
357C2×#557D4311yescharacteristic, complemented
358#3371—4316no—
359C2×#490—431no—
360C2×#489—431no—
361C2×#488—431no—
362C2×#479—431no—
363C2×#478—431no—
364C2×#476—431no—
365C2×#464—431no—
366C2×#464—431no—
367C2×#460—431no—
368C2×#446—431no—
369C2×#441—431no—
370C2×#440—431no—
371C2×C4×SD16—431no—
372C2×C43#337114yescomplemented
373C2×C43C2×#54811yescharacteristic
374C2×C43C2×#57511yescharacteristic
375C2×C43C2×#57711yescharacteristic
376D43—82no—
377D43—82no—
378C22×Q16—431no—
379C22×SD16—431no—
380C22×SD16—431no—
381#559—438no—
382#559—864no—
383#557—24no—
384#557C2×D4318yescomplemented
385C2×C4⋊Q8—21no—
386C2×C4⋊Q8C2×D4311yescharacteristic
387C2×#127—431no—
388C2×#125—21no—
389C2×#125—21no—
390C2×#125C2×D4311yescharacteristic
391C2×#125C2×D4311yescharacteristic
392C2×#124—431no—
393C2×#124—431no—
394C2×#124—861no—
395C2×#123—861no—
396C2×#123—861no—
397C2×C4×Q8—21no—
398C2×C4×Q8—431no—
399C2×C4×Q8C2×D4311yescharacteristic
400C2×C4×Q8C2×D4311yescharacteristic
401C2×C4×Q8C2×D4311yescharacteristic
402C2×C4×Q8C2×D4311yescharacteristic
403C2×C4×D4—431no—
404C2×C4×D4—431no—
405C2×C4×D4—861no—
406#490—438no—
407#489—438no—
408#488—438no—
409#479—438no—
410#478—438no—
411#476—438no—
412#464—438no—
413#464—438no—
414#460—438no—
415#446—438no—
416#441—438no—
417#440—438no—
418C4×SD16—438no—
419C2×#107—431no—
420C2×#106—431no—
421C2×#106—431no—
422C2×C4⋊C8—431no—
423C2×C4⋊C8—431no—
424C2×C4⋊C8—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102—431no—
435C2×#97—431no—
436C2×#97—431no—
437C2×C4×C8—431no—
438C43C2×#337111yescharacteristic, complemented, Sylow
439C22×Q8—21no—
440C22×Q8—431no—
441C22×Q8C22⋊D4311yescharacteristic
442C22×Q8C22×D4311yescharacteristic
443C22×D4—431no—
444C22×D4—431no—
445C22×D4—861no—
446C22×D4—861no—
447C23×C4—861no—
448C23×C4—861no—
449C2×Q16—434no—
450C2×Q16—864no—
451C2×SD16—434no—
452C2×SD16—434no—
453C2×SD16—864no—
454C2×SD16—864no—
455C22×C8—431no—
456C22×C8—431no—
457C22×C8—431no—
458C22×C8—431no—
459C4⋊Q8—28no—
460C4⋊Q8—22no—
461C4⋊Q8C22×D4314yes—
462#127—434no—
463#127—862no—
464#125—28no—
465#125—28no—
466#125—22no—
467#125—22no—
468#125C22×D4314yes—
469#125C22×D4314yes—
470#124—434no—
471#124—434no—
472#124—868no—
473#124—862no—
474#124—862no—
475#123—868no—
476#123—868no—
477C4×Q8—28no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—434no—
482C4×Q8—862no—
483C4×Q8C22⋊D4314yes—
484C4×Q8C22×D4314yes—
485C4×Q8C22×D4314yes—
486C4×Q8C22×D4314yes—
487C4×Q8C22×D4314yes—
488C4×D4—434no—
489C4×D4—434no—
490C4×D4—868no—
491C4×D4—862no—
492C4×D4—862no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C22⋊D4311yescharacteristic
504C2×C4⋊C4C22⋊D4311yescharacteristic
505C2×C4⋊C4C22⋊D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—861no—
519C2×C42C22×D4311yescharacteristic
520C2×C42C22×D4311yescharacteristic
521C2×C42C22×D4311yescharacteristic
522#107—434no—
523#106—434no—
524#106—434no—
525C4⋊C8—434no—
526C4⋊C8—434no—
527C4⋊C8—434no—
528#103—434no—
529#103—434no—
530#103—434no—
531#103—434no—
532#102—434no—
533#102—434no—
534#102—434no—
535#102—434no—
536#102—434no—
537#102—434no—
538#97—434no—
539#97—434no—
540C4×C8—434no—
541C24—861no—
542C24—861no—
543C2×Q8—21no—
544C2×Q8—24no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—44no—
548C2×Q8—432no—
549C2×Q8—861no—
550C2×Q8—862no—
551C2×Q8—862no—
552C2×Q8#1062190214yes—
553C2×Q8C2×C22⋊D4314yes—
554C2×Q8C23×D4312yes—
555C2×D4—432no—
556C2×D4—432no—
557C2×D4—864no—
558C2×D4—864no—
559C2×D4—861no—
560C2×D4—861no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—862no—
565C2×D4—3442no—
566C2×D4—1724no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—864no—
574C22×C4—864no—
575C22×C4—3442no—
