Finite Group Databasebeta

← C2×#22599911 #32872498

Subgroups — C2×#22599911 #32872498

Order 18176.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556159C211yesmaximal, characteristic, complemented
2C23×#11765855C211yesmaximal, characteristic, complemented
3C2×#17986658C211yesmaximal, characteristic
4#22599911C2116yesmaximal, direct product factor
5C2×#17986391C211yesmaximal, characteristic, complemented
6C2×#17986255C211yesmaximal, characteristic, complemented
7C2×#17986230C211yesmaximal, characteristic, complemented
8C2×#17986221C211yesmaximal, characteristic, complemented
9C2×#17986206C211yesmaximal, characteristic, complemented
10C2×#17986159C211yesmaximal, characteristic, complemented
11C2×#17986155C211yesmaximal, characteristic, complemented
12C2×#17986154C211yesmaximal, characteristic, complemented
13C2×#17986138C211yesmaximal, characteristic, complemented
14C2×#17986104C211yesmaximal, characteristic, complemented
15C2×#17986071C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×Dic142C2211yescharacteristic
19C2×#14556159—28no—
20C2×#14556159C2218yescomplemented
21C22×#11765855—28no—
22C22×#11765855C2211yescharacteristic
23C22×#11765855C2211yescharacteristic
24C22×#11765855C2211yescharacteristic
25C22×#11765855C2211yescharacteristic
26C22×#11765855C2211yescharacteristic
27C22×#11765855C2211yescharacteristic
28C22×#11765855C2218yescomplemented
29C22×#11765852C2211yescharacteristic
30C22×#11765852C2211yescharacteristic
31C22×#11765852C2211yescharacteristic
32C22×#11765849C2211yescharacteristic
33C23×C71⋊C8C2211yescharacteristic
34#17986658—24no—
35#17986658C2218yes—
36C2×#14556116C2211yescharacteristic
37C2×#14556114—21no—
38C2×#14556107C2211yescharacteristic
39C2×#14556106—21no—
40C2×#14556102C2211yescharacteristic
41C2×#14556100—21no—
42C2×C4×Dic142C2211yescharacteristic
43C2×(C22⋊D71)⋊C4—21no—
44#17986391C2218yescomplemented
45#17986255C2218yescomplemented
46#17986230C2218yescomplemented
47#17986221C2218yescomplemented
48#17986206C2218yescomplemented
49#17986159C2218yescomplemented
50#17986155C2218yescomplemented
51#17986154C2218yescomplemented
52#17986138C2218yescomplemented
53#17986104C2218yescomplemented
54#17986071C2218yescomplemented
55C2×#14556059C2211yescharacteristic
56C2×C4⋊(C71⋊C8)C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556052C2211yescharacteristic
59C2×#14556052C2211yescharacteristic
60C2×#14556051C2211yescharacteristic
61C2×#14556051C2211yescharacteristic
62C2×#14556048C2211yescharacteristic
63C2×C22⋊(C71⋊C8)C2211yescharacteristic
64C2×C22⋊(C71⋊C8)C2211yescharacteristic
