Finite Group Databasebeta

← C2×#19147549 #25977134

Subgroups — C2×#19147549 #25977134

Order 11008.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583609C211yesmaximal, characteristic, complemented
2#19147549C2116yesmaximal, direct product factor
3C2×#14583309C211yesmaximal, characteristic, complemented
4C2×#14583305C211yesmaximal, characteristic, complemented
5C2×#14583298C211yesmaximal, characteristic, complemented
6C2×#14583199C211yesmaximal, characteristic, complemented
7C2×#14583199C211yesmaximal, characteristic, complemented
8C2×#14583196C211yesmaximal, characteristic, complemented
9C2×#14583196C211yesmaximal, characteristic, complemented
10C2×#14583179C211yesmaximal, characteristic, complemented
11C2×#14583176C211yesmaximal, characteristic, complemented
12C2×#14583030C211yesmaximal, characteristic, complemented
13C2×#14583009C211yesmaximal, characteristic
14C2×#14583009C211yesmaximal, characteristic
15C2×C4×#10621882C211yesmaximal, characteristic
16C2×C43×#554C211yesmaximal, characteristic, complemented
17C22×#10621882C2211yescharacteristic
18#14583609—24no—
19#14583609C2218yescomplemented
20C2×#13063325C2211yescharacteristic
21C2×#13063317C2211yescharacteristic
22C2×#13063317C2211yescharacteristic
23C2×#13063303—21no—
24C2×#13063303—21no—
25C2×#13063301—21no—
26C2×C4×D172C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×C4⋊C4×D43—21no—
30#14583309C2218yescomplemented
31#14583305C2218yescomplemented
32#14583298C2218yescomplemented
33#14583199C2218yescomplemented
34#14583199C2218yescomplemented
35#14583196C2218yescomplemented
36#14583196C2218yescomplemented
37#14583179C2218yescomplemented
38#14583176C2218yescomplemented
39#14583030C2218yescomplemented
40#14583009C2218yes—
41#14583009C2218yes—
42C4×#10621882C2218yes—
43C2×#13063258C2211yescharacteristic
44C2×#13063258C2211yescharacteristic
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063258C2211yescharacteristic
48C2×#13063256C2211yescharacteristic
49C2×#13063256C2211yescharacteristic
50C2×#13063256C2211yescharacteristic
51C2×#13063256C2211yescharacteristic
52C2×C4⋊(C43⋊C8)C2211yescharacteristic
53C2×C4⋊(C43⋊C8)C2211yescharacteristic
54C2×C4⋊(C43⋊C8)C2211yescharacteristic
55C2×#13063246C2211yescharacteristic
56C2×#13063246C2211yescharacteristic
57C2×#13063246C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×#13063236C2211yescharacteristic
62C2×#13063236C2211yescharacteristic
63C2×C4×C43⋊C8C2211yescharacteristic
64C43×#554—24no—
65C43×#554C2218yescomplemented
66C2×C4⋊Q8×C43C2211yescharacteristic
67C2×#125×C43C2211yescharacteristic
68C2×#125×C43C2211yescharacteristic
69C2×C22⋊Q8×C43—21no—
70C2×C22⋊Q8×C43—21no—
71C2×C22⋊Q8×C43—21no—
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43C2211yescharacteristic
74C2×C4×D4×C43C2211yescharacteristic
75C2×C4×D4×C43C2211yescharacteristic
76C22×C4⋊C4×C43—21no—
77C22×Dic86—21no—
78C22×D172C2311yescharacteristic
79C22×C4×D43—21no—
80C22×C4×D43—21no—
81C22×C4×D43—21no—
82C2×#10621882Q818yescomplemented
83C2×#10621882C2314yes—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063325—22no—
89#13063325C2314yes—
90#13063317—22no—
91#13063317—22no—
92#13063317C2314yes—
93#13063317C2314yes—
94#13063303—28no—
95#13063303—28no—
96#13063301—28no—
97C4×D172—22no—
98C4×D172—22no—
99C4×D172—22no—
100C4×D172C2314yes—
101C4×D172C2314yes—
102C4×D172C2314yes—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C4⋊C4×D43—28no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115#13063258C2314yes—
116#13063258C2314yes—
117#13063258C2314yes—
118#13063258C2314yes—
119#13063258C2314yes—
120#13063256C2314yes—
121#13063256C2314yes—
122#13063256C2314yes—
123#13063256C2314yes—
