Finite Group Databasebeta

← C2×#19146700 #25973181

Subgroups — C2×#19146700 #25973181

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583558C211yesmaximal, characteristic
2#19146700C2116yesmaximal, direct product factor
3C2×#14583261C211yesmaximal, characteristic, complemented
4C2×#14583217C211yesmaximal, characteristic, complemented
5C2×#14583229C211yesmaximal, characteristic, complemented
6C2×#14583181C211yesmaximal, characteristic, complemented
7C2×#14583155C211yesmaximal, characteristic, complemented
8C2×#14583130C211yesmaximal, characteristic, complemented
9C2×#14583121C211yesmaximal, characteristic, complemented
10C2×#14583059C211yesmaximal, characteristic, complemented
11C2×#14583054C211yesmaximal, characteristic, complemented
12C2×#14583004C211yesmaximal, characteristic, complemented
13C2×#14582971C211yesmaximal, characteristic, complemented
14C2×#14582898C211yesmaximal, characteristic, complemented
15C22×#13063248C211yesmaximal, characteristic, complemented
16C2×C43×#554C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621877C2211yescharacteristic
23C23×C43⋊C8C2211yescharacteristic
24#14583558—24no—
25#14583558C2218yes—
26C2×#13063313C2211yescharacteristic
27C2×#13063311—21no—
28C2×#13063304C2211yescharacteristic
29C2×#13063303—21no—
30C2×#13063299C2211yescharacteristic
31C2×#13063297—21no—
32C2×C4×Dic86C2211yescharacteristic
33C2×(C22⋊D43)⋊C4—21no—
34#14583261C2218yescomplemented
35#14583229C2218yescomplemented
36#14583217C2218yescomplemented
37#14583181C2218yescomplemented
38#14583155C2218yescomplemented
39#14583130C2218yescomplemented
40#14583121C2218yescomplemented
41#14583059C2218yescomplemented
42#14583054C2218yescomplemented
43#14583004C2218yescomplemented
44#14582971C2218yescomplemented
45C2×#13063256C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49#14582898C2218yescomplemented
50C2×#13063249C2211yescharacteristic
51C2×#13063248C2211yescharacteristic
52C2×#13063248C2211yescharacteristic
53C2×#13063248C2211yescharacteristic
54C2×#13063248C2211yescharacteristic
55C2×#13063248C2211yescharacteristic
56C2×#13063248C2211yescharacteristic
57C2×#13063248C2218yescomplemented
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063236C2211yescharacteristic
64C43×#554—24no—
65C43×#554C2218yescomplemented
66C2×C4⋊Q8×C43C2211yescharacteristic
67C2×#125×C43—21no—
68C2×C22⋊Q8×C43—21no—
69C2×C22⋊Q8×C43—21no—
70C2×C22⋊Q8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43—21no—
74C2×C4×D4×C43C2211yescharacteristic
75C22×C4⋊C4×C43C2211yescharacteristic
76C22×C4⋊C4×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—24no—
79C2×#10621898—42no—
80C2×#10621898C2314yes—
81C22×Dic86—24no—
82C22×Dic86—22no—
83C22×Dic86—21no—
84C22×Dic86—42no—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2314yes—
87C22×Dic86C2311yescharacteristic
88C22×D172C2311yescharacteristic
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C2×#10621885—24no—
94C2×#10621885—42no—
95C2×#10621885C2314yes—
96C2×#10621885C2314yes—
97C2×#10621884—42no—
98C2×#10621884C2314yes—
99C2×#10621877—42no—
100C2×#10621877C2314yes—
101C22×C43⋊C8—42no—
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2314yes—
107#13063313—22no—
108#13063313C2314yes—
