Finite Group Databasebeta

← C2×#19144443 #25964175

Subgroups — C2×#19144443 #25964175

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583526C211yesmaximal, characteristic, complemented
2C2×#14583381C211yesmaximal, characteristic
3#19144443C2116yesmaximal, direct product factor
4C2×#14583206C211yesmaximal, characteristic, complemented
5C2×#14583204C211yesmaximal, characteristic, complemented
6C2×#14583192C211yesmaximal, characteristic, complemented
7C2×#14583202C211yesmaximal, characteristic, complemented
8C2×#14583200C211yesmaximal, characteristic, complemented
9C2×#14583178C211yesmaximal, characteristic, complemented
10C2×#14583176C211yesmaximal, characteristic, complemented
11C2×#14582940C211yesmaximal, characteristic, complemented
12C2×#107×D43C211yesmaximal, characteristic, complemented
13C2×#14582924C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic
15C2×#14582894C211yesmaximal, characteristic
16C2×C43×#477C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583526—24no—
21#14583526C2218yescomplemented
22C2×#13063324C2211yescharacteristic
23C2×#13063323—21no—
24C2×#13063317C2211yescharacteristic
25C2×#13063316C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063303—21no—
28C2×#13063301—21no—
29#14583381—24no—
30#14583381C2218yes—
31C2×Q8×Dic43C2211yescharacteristic
32C2×C4×D172—21no—
33C2×C4×D172C2211yescharacteristic
34C2×#13063287—21no—
35C2×#13063287C2211yescharacteristic
36C2×#13063283C2211yescharacteristic
37C2×#13063282—21no—
38C2×#13063282C2211yescharacteristic
39C2×C4⋊C4×D43—21no—
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583206C2218yescomplemented
43#14583204C2218yescomplemented
44#14583202C2218yescomplemented
45#14583200C2218yescomplemented
46#14583192C2218yescomplemented
47#14583178C2218yescomplemented
48#14583176C2218yescomplemented
49#14582940C2218yescomplemented
50C2×#13063259C2211yescharacteristic
51C2×#13063258C2211yescharacteristic
52C2×#13063258C2211yescharacteristic
53C2×#13063258C2211yescharacteristic
54#107×D43C2218yescomplemented
55C2×#13063257C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57#14582924C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61#14582899C2218yes—
62#14582894C2218yes—
63C2×#13063249C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063245C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#477C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#107×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902Q818yescomplemented
80C2×#10621902C2314yes—
81C22×Dic86—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×#10621872—24no—
91C2×#10621872C2314yes—
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C2×C8×D43—24no—
95C2×C8×D43C2314yes—
96#13063324—22no—
97#13063324C2314yes—
98#13063323—28no—
99#13063317—22no—
100#13063317C2314yes—
101#13063316—22no—
102#13063316C2314yes—
103#13063315—28no—
104#13063303—28no—
105#13063301—28no—
106Q8×Dic43—22no—
107Q8×Dic43C2314yes—
108C4×D172—22no—
109C4×D172—28no—
110C4×D172C2314yes—
111#13063287—28no—
112#13063287—22no—
113#13063287C2314yes—
114#13063283—22no—
115#13063283C2314yes—
116#13063282—28no—
117#13063282D414yes—
118#13063282C2314yes—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C2×Dic43⋊C4D411yescharacteristic
132C4⋊C4×D43—22no—
133C4⋊C4×D43—22no—
134C4⋊C4×D43—28no—
135C4⋊C4×D43C2314yes—
136C4⋊C4×D43C2314yes—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4D411yescharacteristic
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43C2311yescharacteristic
145#13063259C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160C22×Q8×C43—21no—