124C4⋊(C43⋊C8)C2314yes—
125C4⋊(C43⋊C8)C2314yes—
126C4⋊(C43⋊C8)C2314yes—
127#13063246C2314yes—
128#13063246C2314yes—
129#13063246C2314yes—
130#13063245C2314yes—
131#13063245C2314yes—
132#13063245C2314yes—
133#13063236C2314yes—
134#13063236C2314yes—
135C4×C43⋊C8C2314yes—
136C22×Q8×C43—21no—
137C22×Q8×C43D411yescharacteristic
138C22×D4×C43C2311yescharacteristic
139C23×C4×C43—21no—
140C23×C4×C43—21no—
141C23×C4×C43—21no—
142C4⋊Q8×C43—22no—
143C4⋊Q8×C43C2314yes—
144#125×C43—22no—
145#125×C43—22no—
146#125×C43C2314yes—
147#125×C43C2314yes—
148C22⋊Q8×C43—28no—
149C22⋊Q8×C43—28no—
150C22⋊Q8×C43—28no—
151C4×Q8×C43D414yes—
152C4×Q8×C43C2314yes—
153C4×D4×C43—22no—
154C4×D4×C43—22no—
155C4×D4×C43—22no—
156C4×D4×C43C2314yes—
157C4×D4×C43C2314yes—
158C4×D4×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—28no—
165C2×C4⋊C4×C43D411yescharacteristic
166C2×C4⋊C4×C43D411yescharacteristic
167C2×C4⋊C4×C43D411yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C42×C43C2311yescharacteristic
175C2×C42×C43C2311yescharacteristic
176C2×C42×C43C2311yescharacteristic
177C24×C43—21no—
178C23×D43—21no—
179C2×Q8×C43—24no—
180C2×Q8×C43—42no—
181C2×Q8×C43—82no—
182C2×Q8×C43C2×D414yes—
183C2×D4×C43—21no—
184C2×D4×C43—22no—
185C2×D4×C43C2×Q814yes—
186C2×D4×C43C2412yes—
187C22×C4×C43—24no—
188C22×C4×C43—24no—
189C22×C4×C43—24no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—44no—
194C22×C4×C43—82no—
195C22×C4×C43—82no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C2×D172—21no—
207C2×D172—22no—
208C2×D172C2×Q814yes—
209C2×D172C2412yes—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—24no—
213C2×C4×D43—44no—
214C2×C4×D43—82no—
215C2×C4×D43—82no—
216C2×Dic86—24no—
217C2×Dic86—82no—
218C4⋊C4×C43—24no—
219C4⋊C4×C43—24no—
220C4⋊C4×C43—24no—
221C4⋊C4×C43—24no—
222C4⋊C4×C43—24no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43C2×D414yes—
227C4⋊C4×C43C2×D414yes—
228C4⋊C4×C43C2×D414yes—
229C4⋊C4×C43C2412yes—
230C4⋊C4×C43C2412yes—
231C4⋊C4×C43C2412yes—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C42×C43C2×D412yes—
236C42×C43C2×D412yes—
237C42×C43C2×D412yes—
238C42×C43C2412yes—
239C42×C43C2412yes—
240C42×C43C2412yes—
241#10621882C2×Q8116yescomplemented
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245C4⋊Dic43—24no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43C2412yes—
250C4⋊Dic43C2412yes—
251C4⋊Dic43C2412yes—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8C2×Q814yes—
260C2×C43⋊C8C2412yes—
261C2×C43⋊C8C2412yes—
262C2×C43⋊C8C2412yes—
263C2×C43⋊C8C2412yes—
264C23×C43—24no—
265C23×C43—22no—
266C23×C43—42no—
267C23×C43—42no—
268C23×C43C22×D411yescharacteristic
269C22×D43—24no—
270C22×D43—22no—
271C22×D43—42no—
272C22×D43—42no—
273Q8×C43—44no—
274Q8×C43—84no—
275D4×C43—24no—
276D4×C43—22no—
277D4×C43C22×Q814yes—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—48no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—84no—
292C2×C4×C43—84no—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D412yes—
297C2×C4×C43C22×D412yes—
298C2×C4×C43C22×D412yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×Q812yes—
301C2×C4×C432−1+412yes—
302C2×C4×C43C2511yescharacteristic
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309D172—24no—
310D172—22no—
311D172C22×Q814yes—
312C4×D43—48no—
313C4×D43—84no—
314C4×D43—84no—
315Dic86—84no—
316C43⋊C8—22no—
317C43⋊C8—22no—
318C43⋊C8—22no—
319C43⋊C8C22×Q814yes—
320C2×#3389—431nomaximal, Sylow
321C22×C43—24no—
322C22×C43—48no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43D4×Q812yes—
326C22×C43#57512yes—
327C22×C43#57612yes—
328C22×C43C23×D411yescharacteristic
329C2×D43—24no—
330C2×D43—48no—
331C2×D43—42no—
332C2×D43—42no—
