Finite Group Databasebeta

← C2×#19147056 #25975150

Subgroups — C2×#19147056 #25975150

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic
2C2×#14583591C211yesmaximal, characteristic
3#19147056C2116yesmaximal, direct product factor
4C2×#14583307C211yesmaximal, characteristic, complemented
5C2×#14583232C211yesmaximal, characteristic, complemented
6C2×#14583238C211yesmaximal, characteristic, complemented
7C2×#14583228C211yesmaximal, characteristic, complemented
8C2×#14583227C211yesmaximal, characteristic, complemented
9C2×#14583204C211yesmaximal, characteristic, complemented
10C2×#14583182C211yesmaximal, characteristic, complemented
11C2×#14583154C211yesmaximal, characteristic, complemented
12C2×#14583006C211yesmaximal, characteristic, complemented
13C2×#14582970C211yesmaximal, characteristic
14C2×#14582940C211yesmaximal, characteristic, complemented
15C22×#13063257C211yesmaximal, characteristic, complemented
16C2×C43×#467C211yesmaximal, characteristic, complemented
17C22×#10621872C2211yescharacteristic
18#14583607—24no—
19#14583607C2218yes—
20#14583591—24no—
21#14583591C2218yes—
22C2×#13063324C2211yescharacteristic
23C2×#13063320—21no—
24C2×#13063316—21no—
25C2×#13063316C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063309—21no—
28C2×#13063305—21no—
29C2×#13063302—21no—
30C2×#13063301C2211yescharacteristic
31C2×#13063301C2211yescharacteristic
32C2×Q8×Dic43C2211yescharacteristic
33C2×Q8×Dic43C2211yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×(C22⋊D43)⋊C4—21no—
36C2×#13063283C2211yescharacteristic
37C2×#13063281—21no—
38C22×C4⋊Dic43C2211yescharacteristic
39C22×C4⋊Dic43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41#14583307C2218yescomplemented
42#14583238C2218yescomplemented
43#14583232C2218yescomplemented
44#14583228C2218yescomplemented
45#14583227C2218yescomplemented
46#14583204C2218yescomplemented
47#14583182C2218yescomplemented
48#14583154C2218yescomplemented
49#14583006C2218yescomplemented
50#14582970C2218yes—
51#14582940C2218yescomplemented
52C2×#13063258C2211yescharacteristic
53C2×#13063258C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063257C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063257C2218yescomplemented
59C2×#13063256C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#467C2218yescomplemented
74C2×#107×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×C22⋊D43D411yescharacteristic
79C23×Dic43—21no—
80C23×Dic43—21no—
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C2×#10621872—24no—
84C2×#10621872C2314yes—
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063324—22no—
88#13063324C2314yes—
89#13063320—28no—
90#13063316—28no—
91#13063316—22no—
92#13063316C2314yes—
93#13063315—28no—
94#13063309—28no—
95#13063305—28no—
96#13063302—28no—
97#13063301—22no—
98#13063301—22no—
99#13063301C2314yes—
100#13063301C2314yes—
101Q8×Dic43—22no—
102Q8×Dic43—22no—
103Q8×Dic43C2314yes—
104Q8×Dic43C2314yes—
105C4×C22⋊D43D414yes—
106C4×C22⋊D43C2314yes—
107(C22⋊D43)⋊C4—28no—
108#13063283—22no—
109#13063283C2314yes—
110#13063281—28no—
111C2×C4⋊Dic43—22no—
112C2×C4⋊Dic43—22no—
113C2×C4⋊Dic43—21no—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43—21no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43C2314yes—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2314yes—
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⋊C4D411yescharacteristic
130C4⋊C4×D43—22no—
131C4⋊C4×D43C2314yes—
132C2×C22⋊Dic43D411yescharacteristic
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4D411yescharacteristic
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43C2311yescharacteristic