65C2×#14556039C2211yescharacteristic
66C23×Q8×C71C2211yescharacteristic
67C23×Q8×C71C2211yescharacteristic
68D4×Q8×C71—24no—
69D4×Q8×C71C2218yescomplemented
70C2×C4⋊Q8×C71—21no—
71C2×C4⋊Q8×C71C2211yescharacteristic
72C2×C22⋊Q8×C71—21no—
73C2×C22⋊Q8×C71—21no—
74C2×C22⋊Q8×C71C2211yescharacteristic
75C2×C22⋊Q8×C71C2211yescharacteristic
76C2×C4×Q8×C71C2211yescharacteristic
77C2×C4×D4×C71—21no—
78C2×C4×D4×C71C2211yescharacteristic
79C2×#11765865—24no—
80C2×#11765865—22no—
81C2×#11765865—42no—
82C2×#11765865C2314yes—
83C22×Dic142—24no—
84C22×Dic142—22no—
85C22×Dic142—21no—
86C22×Dic142—42no—
87C22×Dic142C2311yescharacteristic
88C22×Dic142C2314yes—
89C22×Dic142C2311yescharacteristic
90C22×D284C2311yescharacteristic
91C22×C22⋊D71—21no—
92C22×C22⋊D71—21no—
93C23×Dic71—21no—
94C22×C4×D71—21no—
95#14556159—232no—
96C2×#11765855—24no—
97C2×#11765855—24no—
98C2×#11765855—232no—
99C2×#11765855—24no—
100C2×#11765855—24no—
101C2×#11765855—42no—
102C2×#11765855D418yescomplemented
103C2×#11765855C2314yes—
104C2×#11765855C2314yes—
105C2×#11765855C2314yes—
106C2×#11765855C2314yes—
107C2×#11765855C2314yes—
108C2×#11765855C2314yes—
109C2×#11765852—24no—
110C2×#11765852—24no—
111C2×#11765852—42no—
112C2×#11765852C2314yes—
113C2×#11765852C2314yes—
114C2×#11765852C2314yes—
115C2×#11765849—24no—
116C2×#11765849C2314yes—
117C22×C71⋊C8—24no—
118C22×C71⋊C8C2314yes—
119C22×C71⋊C8C2311yescharacteristic
120C22×C71⋊C8C2311yescharacteristic
121C22×C71⋊C8C2311yescharacteristic
122C22×C71⋊C8C2311yescharacteristic
123#14556116—22no—
124#14556116C2314yes—
125#14556114—28no—
126#14556107—22no—
127#14556107C2314yes—
128#14556106—28no—
129#14556102—22no—
130#14556102C2314yes—
131#14556100—28no—
132C4×Dic142—22no—
133C4×Dic142C2314yes—
134(C22⋊D71)⋊C4—28no—
135C2×C4⋊Dic71C2311yescharacteristic
136C2×Dic71⋊C4—21no—
137C2×Dic71⋊C4—21no—
138C2×C22⋊Dic71—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×C4×Dic71—21no—
143#14556059C2314yes—
144C4⋊(C71⋊C8)C2314yes—
145#14556052C2314yes—
146#14556052C2314yes—
147#14556052C2314yes—
148#14556051C2314yes—
149#14556051C2314yes—
150#14556048C2314yes—
151C22⋊(C71⋊C8)C2314yes—
152C22⋊(C71⋊C8)C2314yes—
153#14556039C2314yes—
154C22×Q8×C71—21no—
155C22×Q8×C71—21no—
156C22×Q8×C71—22no—
157C22×Q8×C71—22no—
158C22×Q8×C71—24no—
159C22×Q8×C71—24no—
160C22×Q8×C71—42no—
161C22×Q8×C71—42no—
162C22×Q8×C71C2311yescharacteristic
163C22×Q8×C71C2311yescharacteristic
164C22×Q8×C71C2314yes—
165C22×Q8×C71C2314yes—
166C22×Q8×C71C2311yescharacteristic
167C22×D4×C71D411yescharacteristic
168C23×C4×C71—21no—