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—22no—
336C4×C43—22no—
337C4×C43—22no—
338C4×C43—22no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—42no—
342C4×C43D4×Q812yes—
343C4×C43C23×Q811yescharacteristic
344C4×C43C2×2−1+411yescharacteristic
345Dic43—42no—
346Dic43—42no—
347Dic43—42no—
348C2×#554—431no—
349C2×#554D4311yescharacteristic, complemented
350#3389—4316no—
351C2×#501—431no—
352C2×#501—431no—
353C2×#499—431no—
354C2×#478—431no—
355C2×#478—431no—
356C2×#478—431no—
357C2×#478—431no—
358C2×#474—431no—
359C2×#474—431no—
360C2×#446—431no—
361C2×#442—431no—
362C2×#442—431no—
363C2×C4×D8—431no—
364C2×C43—44no—
365C2×C43#338914yescomplemented
366C2×C43C2×D4×Q811yescharacteristic
367C2×C43C2×#57511yescharacteristic
368C2×C43C2×#57611yescharacteristic
369D43—44no—
370C22×D8—431no—
371#554—24no—
372#554—438no—
373#554—864no—
374#554C2×D4318yescomplemented
375C2×C4⋊Q8—431no—
376C2×C4⋊Q8C2×D4311yescharacteristic
377C2×#125—431no—
378C2×#125—431no—
379C2×#125C2×D4311yescharacteristic
380C2×#125C2×D4311yescharacteristic
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—861no—
385C2×C22⋊Q8—861no—
386C2×C22⋊Q8—861no—
387C2×C4×Q8C2×D4311yescharacteristic
388C2×C4×D4—431no—
389C2×C4×D4—431no—
390C2×C4×D4—431no—
391C2×C4×D4C2×D4311yescharacteristic
392C2×C4×D4C2×D4311yescharacteristic
393C2×C4×D4C2×D4311yescharacteristic
394C22×C4⋊C4—21no—
395C22×C4⋊C4—861no—
396#501—438no—
397#501—438no—
398#499—438no—
399#478—438no—
400#478—438no—
401#478—438no—
402#478—438no—
403#474—438no—
404#474—438no—
405#446—438no—
406#442—438no—
407#442—438no—
408C4×D8—438no—
409C2×#107—431no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#107—431no—
414C2×#106—431no—
415C2×#106—431no—
416C2×#106—431no—
417C2×#106—431no—
418C2×C4⋊C8—431no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—431no—
427C2×#97—431no—
428C2×#97—431no—
429C2×C4×C8—431no—
430C43C2×#338911yescharacteristic, complemented, Sylow
431C22×Q8—21no—
432C22×Q8—861no—
433C22×Q8C22⋊D4311yescharacteristic
434C22×D4—431no—
435C22×D4C22×D4311yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—861no—
440C23×C4—861no—
441C23×C4—861no—
442C2×D8—438no—
443C2×D8—434no—
444C22×C8—431no—
445C22×C8—431no—
446C22×C8—431no—
447C22×C8—431no—
448C4⋊Q8—22no—
449C4⋊Q8—434no—
450C4⋊Q8—862no—
451C4⋊Q8C22×D4314yes—
452#125—22no—
453#125—22no—
454#125—434no—
455#125—434no—
456#125—862no—
457#125—862no—
458#125C22×D4314yes—
459#125C22×D4314yes—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—868no—
464C22⋊Q8—868no—
465C22⋊Q8—868no—
466C4×Q8C22⋊D4314yes—
467C4×Q8C22×D4314yes—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—434no—
472C4×D4—434no—
473C4×D4—434no—
474C4×D4—862no—
475C4×D4—862no—
476C4×D4—862no—
477C4×D4C22×D4314yes—
478C4×D4C22×D4314yes—
479C4×D4C22×D4314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—868no—
495C2×C4⋊C4C22⋊D4311yescharacteristic
496C2×C4⋊C4C22⋊D4311yescharacteristic
497C2×C4⋊C4C22⋊D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C42C22×D4311yescharacteristic
508C2×C42C22×D4311yescharacteristic
509C2×C42C22×D4311yescharacteristic
510#107—434no—
511#107—434no—
512#107—434no—
513#107—434no—
514#107—434no—
515#106—434no—
516#106—434no—
517#106—434no—
518#106—434no—
519C4⋊C8—434no—
520C4⋊C8—434no—
521C4⋊C8—434no—
522#102—434no—
523#102—434no—
524#102—434no—
525#102—434no—
526#102—434no—
527#102—434no—
528#97—434no—
529#97—434no—
530C4×C8—434no—
531C24—21no—
532C24—861no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8—82no—
536C2×Q8—864no—
537C2×Q8—3442no—
538C2×Q8C2×C22⋊D4314yes—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—434no—
542C2×D4—432no—
543C2×D4—861no—
544C2×D4—862no—