141#13063258C2314yes—
142#13063258C2314yes—
143#13063257C2314yes—
144#13063257C2314yes—
145#13063257C2314yes—
146#13063257C2314yes—
147#13063256C2314yes—
148#13063256C2314yes—
149Dic43⋊C8C2314yes—
150#13063249C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154C22⋊(C43⋊C8)C2314yes—
155(C2×D43)⋊C8C2314yes—
156#13063235C2314yes—
157C22×Q8×C43C2311yescharacteristic
158C22×Q8×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C2×Q16×C43—24no—
161C2×Q16×C43C2314yes—
162C22×C8×C43—24no—
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22⋊Q8×C43—22no—
167C22⋊Q8×C43—22no—
168C22⋊Q8×C43C2314yes—
169C22⋊Q8×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176#107×C43C2314yes—
177#103×C43C2314yes—
178#103×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C23×D43C2×D411yescharacteristic
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43—22no—
186C2×Q8×C43—22no—
187C2×Q8×C43C2412yes—
188C2×Q8×C43C2412yes—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43C2×D414yes—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—24no—
206C22×Dic43—24no—
207C22×Dic43—44no—
208C22×Dic43—82no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C2×C4×D43—22no—
213C2×C4×D43—22no—
214C2×C4×D43—24no—
215C2×C4×D43—82no—
216C2×C4×D43C2×D412yes—
217C2×C4×D43C2412yes—
218C2×Dic86—24no—
219C2×Dic86—82no—
220Q16×C43—28no—
221C2×C8×C43—22no—
222C2×C8×C43—28no—
223C2×C8×C43#4114yes—
224C2×C8×C43C2412yes—
225C2×C8×C43C2412yes—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43C2412yes—
231C4⋊C4×C43C2412yes—
232C22⋊C4×C43—24no—
233C22⋊C4×C43—24no—
234C22⋊Dic43C2×D414yes—
235(C2×D43)⋊C4—24no—
236(C2×D43)⋊C4—24no—
237(C2×D43)⋊C4—24no—
238(C2×D43)⋊C4C2×D414yes—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—24no—
244C4⋊Dic43—24no—
245C4⋊Dic43—24no—
246C4⋊Dic43—24no—
247C4⋊Dic43—24no—
248C4⋊Dic43C2412yes—
249C4⋊Dic43C2412yes—
250C4⋊Dic43C2412yes—
251C4⋊Dic43C2412yes—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4C2×D414yes—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43—24no—
261C4×Dic43C2×D412yes—
262C4×Dic43C2412yes—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267#10621872—28no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43#13714yes—
271C23×C43C22×D412yes—
272C23×C43C22×D411yescharacteristic
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43C22×D412yes—
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—42no—
282Q8×C43—42no—
283C2×C4×C43—22no—
284C2×C4×C43—24no—
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—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4112yes—
298C2×C4×C432−1+412yes—
299C2×C4×C43C2511yescharacteristic
300C22⋊D43—28no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—48no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—84no—
314C2×Dic43C22×D412yes—
315C2×Dic43C22×D412yes—
316C2×Dic43C22×D412yes—
317C4×D43—24no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—84no—
321Dic86—84no—
322C8×C43—22no—
323C8×C43C2×#4114yes—
324C43⋊C8—22no—
325C43⋊C8—22no—
326C2×#3344—431nomaximal, Sylow
327C22×C43—28no—
328C22×C43—22no—
329C22×C43—22no—
330C22×C43#54712yes—
331C22×C43C2×#13714yes—
332C22×C43C2×#13712yes—
333C22×C43#57712yes—
334C22×C43C23×D411yescharacteristic
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—44no—
339C4×C43—22no—
340C4×C43—42no—
341C4×C43—42no—
342C4×C43—42no—
343C4×C43—42no—
344C4×C43#54712yes—
345C4×C43C22×#4111yescharacteristic
346C4×C43C2×2−1+411yescharacteristic
347Dic43—22no—
348Dic43—22no—
349Dic43—22no—
350Dic43—42no—
351Dic43—42no—
352Dic43—42no—
353Dic43—42no—
354C2×#554—431no—
355C2×#552—431no—