161C22×Q8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C4⋊Q8×C43—22no—
165C4⋊Q8×C43C2314yes—
166C4×Q8×C43—22no—
167C4×Q8×C43C2314yes—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C42×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#107×C43C2314yes—
176#107×C43C2314yes—
177C4⋊C8×C43C2314yes—
178#103×C43C2314yes—
179#103×C43C2314yes—
180C23×D43—21no—
181C23×D43C2×D411yescharacteristic
182C2×Q8×C43—21no—
183C2×Q8×C43—24no—
184C2×Q8×C43—22no—
185C2×Q8×C43—82no—
186C2×Q8×C43C2×Q814yes—
187C2×Q8×C43C2412yes—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201#10621902—216no—
202#10621902—28no—
203#10621902C2×Q8116yescomplemented
204C2×D172—21no—
205C2×D172—22no—
206C2×D172—28no—
207C2×D172—24no—
208C2×D172C2×Q814yes—
209C2×D172C2412yes—
210C2×C4×D43—28no—
211C2×C4×D43—24no—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—82no—
217C2×C4×D43—82no—
218C2×C4×D43—82no—
219C2×C4×D43—82no—
220C2×C4×D43C2×D412yes—
221C2×C4×D43C2×Q814yes—
222C2×C4×D43#4114yes—
223C2×C4×D43C2412yes—
224C2×Dic86—24no—
225C2×Dic86—82no—
226C2×C8×C43—22no—
227C2×C8×C43—22no—
228C2×C8×C43C2412yes—
229C2×C8×C43C2412yes—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C42×C43—24no—
239C42×C43C2×D412yes—
240C42×C43C2412yes—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4C2×D414yes—
245(C2×D43)⋊C4C2×D414yes—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43C2412yes—
252C4⋊Dic43C2412yes—
253C4⋊Dic43C2412yes—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4C2×D414yes—
261Dic43⋊C4C2×D414yes—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2412yes—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270#10621872—28no—
271C8×D43—28no—
272C23×C43C22×D411yescharacteristic
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—24no—
276C22×D43—22no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43C22⋊Q814yes—
280C22×D43C22×D412yes—
281Q8×C43—24no—
282Q8×C43—22no—
283Q8×C43—84no—
284Q8×C43C22×Q814yes—
285C2×C4×C43—24no—
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—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D412yes—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×Q812yes—
299C2×C4×C43C2×#4112yes—
300C2×C4×C43C2511yescharacteristic
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43C22⋊Q814yes—
310C2×Dic43C22×D412yes—
311C2×Dic43C22×D412yes—
312C2×Dic43C22×D412yes—
313D172—216no—
314D172—24no—
315D172—22no—
316D172C22×Q814yes—
317C4×D43—216no—
318C4×D43—84no—
319C4×D43—84no—
320C4×D43—84no—
321C4×D43—84no—
322C4×D43C22⋊Q818yes—
323C4×D43C22×Q814yes—
324C4×D43C2×#4114yes—
325Dic86—84no—
326C8×C43—22no—
327C8×C43—22no—
328C43⋊C8—22no—
329C43⋊C8—22no—
330C2×#3083—431nomaximal, Sylow
331C22×C43C2×C22⋊Q812yes—
332C22×C43#57612yes—
333C22×C43#57812yes—
334C22×C43C23×D411yescharacteristic
335C2×D43—28no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—24no—
339C2×D43—48no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43C2×C22⋊Q814yes—
343C4×C43—24no—
344C4×C43—22no—
345C4×C43—22no—
346C4×C43—42no—
347C4×C43—42no—
348C4×C43—42no—
349C4×C43C2×C22⋊Q812yes—
350C4×C43C23×Q811yescharacteristic
351C4×C43C22×#4111yescharacteristic
352Dic43—22no—
353Dic43—22no—
354Dic43—42no—
355Dic43—42no—
356Dic43—42no—
357Dic43C2×C22⋊Q814yes—
358C2×#544—431no—
359C2×#520—431no—
360#3083—4316no—
361C2×#479—431no—
362C2×#479—431no—
363C2×#477—431no—
364C2×#477D4311yescharacteristic, complemented
365C2×#478—431no—
366C2×#478—431no—
367C2×#474—431no—
368C2×#474—431no—
369C2×#428—431no—
370C22×#107—431no—
371C2×#424—431no—
372C2×#417—431no—
373C2×#416—431no—