576C22×C4—3442no—
577C22×C4C2×C22⋊D4311yescharacteristic
578C22×C4C2×C22⋊D4311yescharacteristic
579C22×C4C2×C22⋊D4311yescharacteristic
580C22×C4C2×C22⋊D4311yescharacteristic
581C22×C4C2×C22⋊D4311yescharacteristic
582C22×C4C2×C22⋊D4311yescharacteristic
583C22×C4C23×D4311yescharacteristic
584Q16—868no—
585SD16—868no—
586SD16—868no—
587C2×C8—432no—
588C2×C8—432no—
589C2×C8—432no—
590C2×C8—432no—
591C2×C8—862no—
592C2×C8—862no—
593C2×C8—862no—
594C2×C8—862no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—432no—
607C4⋊C4—861no—
608C4⋊C4—864no—
609C4⋊C4C2×C22⋊D4314yes—
610C4⋊C4C2×C22⋊D4314yes—
611C4⋊C4C2×C22⋊D4314yes—
612C4⋊C4C23×D4312yes—
613C4⋊C4C23×D4312yes—
614C4⋊C4C23×D4312yes—
615C22⋊C4—864no—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C22⋊C4—864no—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C42—24no—
622C42—24no—
623C42—24no—
624C42—864no—
625C42C2×C22⋊D4312yes—
626C42C2×C22⋊D4312yes—
627C42C2×C22⋊D4312yes—
628C42C23×D4312yes—
629C42C23×D4312yes—
630C42C23×D4312yes—
631C23—862no—
632C23—862no—
633C23—1722no—
634C23—1722no—
635C23—1722no—
636C23—1722no—
637C23—1722no—
638C23—1722no—
639C23C22×C22⋊D4311yescharacteristic
640Q8—24no—
641Q8—22no—
642Q8—44no—
643Q8—48no—
644Q8—862no—
645Q8—862no—
646Q8—1722no—
647Q8C2×#1062190214yes—
648D4—862no—
649D4—862no—
650D4—862no—
651D4—862no—
652D4—3444no—
653D4—1728no—
654D4—1722no—
655D4—1722no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—3444no—
673C2×C4—3444no—
674C2×C4—1722no—
675C2×C4—1722no—
676C2×C4C22×C22⋊D4312yes—
677C2×C4C22×C22⋊D4312yes—
678C2×C4C22×C22⋊D4312yes—
679C2×C4C22×C22⋊D4312yes—
680C2×C4C22×C22⋊D4312yes—
681C2×C4C22×C22⋊D4312yes—
682C2×C4C22×C22⋊D4311yescharacteristic
683C2×C4C2×#1062190212yes—
684C2×C4#1306337312yes—
685C2×C4C24×D4311yescharacteristic
686C8—862no—
687C8—862no—
688C8—862no—
689C8—862no—
690C22—3444no—
691C22—3444no—
692C22—1722no—
693C22—1722no—
694C22—1722no—
695C22—1722no—
696C22—1722no—
697C22—1722no—
698C22#1458356012yes—
699C22#1458369712yes—
700C22#1458370712yes—
701C22C23×C22⋊D4311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—1722no—
713C4—1722no—
714C4#1458356012yes—
715C4C22×#1062190211yescharacteristic
716C4C2×#1306337311yescharacteristic
717C2—3442no—
718C2—3442no—
719C2#1914736314yesdirect product factor
720C2C2×#1458356011yescharacteristic
721C2C2×#1458369711yescharacteristic
722C2C2×#1458370711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#557C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenterC2×#557D43
hypocenterC43C2×#3371
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #19147363C2direct (N × H)
4. C2×#14583261C2semidirect
5. C2×#14583256C2semidirect
6. C2×#14583203C2semidirect
7. C2×#14583196C2semidirect
8. C2×#14583186C2semidirect
9. C2×#14583121C2semidirect
10. C2×#14583121C2semidirect
12. C2×#14583030C2semidirect
13. C2×#14583004C2semidirect
14. C2×#14582997C2semidirect
15. C2×C4×#10621884C2semidirect
16. C2×C43×#557C2semidirect
33. #14583261C22semidirect
34. #14583256C22semidirect
35. #14583203C22semidirect
36. #14583196C22semidirect
37. #14583186C22semidirect
38. #14583121C22semidirect
39. #14583121C22semidirect
41. #14583030C22semidirect
42. #14583004C22semidirect
43. #14582997C22semidirect
44. C4×#10621884C22semidirect
65. C43×#557C22semidirect
357. C2×#557D43semidirect
372. C2×C43#3371semidirect
384. #557C2×D43semidirect
438. C43C2×#3371semidirect
719. C2#19147363direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836342
#191473632
C2×#145832652
C2×#145832612
C2×#145832562
C2×#145832032
C2×#145831962
C2×#145831862
C2×#145831212
C2×#145830992
C2×#145830302
C2×#145830042
C2×#145829972
C2×C4×#106218842
C2×C43×#5572
C2×#337143