356#3344—4316no—
357C2×#501—431no—
358C2×#484—431no—
359C2×#485—431no—
360C2×#483—431no—
361C2×#483—431no—
362C2×#479—431no—
363C2×#475—431no—
364C2×#470—431no—
365C2×#467D4311yescharacteristic, complemented
366C2×#441—431no—
367C2×#435—431no—
368C2×#428—431no—
369C22×#106—431no—
370C2×C43—24no—
371C2×C43#334414yescomplemented
372C2×C43C2×#54711yescharacteristic
373C2×C43C22×#13711yescharacteristic
374C2×C43C2×#57711yescharacteristic
375D43—42no—
376C22×Q16C2×D4311yescharacteristic
377C22×M16—431no—
378C23×C8C2×D4311yescharacteristic
379#554—438no—
380#554—864no—
381#552—438no—
382#552—864no—
383C2×C4⋊Q8—431no—
384C2×#126—861no—
385C2×#125—431no—
386C2×#125—861no—
387C2×#125—861no—
388C2×#123—861no—
389C2×C22⋊Q8—431no—
390C2×C22⋊Q8—431no—
391C2×C22⋊Q8—861no—
392C2×C22⋊Q8—861no—
393C2×C22⋊Q8C2×D4311yescharacteristic
394C2×C22⋊Q8C2×D4311yescharacteristic
395C2×C4×Q8—431no—
396C2×C4×Q8—431no—
397C2×C4×D4—431no—
398C2×C4×D4—861no—
399C2×#117—431no—
400C2×#117—861no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4—431no—
404#501—438no—
405#485—438no—
406#484—438no—
407#483—438no—
408#483—438no—
409#479—438no—
410#475—438no—
411#470—438no—
412#467C2×D4318yescomplemented
413#441—438no—
414#435—438no—
415#428—438no—
416C2×#107—431no—
417C2×#107—431no—
418C2×#107C2×D4311yescharacteristic
419C2×#106—431no—
420C2×#106—431no—
421C2×#106—438no—
422C2×#106—431no—
423C2×#106—431no—
424C2×#106—431no—
425C2×#106—431no—
426C2×C4⋊C8—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103—431no—
431C2×#103C2×D4311yescharacteristic
432C2×#103C2×D4311yescharacteristic
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×#97—431no—
436C43C2×#334411yescharacteristic, complemented, Sylow
437C22×Q8—861no—
438C22×Q8C22×D4311yescharacteristic
439C22×Q8C22×D4311yescharacteristic
440C22×D4—431no—
441C23×C4—431no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4—861no—
445C23×C4C22×D4311yescharacteristic
446C2×Q16—24no—
447C2×Q16C22×D4314yes—
448C2×M16—434no—
449C2×M16—864no—
450C22×C8—24no—
451C22×C8—431no—
452C22×C8—431no—
453C22×C8C22×D4311yescharacteristic
454C22×C8C22×D4314yes—
455C22×C8C22×D4311yescharacteristic
456C4⋊Q8—434no—
457C4⋊Q8—862no—
458#126—868no—
459#125—434no—
460#125—862no—
461#125—868no—
462#125—868no—
463#123—868no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—434no—
467C22⋊Q8—434no—
468C22⋊Q8—868no—
469C22⋊Q8—868no—
470C22⋊Q8—862no—
471C22⋊Q8—862no—
472C22⋊Q8C22×D4314yes—
473C22⋊Q8C22×D4314yes—
474C4×Q8—434no—
475C4×Q8—434no—
476C4×Q8—862no—
477C4×Q8—862no—
478C4×D4—434no—
479C4×D4—434no—
480C4×D4—868no—
481#117—434no—
482#117—868no—
483#117—862no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—434no—
492C2×C4⋊C4—434no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—862no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—862no—
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—431no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C42—431no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520#107—434no—
521#107—434no—
522#107C22×D4314yes—
523#106—434no—
524#106—434no—
525#106—434no—
526#106—434no—
527#106—434no—
528#106—434no—
529C4⋊C8—434no—
530#103—434no—
531#103—434no—
532#103—434no—
533#103—434no—
534#103C22×D4314yes—
535#103C22×D4314yes—
536C22⋊C8—434no—
537C22⋊C8—434no—
538#97—434no—
539C24—431no—
540C24D4×D4311yescharacteristic
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—864no—
548C2×Q8—3442no—
549C2×Q8C23×D4312yes—
550C2×Q8C23×D4312yes—
551C2×D4—434no—
552C2×D4—864no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—864no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—864no—
