Finite Group Databasebeta

← C2×#19146768 #25973221

Subgroups — C2×#19146768 #25973221

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×#14583595C211yesmaximal, characteristic
2C2×D4×Dic86C211yesmaximal, characteristic, complemented
3#19146768C2116yesmaximal, direct product factor
4C2×#14583268C211yesmaximal, characteristic, complemented
5C2×#14583235C211yesmaximal, characteristic, complemented
6C2×#14583241C211yesmaximal, characteristic, complemented
7C2×#14583207C211yesmaximal, characteristic, complemented
8C2×#14583145C211yesmaximal, characteristic, complemented
9C2×#14583128C211yesmaximal, characteristic, complemented
10C2×#14583105C211yesmaximal, characteristic, complemented
11C2×#14583040C211yesmaximal, characteristic, complemented
12C2×#14583040C211yesmaximal, characteristic, complemented
13C2×#14583001C211yesmaximal, characteristic, complemented
14C2×#14582909C211yesmaximal, characteristic, complemented
15C22×#13063250C211yesmaximal, characteristic, complemented
16C2×C43×#435C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22#14583595—24no—
23#14583595C2218yes—
24D4×Dic86—24no—
25D4×Dic86C2218yescomplemented
26C2×#13063325C2211yescharacteristic
27C2×#13063324—21no—
28C2×#13063320—21no—
29C2×#13063317C2211yescharacteristic
30C2×#13063307—21no—
31C2×#13063304C2211yescharacteristic
32C2×#13063304C2211yescharacteristic
33C2×#13063302—21no—
34C2×#13063302—21no—
35C2×#13063299C2211yescharacteristic
36C2×#13063299C2211yescharacteristic
37C2×#13063297—21no—
38C2×C4×Dic86C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×D4×Dic43—21no—
41C2×(C22⋊D43)⋊C4—21no—
42C2×#13063284C2211yescharacteristic
43C22×C4⋊Dic43C2211yescharacteristic
44#14583268C2218yescomplemented
45#14583241C2218yescomplemented
46#14583235C2218yescomplemented
47#14583207C2218yescomplemented
48#14583145C2218yescomplemented
49#14583128C2218yescomplemented
50#14583105C2218yescomplemented
51#14583040C2218yescomplemented
52#14583040C2218yescomplemented
53#14583001C2218yescomplemented
54C2×#13063259C2211yescharacteristic
55C2×#13063259C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57#14582909C2218yescomplemented
58C2×#13063250C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063250C2211yescharacteristic
67C2×#13063250C2218yescomplemented
68C2×#13063247C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#435C2218yescomplemented
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—24no—
78C22×Dic86—24no—
79C22×Dic86—22no—
80C22×Dic86—22no—
81C22×Dic86—21no—
82C22×Dic86—21no—
83C22×Dic86—42no—
84C22×Dic86—42no—
85C22×Dic86C2311yescharacteristic
86C22×Dic86C2311yescharacteristic
87C22×Dic86C2314yes—
88C22×Dic86C2314yes—
89C22×Dic86C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C23×Dic43—21no—
94C23×Dic43—21no—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C2×#10621873—24no—
98C2×#10621873—42no—
99C2×#10621873—42no—
100C2×#10621873C2314yes—
101C2×#10621873C2314yes—
102C2×#10621873C2314yes—
103#13063325—22no—
104#13063325C2314yes—
105#13063324—28no—
106#13063320—28no—
107#13063317—22no—
108#13063317C2314yes—
109#13063307—28no—
110#13063304—22no—
111#13063304—22no—
112#13063304C2314yes—
113#13063304C2314yes—
114#13063302—28no—
115#13063302—28no—
116#13063299—22no—
117#13063299—22no—
118#13063299C2314yes—
119#13063299C2314yes—
120#13063297—28no—
121C4×Dic86—22no—
122C4×Dic86C2314yes—
123C4×D172—22no—
124C4×D172C2314yes—
125D4×Dic43—28no—
126(C22⋊D43)⋊C4—28no—
127#13063284—22no—
128#13063284C2314yes—
129C2×C4⋊Dic43—22no—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43C2314yes—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×C22⋊Dic43—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×C4×Dic43—21no—
150C2×C4×Dic43—21no—
151#13063259C2314yes—
152#13063259C2314yes—
153#13063257C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063250C2314yes—