109#13063311—28no—
110#13063304—22no—
111#13063304C2314yes—
112#13063303—28no—
113#13063299—22no—
114#13063299C2314yes—
115#13063297—28no—
116C4×Dic86—22no—
117C4×Dic86C2314yes—
118(C22⋊D43)⋊C4—28no—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C2×C22⋊Dic43—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×C4×Dic43—21no—
127#13063256C2314yes—
128#13063256C2314yes—
129#13063256C2314yes—
130C4⋊(C43⋊C8)C2314yes—
131#13063249C2314yes—
132#13063248C2314yes—
133#13063248C2314yes—
134#13063248C2314yes—
135#13063248C2314yes—
136#13063248C2314yes—
137#13063248C2314yes—
138#13063245C2314yes—
139#13063245C2314yes—
140#13063245C2314yes—
141C22⋊(C43⋊C8)C2314yes—
142C22⋊(C43⋊C8)C2314yes—
143#13063236C2314yes—
144C22×Q8×C43—21no—
145C22×Q8×C43C2311yescharacteristic
146C22×D4×C43D411yescharacteristic
147C23×C4×C43—21no—
148C23×C4×C43—21no—
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C4⋊Q8×C43—22no—
152C4⋊Q8×C43C2314yes—
153#125×C43—28no—
154C22⋊Q8×C43—22no—
155C22⋊Q8×C43—22no—
156C22⋊Q8×C43—28no—
157C22⋊Q8×C43—28no—
158C22⋊Q8×C43C2314yes—
159C22⋊Q8×C43C2314yes—
160C4×Q8×C43—22no—
161C4×Q8×C43C2314yes—
162C4×D4×C43—28no—
163C4×D4×C43D414yes—
164C4×D4×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43—22no—
168C2×C4⋊C4×C43—22no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43D411yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2314yes—
178C2×C4⋊C4×C43C2314yes—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43D411yescharacteristic
182C2×C22⋊C4×C43D411yescharacteristic
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—24no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43—82no—
193C2×Q8×C43C2412yes—
194C2×D4×C43—24no—
195C2×D4×C43C2×D414yes—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—24no—
205C22×C4×C43—24no—
206C22×C4×C43—82no—
207C22×C4×C43—82no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D412yes—
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—44no—
220C2×C22⋊D43—44no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—24no—
225C22×Dic43—44no—
226#10621898—28no—
227#10621898—44no—
228#10621898—48no—
229C2×D172—21no—
230C2×D172—22no—
231C2×D172—22no—
232C2×D172C2412yes—
233C2×C4×D43—24no—
234C2×C4×D43—44no—
235C2×Dic86—21no—
236C2×Dic86—22no—
237C2×Dic86—22no—
238C2×Dic86—22no—
239C2×Dic86—28no—
240C2×Dic86—24no—
241C2×Dic86—21no—
242C2×Dic86—44no—
243C2×Dic86—48no—
244C2×Dic86—44no—
245C2×Dic86#4114yes—
246C2×Dic86C2412yes—
247C2×Dic86C2412yes—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—24no—
257C4⋊C4×C43C2×D414yes—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C4⋊C4×C43C2412yes—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C22⋊C4×C43C2×D414yes—
264C22⋊C4×C43C2×D414yes—
265C42×C43—24no—
266C42×C43C2×D412yes—
267C42×C43C2412yes—
268C22⋊Dic43—24no—
269#10621885—28no—
270#10621885—44no—
271#10621884—44no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275C4⋊Dic43—21no—
276C4⋊Dic43C2412yes—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279C4×Dic43—24no—
280#10621877—44no—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8—44no—
286C2×C43⋊C8C2412yes—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43#13714yes—