568C22×C4—864no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—3442no—
574C22×C4—3442no—
575C22×C4—1724no—
576C22×C4D4×D4312yes—
577C22×C4D4×D4311yescharacteristic
578C22×C4C23×D4312yes—
579C22×C4C23×D4311yescharacteristic
580Q16—28no—
581M16—868no—
582C2×C8—22no—
583C2×C8—28no—
584C2×C8—432no—
585C2×C8—432no—
586C2×C8—862no—
587C2×C8—862no—
588C2×C8#1062190014yes—
589C2×C8C23×D4312yes—
590C2×C8C23×D4312yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—434no—
596C4⋊C4—432no—
597C4⋊C4—432no—
598C4⋊C4—432no—
599C4⋊C4—432no—
600C4⋊C4—864no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—864no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—864no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—864no—
614C4⋊C4C23×D4312yes—
615C4⋊C4C23×D4312yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—434no—
619C22⋊C4—434no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C42—432no—
624C42—432no—
625C42—864no—
626C42—864no—
627C42—864no—
628C23—22no—
629C23—22no—
630C23—432no—
631C23—862no—
632C23—862no—
633C23—862no—
634C23#1306335714yes—
635C23C2×D4×D4312yes—
636C23C2×D4×D4311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—3444no—
644D4—868no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—432no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—864no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—3444no—
671C2×C4—3444no—
672C2×C4—1728no—
673C2×C4—1722no—
674C2×C4—1722no—
675C2×C4—1722no—
676C2×C4—1722no—
677C2×C4C2×D4×D4312yes—
678C2×C4C2×D4×D4311yescharacteristic
679C2×C4C2×#1062190012yes—
680C2×C4#1306337212yes—
681C2×C4C24×D4311yescharacteristic
682C8—22no—
683C8—862no—
684C8—862no—
685C8C2×#1062190014yes—
686C22—22no—
687C22—22no—
688C22—28no—
689C22—862no—
690C22—862no—
691C22—862no—
692C22—1724no—
693C22#1458354912yes—
694C22C2×#1306335714yes—
695C22C2×#1306335712yes—
696C22#1458370612yes—
697C22C22×D4×D4311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—862no—
704C4—862no—
705C4—862no—
706C4—1722no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C4#1458354912yes—
711C4C22×#1062190011yescharacteristic
712C4C2×#1306337211yescharacteristic
713C2—24no—
714C2—1722no—
715C2#1914705614yesdirect product factor
716C2C2×#1458354911yescharacteristic
717C2C22×#1306335711yescharacteristic
718C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#467C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#467D43
hypocenterC43C2×#3344
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #19147056C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583232C2semidirect
6. C2×#14583238C2semidirect
7. C2×#14583228C2semidirect
8. C2×#14583227C2semidirect
9. C2×#14583204C2semidirect
10. C2×#14583182C2semidirect
11. C2×#14583154C2semidirect
12. C2×#14583006C2semidirect
14. C2×#14582940C2semidirect
15. C22×#13063257C2semidirect
16. C2×C43×#467C2semidirect
41. #14583307C22semidirect
42. #14583238C22semidirect
43. #14583232C22semidirect
44. #14583228C22semidirect
45. #14583227C22semidirect
46. #14583204C22semidirect
47. #14583182C22semidirect
48. #14583154C22semidirect
49. #14583006C22semidirect
51. #14582940C22semidirect
58. C2×#13063257C22semidirect
73. C43×#467C22semidirect
365. C2×#467D43semidirect
371. C2×C43#3344semidirect
412. #467C2×D43semidirect
436. C43C2×#3344semidirect
715. C2#19147056direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145835912
#191470562
C2×#145833072
C2×#145832322
C2×#145832382
C2×#145832282
C2×#145832272
C2×#145832042
C2×#145831822
C2×#145831542
C2×#145830062
C2×#145829702
C2×#145829402
C22×#130632572
C2×C43×#4672
C2×#334443