374C2×C43#308314yescomplemented
375C2×C43C22×C22⋊Q811yescharacteristic
376C2×C43C2×#57611yescharacteristic
377C2×C43C2×#57811yescharacteristic
378D43—24no—
379D43—44no—
380C22×#41—431no—
381C22×M16—431no—
382C23×C8—431no—
383#544—438no—
384#544—864no—
385C2×C4⋊Q8—431no—
386C2×C4⋊Q8—861no—
387C2×C4⋊Q8C2×D4311yescharacteristic
388C2×#125—431no—
389C2×#125—431no—
390C2×#125—861no—
391C2×C22⋊Q8—861no—
392C2×C22⋊Q8—861no—
393#520—438no—
394#520—864no—
395C2×C4×Q8—431no—
396C2×C4×Q8C2×D4311yescharacteristic
397C2×C4×D4—431no—
398C2×C4×D4—431no—
399C2×C4×D4—861no—
400C2×C4×D4—861no—
401C2×#117—431no—
402C2×#117—431no—
403C2×#117—861no—
404C22×C4⋊C4—431no—
405C22×C4⋊C4—431no—
406C22×C4⋊C4—861no—
407#479—438no—
408#479—438no—
409#478—438no—
410#478—438no—
411#477—438no—
412#477C2×D4318yescomplemented
413#474—438no—
414#474—438no—
415#428—438no—
416C2×#107—431no—
417C2×#107—431no—
418C2×#107—431no—
419C2×#107—431no—
420C2×#107—438no—
421C2×#107C2×D4311yescharacteristic
422C2×#107C2×D4311yescharacteristic
423C2×#106—431no—
424C2×#106—431no—
425#424—438no—
426C2×C4⋊C8—431no—
427C2×C4⋊C8—431no—
428C2×C4⋊C8—431no—
429C2×C4⋊C8C2×D4311yescharacteristic
430#417—438no—
431#416—438no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103C2×D4311yescharacteristic
435C2×#103C2×D4311yescharacteristic
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C43C2×#308311yescharacteristic, complemented, Sylow
441C2×#41—438no—
442C2×#41—434no—
443C2×#41—862no—
444C2×#41—864no—
445C22×Q8—21no—
446C22×Q8—861no—
447C22×Q8C22×D4311yescharacteristic
448C22×D4—431no—
449C22×D4—861no—
450C23×C4—431no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4—861no—
454C23×C4—861no—
455C23×C4—861no—
456C2×M16—434no—
457C2×M16—864no—
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—434no—
461C22×C8—864no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464C4⋊Q8—22no—
465C4⋊Q8—434no—
466C4⋊Q8—862no—
467C4⋊Q8—868no—
468C4⋊Q8C22×D4314yes—
469#125—434no—
470#125—434no—
471#125—862no—
472#125—868no—
473#125—862no—
474C22⋊Q8—868no—
475C22⋊Q8—868no—
476C4×Q8—22no—
477C4×Q8—434no—
478C4×Q8—862no—
479C4×Q8C22×D4314yes—
480C4×D4—434no—
481C4×D4—434no—
482C4×D4—868no—
483C4×D4—862no—
484C4×D4—868no—
485C4×D4—862no—
486#117—434no—
487#117—434no—
488#117—434no—
489#117—868no—
490#117—862no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4—434no—
500C2×C4⋊C4—868no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C22⋊C4—431no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C42—21no—
520C2×C42—431no—
521C2×C42—861no—
522C2×C42—861no—
523C2×C42C22×D4311yescharacteristic
524#107—434no—
525#107—434no—
526#107—434no—
527#107—434no—
528#107C22×D4314yes—
529#107C22×D4314yes—
530#106—434no—
531#106—434no—
532C4⋊C8—434no—
533C4⋊C8—434no—
534C4⋊C8—434no—
535C4⋊C8C22×D4314yes—
536#103—434no—
537#103—434no—
538#103C22×D4314yes—
539#103C22×D4314yes—
540#102—434no—
541#102—434no—
542#102—434no—
543#102—434no—
544C24—431no—
545C24—861no—
546#41—4316no—
547#41—8616no—
548#41—868no—
549C2×Q8—21no—
550C2×Q8—24no—
551C2×Q8—22no—
552C2×Q8—82no—
553C2×Q8—864no—
554C2×Q8—3442no—
555C2×Q8Q8×D4314yes—
556C2×Q8C23×D4312yes—
557C2×D4—434no—
558C2×D4—432no—
559C2×D4—864no—
560C2×D4—868no—
561C2×D4—861no—
562C2×D4—862no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—431no—
568C22×C4—432no—
569C22×C4—434no—
570C22×C4—434no—
571C22×C4—432no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—864no—
575C22×C4—868no—
576C22×C4—864no—
577C22×C4—864no—
578C22×C4—864no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—864no—