296C23×C43C22×D412yes—
297C23×C43C22×D412yes—
298C23×C43C22×D411yescharacteristic
299C22×D43—22no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—42no—
306Q8×C43—84no—
307D4×C43—28no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—24no—
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—22no—
321C2×C4×C43—22no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—42no—
326C2×C4×C43—84no—
327C2×C4×C43—84no—
328C2×C4×C43C22×D412yes—
329C2×C4×C43C22×D412yes—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C2×#4112yes—
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43C2511yescharacteristic
336C22⋊D43—48no—
337C22⋊D43—48no—
338C2×Dic43—24no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—48no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345D172—22no—
346D172—22no—
347D172—42no—
348C4×D43—48no—
349Dic86—24no—
350Dic86—22no—
351Dic86—22no—
352Dic86—22no—
353Dic86—48no—
354Dic86—42no—
355Dic86C2×#4114yes—
356C43⋊C8—22no—
357C43⋊C8—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3316—431nomaximal, Sylow
361C22×C43—22no—
362C22×C43—28no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—44no—
368C22×C43#54612yes—
369C22×C43C2×#13714yes—
370C22×C43C2×#13712yes—
371C22×C43#57712yes—
372C22×C43C23×D411yescharacteristic
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—84no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—22no—
380C4×C43—22no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—42no—
385C4×C43#54612yes—
386C4×C43C22×#4111yescharacteristic
387C4×C43C2×H(5,𝔽2)11yescharacteristic
388Dic43—24no—
389Dic43—42no—
390Dic43—42no—
391C2×#554D4311yescharacteristic, complemented
392C2×#548—431no—
393#3316—4316no—
394C2×#489—431no—
395C2×#481—431no—
396C2×#483—431no—
397C2×#475—431no—
398C2×#470—431no—
399C2×#465—431no—
400C2×#464—431no—
401C2×#452—431no—
402C2×#451—431no—
403C2×#441—431no—
404C2×#435—431no—
405C2×#417—431no—
406C22×#103—431no—
407C2×C43—24no—
408C2×C43—42no—
409C2×C43#331614yescomplemented
410C2×C43C2×#54611yescharacteristic
411C2×C43C22×#13711yescharacteristic
412C2×C43C2×#57711yescharacteristic
413D43—82no—
414C22×#41—431no—
415C23×Q8—431no—
416C22×Q16—431no—
417C22×Q16—431no—
418C22×SD16—431no—
419C22×M16—431no—
420C23×C8—431no—
421#554—24no—
422#554C2×D4318yescomplemented
423#548—438no—
424#548—864no—
425C2×C4⋊Q8C2×D4311yescharacteristic
426C2×#125—21no—
427C2×#124—431no—
428C2×#124—861no—
429C2×C22⋊Q8—21no—
430C2×C22⋊Q8—21no—
431C2×C22⋊Q8—431no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8C2×D4311yescharacteristic
434C2×C22⋊Q8C2×D4311yescharacteristic
435C2×#121—431no—
436C2×#121—861no—
437C2×C4×Q8—431no—
438C2×C4×Q8C2×D4311yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4—861no—
441C2×C4×D4C2×D4311yescharacteristic
442C22×C4⋊C4C2×D4311yescharacteristic
443C22×C4⋊C4C2×D4311yescharacteristic
444#489—438no—
445#483—438no—
446#481—438no—
447#475—438no—
448#470—438no—
449#465—438no—
450#464—438no—
451#452—438no—
452#451—438no—
453#441—438no—
454#435—438no—
455C2×#106—431no—
456C2×#106—431no—
457C2×#106—431no—
458C2×C4⋊C8—431no—
459#417—438no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—438no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×#97—431no—