158#13063250C2314yes—
159#13063250C2314yes—
160#13063250C2314yes—
161#13063250C2314yes—
162#13063250C2314yes—
163#13063247C2314yes—
164C22×D4×C43D411yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C2×M16×C43—42no—
168C2×M16×C43C2314yes—
169C22×C8×C43—42no—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2314yes—
175C4×D4×C43D414yes—
176C4×D4×C43C2314yes—
177C2×C4⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C22⋊C4×C43D411yescharacteristic
180C2×C42×C43C2311yescharacteristic
181C4⋊C8×C43C2314yes—
182C22⋊C8×C43C2314yes—
183C22⋊C8×C43C2314yes—
184#97×C43C2314yes—
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C2×D4×C43—24no—
189C2×D4×C43C2×D414yes—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—44no—
206C2×C22⋊D43—82no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—24no—
215C22×Dic43—24no—
216C22×Dic43—24no—
217C22×Dic43—44no—
218C22×Dic43—44no—
219C22×Dic43—82no—
220C2×D172—21no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172C2412yes—
224C2×C4×D43—24no—
225C2×C4×D43—82no—
226C2×Dic86—21no—
227C2×Dic86—22no—
228C2×Dic86—22no—
229C2×Dic86—22no—
230C2×Dic86—22no—
231C2×Dic86—22no—
232C2×Dic86—28no—
233C2×Dic86—28no—
234C2×Dic86—24no—
235C2×Dic86—24no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—44no—
239C2×Dic86—44no—
240C2×Dic86—48no—
241C2×Dic86—48no—
242C2×Dic86—44no—
243C2×Dic86—44no—
244C2×Dic86#4114yes—
245C2×Dic86C2412yes—
246C2×Dic86C2412yes—
247C2×Dic86C2412yes—
248M16×C43—44no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43—22no—
253C2×C8×C43—44no—
254C2×C8×C43C2412yes—
255C2×C8×C43C2412yes—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C4⋊C4×C43C2×D414yes—
259C22⋊C4×C43C2×D414yes—
260C22⋊C4×C43C2×D414yes—
261C42×C43C2×D412yes—
262C42×C43C2412yes—
263C22⋊Dic43—24no—
264C22⋊Dic43—24no—
265C22⋊Dic43—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—24no—
272C4⋊Dic43—24no—
273C4⋊Dic43—24no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43C2412yes—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2412yes—
279C4⋊Dic43C2412yes—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282Dic43⋊C4—24no—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285C4×Dic43—24no—
286C4×Dic43—24no—
287#10621873—28no—
288#10621873—44no—
289#10621873—44no—
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—
303D4×C43—28no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—24no—
309C2×C4×C43—24no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4112yes—
320C2×C4×C43H(5,𝔽2)12yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—48no—
323C22⋊D43—84no—
324C2×Dic43—24no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—48no—
333C2×Dic43—48no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—84no—
341D172—22no—
342D172—22no—
343D172—42no—
344C4×D43—84no—
345Dic86—24no—
346Dic86—22no—
347Dic86—22no—
348Dic86—22no—
349Dic86—22no—
350Dic86—22no—
351Dic86—48no—
352Dic86—48no—
353Dic86—42no—
354Dic86—42no—
355Dic86C2×#4114yes—
356C8×C43—22no—
357C8×C43—22no—
358C8×C43—22no—
359C8×C43—22no—
360C2×#3320—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#54612yes—
382C4×C43C22×#4111yescharacteristic
383C4×C43C2×H(5,𝔽2)11yescharacteristic
384Dic43—24no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390Dic43—42no—
391C2×#553—431no—
392C2×D4×Q8—431no—
393#3320—4316no—
394C2×#491—431no—
395C2×#484—431no—
396C2×#485—431no—
397C2×#479—431no—
398C2×#468—431no—
399C2×#465—431no—
400C2×#461—431no—
401C2×#448—431no—
402C2×#448—431no—
403C2×#440—431no—
404C2×#435D4311yescharacteristic, complemented
405C2×#419—431no—
406C22×#103—431no—
407C2×C43—24no—
408C2×C43—42no—
409C2×C43#332014yescomplemented
410C2×C43C2×#54611yescharacteristic
411C2×C43C22×#13711yescharacteristic
412C2×C43C2×#57711yescharacteristic
413D43—82no—
414C23×Q8—431no—