545C2×D4Q8×D4314yes—
546C2×D4C23×D4312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—864no—
560C22×C4—864no—
561C22×C4—864no—
562C22×C4—3442no—
563C22×C4—3442no—
564C22×C4—1724no—
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C2×C22⋊D4311yescharacteristic
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C2×C22⋊D4311yescharacteristic
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C23×D4311yescharacteristic
572D8—4316no—
573C2×C8—434no—
574C2×C8—432no—
575C2×C8—432no—
576C2×C8—432no—
577C2×C8—432no—
578C2×C8—862no—
579C2×C8—862no—
580C2×C8—862no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—432no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—864no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—864no—
600C4⋊C4C2×C22⋊D4314yes—
601C4⋊C4C2×C22⋊D4314yes—
602C4⋊C4C2×C22⋊D4314yes—
603C4⋊C4C23×D4312yes—
604C4⋊C4C23×D4312yes—
605C4⋊C4C23×D4312yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—864no—
610C22⋊C4—864no—
611C22⋊C4—864no—
612C42C2×C22⋊D4312yes—
613C42C2×C22⋊D4312yes—
614C42C2×C22⋊D4312yes—
615C42C23×D4312yes—
616C42C23×D4312yes—
617C42C23×D4312yes—
618C23—24no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—864no—
623C23—862no—
624C23—1722no—
625C23—1722no—
626C23C22×C22⋊D4311yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—3444no—
630D4—24no—
631D4—22no—
632D4—434no—
633D4—864no—
634D4—862no—
635D4C2×Q8×D4314yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—3444no—
655C2×C4—3444no—
656C2×C4—1728no—
657C2×C4—1722no—
658C2×C4—1722no—
659C2×C4—1722no—
660C2×C4C22×C22⋊D4312yes—
661C2×C4C22×C22⋊D4312yes—
662C2×C4C22×C22⋊D4312yes—
663C2×C4C22×C22⋊D4312yes—
664C2×C4C22×C22⋊D4312yes—
665C2×C4C22×C22⋊D4312yes—
666C2×C4C22×C22⋊D4311yescharacteristic
667C2×C4C2×Q8×D4312yes—
668C2×C4#1306337312yes—
669C2×C4C24×D4311yescharacteristic
670C8—434no—
671C8—862no—
672C8—862no—
673C8—862no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—864no—
679C22—1722no—
680C22—1728no—
681C22—1722no—
682C22Q8×C22⋊D4312yes—
683C22#1458369712yes—
684C22#1458370212yes—
685C22C23×C22⋊D4311yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—1722no—
696C4—1722no—
697C4—1722no—
698C4Q8×C22⋊D4312yes—
699C4C22×Q8×D4311yescharacteristic
700C4C2×#1306337311yescharacteristic
701C2—44no—
702C2—1724no—
703C2#1914754914yesdirect product factor
704C2C2×Q8×C22⋊D4311yescharacteristic
705C2C2×#1458369711yescharacteristic
706C2C2×#1458370211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC2×#554D43
hypocenterC43C2×#3389
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#14583609C2semidirect
2. #19147549C2direct (N × H)
3. C2×#14583309C2semidirect
4. C2×#14583305C2semidirect
5. C2×#14583298C2semidirect
6. C2×#14583199C2semidirect
7. C2×#14583199C2semidirect
8. C2×#14583196C2semidirect
9. C2×#14583196C2semidirect
10. C2×#14583179C2semidirect
11. C2×#14583176C2semidirect
12. C2×#14583030C2semidirect
16. C2×C43×#554C2semidirect
19. #14583609C22semidirect
30. #14583309C22semidirect
31. #14583305C22semidirect
32. #14583298C22semidirect
33. #14583199C22semidirect
34. #14583199C22semidirect
35. #14583196C22semidirect
36. #14583196C22semidirect
37. #14583179C22semidirect
38. #14583176C22semidirect
39. #14583030C22semidirect
65. C43×#554C22semidirect
82. C2×#10621882Q8semidirect
241. #10621882C2×Q8semidirect
349. C2×#554D43semidirect
365. C2×C43#3389semidirect
374. #554C2×D43semidirect
430. C43C2×#3389semidirect
703. C2#19147549direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836092
#191475492
C2×#145833092
C2×#145833052
C2×#145832982
C2×#145831992
C2×#145831962
C2×#145831792
C2×#145831762
C2×#145830302
C2×#145830092
C2×C4×#106218822
C2×C43×#5542
C2×#338943