474C43C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—434no—
476C2×#41—864no—
477C2×#41—862no—
478C2×#41—1722no—
479C22×Q8—21no—
480C22×Q8—431no—
481C22×Q8—431no—
482C22×Q8—434no—
483C22×Q8—864no—
484C22×Q8—861no—
485C22×Q8—862no—
486C22×Q8—1722no—
487C22×Q8C22×D4311yescharacteristic
488C22×D4—431no—
489C22×D4—861no—
490C22×D4—861no—
491C22×D4C22⋊D4311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497C23×C4C22×D4311yescharacteristic
498C2×Q16—434no—
499C2×Q16—434no—
500C2×Q16—864no—
501C2×Q16—1722no—
502C2×SD16—434no—
503C2×SD16—1722no—
504C2×M16—434no—
505C2×M16—1722no—
506C22×C8—431no—
507C22×C8—431no—
508C22×C8—431no—
509C22×C8—431no—
510C22×C8—434no—
511C22×C8—1722no—
512C4⋊Q8—22no—
513C4⋊Q8C22×D4314yes—
514#125—28no—
515#124—434no—
516#124—868no—
517#124—862no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522C22⋊Q8—434no—
523C22⋊Q8—862no—
524C22⋊Q8—868no—
525C22⋊Q8C22×D4314yes—
526C22⋊Q8C22×D4314yes—
527#121—434no—
528#121—868no—
529#121—862no—
530C4×Q8—22no—
531C4×Q8—434no—
532C4×Q8—862no—
533C4×Q8C22×D4314yes—
534C4×D4—28no—
535C4×D4—868no—
536C4×D4C22⋊D4314yes—
537C4×D4C22×D4314yes—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4C22⋊D4311yescharacteristic
550C2×C4⋊C4C22×D4311yescharacteristic
551C2×C4⋊C4C22×D4311yescharacteristic
552C2×C4⋊C4C22×D4311yescharacteristic
553C2×C4⋊C4C22×D4314yes—
554C2×C4⋊C4C22×D4314yes—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4C22⋊D4311yescharacteristic
562C2×C22⋊C4C22⋊D4311yescharacteristic
563C2×C42—21no—
564C2×C42—861no—
565C2×C42C22×D4311yescharacteristic
566#106—434no—
567#106—434no—
568#106—434no—
569C4⋊C8—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#103—434no—
574#103—434no—
575#103—434no—
576#103—434no—
577#102—434no—
578#102—434no—
579#102—434no—
580C22⋊C8—434no—
581C22⋊C8—434no—
582#97—434no—
583C24—861no—
584C24C2×C22⋊D4311yescharacteristic
585C24C2×C22⋊D4311yescharacteristic
586#41—868no—
587#41—1724no—
588#41—1728no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—82no—
594C2×Q8—434no—
595C2×Q8—432no—
596C2×Q8—432no—
597C2×Q8—868no—
598C2×Q8—861no—
599C2×Q8—864no—
600C2×Q8—861no—
601C2×Q8—862no—
602C2×Q8—862no—
603C2×Q8—862no—
604C2×Q8—1724no—
605C2×Q8—1724no—
606C2×Q8—1728no—
607C2×Q8C23×D4312yes—
608C2×D4—24no—
609C2×D4—432no—
610C2×D4—864no—
611C2×D4—864no—
612C2×D4—861no—
613C2×D4—862no—
614C2×D4—862no—
615C2×D4—1724no—
616C2×D4—1724no—
617C2×D4C2×C22⋊D4314yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—82no—
630C22×C4—861no—
631C22×C4—864no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—864no—
635C22×C4—1724no—
636C22×C4—1724no—
637C22×C4C2×C22⋊D4312yes—
638C22×C4C2×C22⋊D4312yes—
639C22×C4C2×C22⋊D4311yescharacteristic
640C22×C4C2×C22⋊D4311yescharacteristic
641C22×C4C2×C22⋊D4311yescharacteristic
642C22×C4C2×C22⋊D4311yescharacteristic
643C22×C4C23×D4312yes—
644C22×C4C23×D4312yes—
645C22×C4C23×D4311yescharacteristic
646Q16—868no—
647Q16—1724no—
648SD16—1724no—
649M16—1724no—
650C2×C8—432no—
651C2×C8—432no—
652C2×C8—432no—
653C2×C8—432no—
654C2×C8—862no—
655C2×C8—862no—
656C2×C8—862no—
657C2×C8—862no—
658C2×C8—1724no—
659C4⋊C4—21no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—432no—
669C4⋊C4—861no—