415C23×Q8—431no—
416C22×SD16—431no—
417C22×SD16—431no—
418C22×SD16—431no—
419C22×M16C2×D4311yescharacteristic
420C23×C8C2×D4311yescharacteristic
421#553—438no—
422#553—864no—
423D4×Q8—438no—
424D4×Q8—864no—
425C2×C4⋊Q8—431no—
426C2×C4⋊Q8—861no—
427C2×#126—861no—
428C2×#125—431no—
429C2×#123—861no—
430C2×C22⋊Q8—431no—
431C2×C22⋊Q8—431no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8—861no—
434C2×#121—431no—
435C2×#121—431no—
436C2×#121—861no—
437C2×C4×Q8—431no—
438C2×C4×D4—431no—
439C2×C4×D4—861no—
440C2×C4×D4—861no—
441C2×C4×D4C2×D4311yescharacteristic
442C2×#117—431no—
443C22×C4⋊C4—431no—
444#491—438no—
445#485—438no—
446#484—438no—
447#479—438no—
448#468—438no—
449#465—438no—
450#461—438no—
451#448—438no—
452#448—438no—
453#440—438no—
454#435C2×D4318yescomplemented
455C2×#107—431no—
456C2×#107—431no—
457C2×#106—431no—
458C2×C4⋊C8C2×D4311yescharacteristic
459#419—438no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—438no—
470C2×#102—431no—
471C2×C22⋊C8C2×D4311yescharacteristic
472C2×C22⋊C8C2×D4311yescharacteristic
473C2×#97C2×D4311yescharacteristic
474C43C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—431no—
476C22×Q8—431no—
477C22×Q8—431no—
478C22×Q8—434no—
479C22×Q8—434no—
480C22×Q8—864no—
481C22×Q8—864no—
482C22×Q8—861no—
483C22×Q8—861no—
484C22×Q8—862no—
485C22×Q8—862no—
486C22×Q8—1722no—
487C22×Q8—1722no—
488C22×D4—431no—
489C22×D4—861no—
490C22×D4—861no—
491C22×D4D17211yescharacteristic
492C23×C4—861no—
493C23×C4—861no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4C22×D4311yescharacteristic
497C23×C4C22×D4311yescharacteristic
498C2×SD16—434no—
499C2×SD16—434no—
500C2×SD16—434no—
501C2×SD16—864no—
502C2×SD16—1722no—
503C2×SD16—1722no—
504C2×M16—42no—
505C2×M16C22×D4314yes—
506C22×C8—42no—
507C22×C8C22×D4311yescharacteristic
508C22×C8C22×D4311yescharacteristic
509C22×C8C22×D4311yescharacteristic
510C22×C8C22×D4311yescharacteristic
511C22×C8C22×D4314yes—
512C4⋊Q8—434no—
513C4⋊Q8—868no—
514C4⋊Q8—862no—
515#126—868no—
516#125—434no—
517#125—862no—
518#123—868no—
519C22⋊Q8—434no—
520C22⋊Q8—434no—
521C22⋊Q8—862no—
522C22⋊Q8—862no—
523C22⋊Q8—868no—
524C22⋊Q8—868no—
525#121—434no—
526#121—434no—
527#121—868no—
528#121—862no—
529#121—862no—
530C4×Q8—434no—
531C4×Q8—862no—
532C4×D4—434no—
533C4×D4—868no—
534C4×D4—868no—
535C4×D4—862no—
536C4×D4D17214yes—
537C4×D4C22×D4314yes—
538#117—434no—
539#117—862no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—434no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—861no—
546C2×C4⋊C4—862no—
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⋊C4D17211yescharacteristic
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4D17211yescharacteristic
562C2×C22⋊C4D17211yescharacteristic
563C2×C42—861no—
564C2×C42—861no—
565C2×C42C22×D4311yescharacteristic
566#107—434no—
567#107—434no—
568#106—434no—
569C4⋊C8C22×D4314yes—
570#103—434no—
571#103—434no—
572#103—434no—
573#103—434no—
574#103—434no—
575#103—434no—
576#103—434no—
577#103—434no—
578#103—434no—
579#102—434no—
580C22⋊C8C22×D4314yes—
581C22⋊C8C22×D4314yes—
582#97C22×D4314yes—
583C24—861no—
584C24C2×D17211yescharacteristic
585C24C2×D17211yescharacteristic
586C2×Q8—434no—
587C2×Q8—432no—
588C2×Q8—432no—
589C2×Q8—432no—
590C2×Q8—868no—
591C2×Q8—868no—
592C2×Q8—861no—
593C2×Q8—864no—
594C2×Q8—864no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—862no—
598C2×Q8—862no—
599C2×Q8—862no—
600C2×Q8—862no—
601C2×Q8—862no—
602C2×Q8—1724no—
603C2×Q8—1724no—
604C2×Q8—1724no—
605C2×Q8—1724no—
606C2×Q8—1728no—
607C2×Q8—1728no—
608C2×D4—24no—
609C2×D4—432no—
610C2×D4—864no—
611C2×D4—864no—
612C2×D4—861no—
613C2×D4—862no—
614C2×D4—862no—
615C2×D4—3442no—
616C2×D4—1724no—
617C2×D4C2×D17214yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—861no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—864no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—864no—