169C23×C4×C71—21no—
170C23×C4×C71C2311yescharacteristic
171C23×C4×C71C2311yescharacteristic
172C4⋊Q8×C71—28no—
173C4⋊Q8×C71—22no—
174C4⋊Q8×C71C2314yes—
175C22⋊Q8×C71—22no—
176C22⋊Q8×C71—22no—
177C22⋊Q8×C71—28no—
178C22⋊Q8×C71—28no—
179C22⋊Q8×C71C2314yes—
180C22⋊Q8×C71C2314yes—
181C4×Q8×C71—22no—
182C4×Q8×C71C2314yes—
183C4×D4×C71—28no—
184C4×D4×C71D414yes—
185C4×D4×C71C2314yes—
186C2×C4⋊C4×C71—21no—
187C2×C4⋊C4×C71—21no—
188C2×C4⋊C4×C71—21no—
189C2×C4⋊C4×C71—21no—
190C2×C4⋊C4×C71—21no—
191C2×C4⋊C4×C71D411yescharacteristic
192C2×C4⋊C4×C71C2311yescharacteristic
193C2×C22⋊C4×C71—21no—
194C2×C22⋊C4×C71—21no—
195C2×C22⋊C4×C71D411yescharacteristic
196C2×C22⋊C4×C71D411yescharacteristic
197C2×C42×C71—21no—
198C2×C42×C71C2311yescharacteristic
199C23×D71—21no—
200#11765865—28no—
201#11765865—44no—
202#11765865—48no—
203C2×Dic142—21no—
204C2×Dic142—22no—
205C2×Dic142—22no—
206C2×Dic142—22no—
207C2×Dic142—28no—
208C2×Dic142—24no—
209C2×Dic142—21no—
210C2×Dic142—44no—
211C2×Dic142—48no—
212C2×Dic142—44no—
213C2×Dic142C2×D414yes—
214C2×Dic142C2412yes—
215C2×Dic142C2412yes—
216C2×D284—22no—
217C2×D284—22no—
218C2×D284—21no—
219C2×D284C2412yes—
220C2×C22⋊D71—24no—
221C2×C22⋊D71—24no—
222C2×C22⋊D71—44no—
223C2×C22⋊D71—44no—
224C22×Dic71—21no—
225C22×Dic71—21no—
226C22×Dic71—24no—
227C22×Dic71—21no—
228C22×Dic71—44no—
229C2×C4×D71—24no—
230C2×C4×D71—44no—
231#11765855—28no—
232#11765855—28no—
233#11765855—28no—
234#11765855—28no—
235#11765855—44no—
236#11765855C2×D4116yescomplemented
237#11765852—28no—
238#11765852—28no—
239#11765852—44no—
240#11765849—28no—
241C2×C71⋊C8—22no—
242C2×C71⋊C8—22no—
243C2×C71⋊C8—22no—
244C2×C71⋊C8—28no—
245C2×C71⋊C8C2×D414yes—
246C2×C71⋊C8C2412yes—
247C2×C71⋊C8C2412yes—
248C2×C71⋊C8C2412yes—
249C2×C71⋊C8C2412yes—
250C4⋊Dic71—21no—
251C4⋊Dic71C2412yes—
252Dic71⋊C4—24no—
253Dic71⋊C4—24no—
254C22⋊Dic71—24no—
255(C2×D71)⋊C4—24no—
256(C2×D71)⋊C4—24no—
257(C2×D71)⋊C4—24no—
258C4×Dic71—24no—
259C24×C71C2×D411yescharacteristic
260C24×C71C2×D411yescharacteristic
261C2×Q8×C71—21no—
262C2×Q8×C71—24no—
263C2×Q8×C71—24no—
264C2×Q8×C71—21no—
265C2×Q8×C71—21no—
266C2×Q8×C71—22no—
267C2×Q8×C71—28no—
268C2×Q8×C71—28no—
269C2×Q8×C71—22no—
270C2×Q8×C71—22no—
271C2×Q8×C71—22no—
272C2×Q8×C71—22no—
273C2×Q8×C71—44no—
274C2×Q8×C71—44no—
275C2×Q8×C71—44no—
276C2×Q8×C71—44no—
277C2×Q8×C71—48no—
278C2×Q8×C71—48no—
279C2×Q8×C71C2×D414yes—
280C2×Q8×C71C2412yes—
281C2×Q8×C71C2412yes—
282C2×Q8×C71C2412yes—
283C2×D4×C71—24no—
284C2×D4×C71C2×D414yes—
285C22×C4×C71—21no—
286C22×C4×C71—22no—
287C22×C4×C71—22no—
288C22×C4×C71—22no—