583C22×C4—3442no—
584C22×C4—3442no—
585C22×C4—3442no—
586C22×C4—3442no—
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590M16—868no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—432no—
594C2×C8—432no—
595C2×C8—868no—
596C2×C8—862no—
597C2×C8—862no—
598C2×C8C23×D4312yes—
599C2×C8C23×D4312yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—434no—
606C4⋊C4—434no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—432no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4C23×D4312yes—
622C4⋊C4C23×D4312yes—
623C4⋊C4C23×D4312yes—
624C22⋊C4—434no—
625C22⋊C4—434no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C42—24no—
630C42—432no—
631C42—432no—
632C42—864no—
633C42—864no—
634C42D4×D4312yes—
635C42C23×D4312yes—
636C23—434no—
637C23—432no—
638C23—862no—
639C23—862no—
640C23—864no—
641C23—862no—
642C23—1722no—
643C23—1722no—
644C23C2×D4×D4311yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—84no—
648Q8—3444no—
649Q8C2×Q8×D4314yes—
650D4—434no—
651D4—8616no—
652D4—864no—
653D4—862no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—434no—
665C2×C4—432no—
666C2×C4—438no—
667C2×C4—434no—
668C2×C4—434no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—8616no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—3444no—
678C2×C4—3444no—
679C2×C4—3444no—
680C2×C4—3444no—
681C2×C4—1722no—
682C2×C4—1722no—
683C2×C4—1722no—
684C2×C4C2×D4×D4312yes—
685C2×C4C2×D4×D4312yes—
686C2×C4C2×D4×D4311yescharacteristic
687C2×C4C2×Q8×D4312yes—
688C2×C4#41×D4312yes—
689C2×C4C24×D4311yescharacteristic
690C8—22no—
691C8—22no—
692C8—862no—
693C8—862no—
694C22—434no—
695C22—862no—
696C22—862no—
697C22—868no—
698C22—864no—
699C22—1722no—
700C22—1722no—
701C22—1728no—
702C22C22⋊Q8×D4312yes—
703C22#1458370312yes—
704C22#1458371212yes—
705C22C22×D4×D4311yescharacteristic
706C4—22no—
707C4—24no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—434no—
713C4—862no—
714C4—862no—
715C4—1722no—
716C4—1722no—
717C4—1722no—
718C4C22⋊Q8×D4312yes—
719C4C22×Q8×D4311yescharacteristic
720C4C2×#41×D4311yescharacteristic
721C2—864no—
722C2—1724no—
723C2#1914444314yesdirect product factor
724C2C2×C22⋊Q8×D4311yescharacteristic
725C2C2×#1458370311yescharacteristic
726C2C2×#1458371211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#477C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenterC2×#477D43
hypocenterC43C2×#3083
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#14583526C2semidirect
3. #19144443C2direct (N × H)
4. C2×#14583206C2semidirect
5. C2×#14583204C2semidirect
6. C2×#14583192C2semidirect
7. C2×#14583202C2semidirect
8. C2×#14583200C2semidirect
9. C2×#14583178C2semidirect
10. C2×#14583176C2semidirect
11. C2×#14582940C2semidirect
12. C2×#107×D43C2semidirect
13. C2×#14582924C2semidirect
16. C2×C43×#477C2semidirect
21. #14583526C22semidirect
42. #14583206C22semidirect
43. #14583204C22semidirect
44. #14583202C22semidirect
45. #14583200C22semidirect
46. #14583192C22semidirect
47. #14583178C22semidirect
48. #14583176C22semidirect
49. #14582940C22semidirect
54. #107×D43C22semidirect
57. #14582924C22semidirect
71. C43×#477C22semidirect
79. C2×#10621902Q8semidirect
203. #10621902C2×Q8semidirect
364. C2×#477D43semidirect
374. C2×C43#3083semidirect
412. #477C2×D43semidirect
440. C43C2×#3083semidirect
723. C2#19144443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835262
C2×#145833812
#191444432
C2×#145832062
C2×#145832042
C2×#145831922
C2×#145832022
C2×#145832002
C2×#145831782
C2×#145831762
C2×#145829402
C2×#107×D432
C2×#145829242
C2×#145828992
C2×#145828942
C2×C43×#4772
C2×#308343