670C4⋊C4—864no—
671C4⋊C4—864no—
672C4⋊C4C2×C22⋊D4314yes—
673C4⋊C4C23×D4312yes—
674C4⋊C4C23×D4312yes—
675C4⋊C4C23×D4312yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C22⋊C4C2×C22⋊D4314yes—
683C22⋊C4C2×C22⋊D4314yes—
684C42—24no—
685C42—864no—
686C42C2×C22⋊D4312yes—
687C42C23×D4312yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—862no—
694C23—1722no—
695C23—1722no—
696C23—1722no—
697C23#1306335614yes—
698C23C22×C22⋊D4312yes—
699C23C22×C22⋊D4312yes—
700C23C22×C22⋊D4311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—84no—
705Q8—434no—
706Q8—862no—
707Q8—864no—
708Q8—862no—
709Q8—862no—
710Q8—1728no—
711Q8—1722no—
712D4—28no—
713D4—862no—
714D4—862no—
715D4—1728no—
716D4—1728no—
717D4—1722no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—862no—
739C2×C4—864no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—1728no—
743C2×C4—1728no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4C22×C22⋊D4312yes—
747C2×C4C22×C22⋊D4312yes—
748C2×C4C22×C22⋊D4312yes—
749C2×C4C22×C22⋊D4312yes—
750C2×C4C22×C22⋊D4311yescharacteristic
751C2×C4#41×D4312yes—
752C2×C4#1306337112yes—
753C2×C4C24×D4311yescharacteristic
754C8—862no—
755C8—862no—
756C8—862no—
757C8—862no—
758C22—22no—
759C22—22no—
760C22—28no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—3444no—
766C22—1722no—
767C22—1722no—
768C22—1722no—
769C22#1458353712yes—
770C22C2×#1306335614yes—
771C22C2×#1306335612yes—
772C22#1458371012yes—
773C22C23×C22⋊D4311yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—864no—
783C4—1722no—
784C4—1722no—
785C4#1458353712yes—
786C4C2×#41×D4311yescharacteristic
787C4C2×#1306337111yescharacteristic
788C2—24no—
789C2—42no—
790C2—3442no—
791C2#1914670014yesdirect product factor
792C2C2×#1458353711yescharacteristic
793C2C22×#1306335611yescharacteristic
794C2C2×#1458371011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radicalC2×#14583558C2
hypercenterC2×#554D43
hypocenterC43C2×#3316
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #19146700C2direct (N × H)
3. C2×#14583261C2semidirect
4. C2×#14583217C2semidirect
5. C2×#14583229C2semidirect
6. C2×#14583181C2semidirect
7. C2×#14583155C2semidirect
8. C2×#14583130C2semidirect
9. C2×#14583121C2semidirect
10. C2×#14583059C2semidirect
11. C2×#14583054C2semidirect
12. C2×#14583004C2semidirect
13. C2×#14582971C2semidirect
14. C2×#14582898C2semidirect
15. C22×#13063248C2semidirect
16. C2×C43×#554C2semidirect
34. #14583261C22semidirect
35. #14583229C22semidirect
36. #14583217C22semidirect
37. #14583181C22semidirect
38. #14583155C22semidirect
39. #14583130C22semidirect
40. #14583121C22semidirect
41. #14583059C22semidirect
42. #14583054C22semidirect
43. #14583004C22semidirect
44. #14582971C22semidirect
49. #14582898C22semidirect
57. C2×#13063248C22semidirect
65. C43×#554C22semidirect
391. C2×#554D43semidirect
409. C2×C43#3316semidirect
422. #554C2×D43semidirect
474. C43C2×#3316semidirect
791. C2#19146700direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835582
#191467002
C2×#145832612
C2×#145832172
C2×#145832292
C2×#145831812
C2×#145831552
C2×#145831302
C2×#145831212
C2×#145830592
C2×#145830542
C2×#145830042
C2×#145829712
C2×#145828982
C22×#130632482
C2×C43×#5542
C2×#331643