633C22×C4—3442no—
634C22×C4—3442no—
635C22×C4—1724no—
636C22×C4—1724no—
637C22×C4C2×D17212yes—
638C22×C4C2×D17212yes—
639C22×C4C2×D17211yescharacteristic
640C22×C4C2×D17211yescharacteristic
641C22×C4C2×D17211yescharacteristic
642C22×C4C2×D17211yescharacteristic
643C22×C4C23×D4312yes—
644C22×C4C23×D4312yes—
645C22×C4C23×D4311yescharacteristic
646SD16—868no—
647SD16—1724no—
648SD16—1724no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—44no—
655C2×C8C23×D4312yes—
656C2×C8C23×D4312yes—
657C2×C8C23×D4312yes—
658C2×C8C23×D4312yes—
659C4⋊C4—432no—
660C4⋊C4—432no—
661C4⋊C4—432no—
662C4⋊C4—432no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—864no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—864no—
672C4⋊C4—864no—
673C4⋊C4—864no—
674C4⋊C4—864no—
675C4⋊C4C2×D17214yes—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C22⋊C4C2×D17214yes—
683C22⋊C4C2×D17214yes—
684C42—864no—
685C42—864no—
686C42C2×D17212yes—
687C42C23×D4312yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—862no—
694C23—1722no—
695C23—1722no—
696C23—1722no—
697C23#1306335814yes—
698C23C22×D17212yes—
699C23C22×D17212yes—
700C23C22×D17211yescharacteristic
701Q8—434no—
702Q8—862no—
703Q8—864no—
704Q8—862no—
705Q8—862no—
706Q8—862no—
707Q8—862no—
708Q8—1728no—
709Q8—1728no—
710Q8—1722no—
711Q8—1722no—
712D4—28no—
713D4—862no—
714D4—862no—
715D4—3444no—
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—862no—
729C2×C4—864no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—3444no—
737C2×C4—3444no—
738C2×C4—1728no—
739C2×C4—1728no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4C22×D17212yes—
747C2×C4C22×D17212yes—
748C2×C4C22×D17212yes—
749C2×C4C22×D17212yes—
750C2×C4C22×D17211yescharacteristic
751C2×C4#41×D4312yes—
752C2×C4#1306337012yes—
753C2×C4C24×D4311yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—3444no—
766C22—1722no—
767C22—1722no—
768C22—1722no—
769C22#1458354412yes—
770C22C2×#1306335814yes—
771C22C2×#1306335812yes—
772C22#1458371112yes—
773C22C23×D17211yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—864no—
779C4—1722no—
780C4—1722no—
781C4—1722no—
782C4—1722no—
783C4—1722no—
784C4—1722no—
785C4#1458354412yes—
786C4C2×#41×D4311yescharacteristic
787C4C2×#1306337011yescharacteristic
788C2—24no—
789C2—42no—
790C2—3442no—
791C2#1914676814yesdirect product factor
792C2C2×#1458354411yescharacteristic
793C2C22×#1306335811yescharacteristic
794C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583595C2
hypercenterC2×#435D43
hypocenterC43C2×#3320
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic86C2semidirect
3. #19146768C2direct (N × H)
4. C2×#14583268C2semidirect
5. C2×#14583235C2semidirect
6. C2×#14583241C2semidirect
7. C2×#14583207C2semidirect
8. C2×#14583145C2semidirect
9. C2×#14583128C2semidirect
10. C2×#14583105C2semidirect
11. C2×#14583040C2semidirect
12. C2×#14583040C2semidirect
13. C2×#14583001C2semidirect
14. C2×#14582909C2semidirect
15. C22×#13063250C2semidirect
16. C2×C43×#435C2semidirect
25. D4×Dic86C22semidirect
44. #14583268C22semidirect
45. #14583241C22semidirect
46. #14583235C22semidirect
47. #14583207C22semidirect
48. #14583145C22semidirect
49. #14583128C22semidirect
50. #14583105C22semidirect
51. #14583040C22semidirect
52. #14583040C22semidirect
53. #14583001C22semidirect
57. #14582909C22semidirect
67. C2×#13063250C22semidirect
72. C43×#435C22semidirect
404. C2×#435D43semidirect
409. C2×C43#3320semidirect
454. #435C2×D43semidirect
474. C43C2×#3320semidirect
791. C2#19146768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×D4×Dic862
#191467682
C2×#145832682
C2×#145832352
C2×#145832412
C2×#145832072
C2×#145831452
C2×#145831282
C2×#145831052
C2×#145830402
C2×#145830012
C2×#145829092
C22×#130632502
C2×C43×#4352
C2×#332043