289C22×C4×C71—22no—
290C22×C4×C71—21no—
291C22×C4×C71—21no—
292C22×C4×C71—21no—
293C22×C4×C71—24no—
294C22×C4×C71—24no—
295C22×C4×C71—44no—
296C22×C4×C71—44no—
297C22×C4×C71C2×D411yescharacteristic
298C22×C4×C71C2×D411yescharacteristic
299C22×C4×C71C2×D412yes—
300C22×C4×C71C2×D412yes—
301C22×C4×C71C2×D411yescharacteristic
302C22×C4×C71C2×D411yescharacteristic
303C22×C4×C71C2412yes—
304C22×C4×C71C2412yes—
305C22×C4×C71C2411yescharacteristic
306C4⋊C4×C71—24no—
307C4⋊C4×C71—24no—
308C4⋊C4×C71—24no—
309C4⋊C4×C71—24no—
310C4⋊C4×C71—24no—
311C4⋊C4×C71—21no—
312C4⋊C4×C71C2×D414yes—
313C4⋊C4×C71C2412yes—
314C22⋊C4×C71—24no—
315C22⋊C4×C71—24no—
316C22⋊C4×C71C2×D414yes—
317C22⋊C4×C71C2×D414yes—
318C42×C71—24no—
319C42×C71C2×D412yes—
320C42×C71C2412yes—
321C23×C71—22no—
322C23×C71—22no—
323C23×C71—22no—
324C23×C71—22no—
325C23×C71—22no—
326C23×C71#13714yescomplemented
327C23×C71C22×D412yes—
328C23×C71C22×D412yes—
329C23×C71C22×D411yescharacteristic
330C22×D71—22no—
331C22×D71—42no—
332C22×D71—42no—
333C22×D71—42no—
334Q8×C71—24no—
335Q8×C71—22no—
336Q8×C71—22no—
337Q8×C71—22no—
338Q8×C71—22no—
339Q8×C71—22no—
340Q8×C71—48no—
341Q8×C71—48no—
342Q8×C71—42no—
343Q8×C71—42no—
344Q8×C71C22×D414yes—
345D4×C71—28no—
346C2×C4×C71—22no—
347C2×C4×C71—22no—
348C2×C4×C71—24no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—24no—
353C2×C4×C71—24no—
354C2×C4×C71—22no—
355C2×C4×C71—22no—
356C2×C4×C71—22no—
357C2×C4×C71—22no—
358C2×C4×C71—22no—
359C2×C4×C71—22no—
360C2×C4×C71—22no—
361C2×C4×C71—48no—
362C2×C4×C71—48no—
363C2×C4×C71—42no—
364C2×C4×C71—42no—
365C2×C4×C71—42no—
366C2×C4×C71C22×D412yes—
367C2×C4×C71C22×D412yes—
368C2×C4×C71C22×D412yes—
369C2×C4×C71C22×D412yes—
370C2×C4×C71C22×D412yes—
371C2×C4×C71C22×D411yescharacteristic
372C2×C4×C71H(5,𝔽2)12yes—
373C2×C4×C71C2511yescharacteristic
374C22⋊D71—48no—
375C22⋊D71—48no—
376C2×Dic71—24no—
377C2×Dic71—22no—
378C2×Dic71—22no—
379C2×Dic71—22no—
380C2×Dic71—48no—
381C2×Dic71—42no—
382C2×Dic71—42no—
383D284—22no—
384D284—22no—
385D284—42no—
386C4×D71—48no—
387Dic142—24no—
388Dic142—22no—
389Dic142—22no—
390Dic142—22no—
391Dic142—48no—
392Dic142—42no—
393Dic142C22×D414yes—
394C71⋊C8—22no—
395C71⋊C8—22no—
396C71⋊C8—22no—
397C71⋊C8C22×D414yes—
398C22×C71—22no—
399C22×C71—28no—
400C22×C71—22no—
401C22×C71—22no—
402C22×C71—22no—
403C22×C71—22no—
404C22×C71—44no—
405C22×C71D4212yes—
406C22×C71C2×#13712yes—
407C22×C71C2×#13714yescomplemented
408C22×C71#57812yes—
409C22×C71C23×D411yescharacteristic
410C2×D71—42no—
411C2×D71—42no—
412C2×D71—42no—
413C2×D71—84no—
414C4×C71—22no—
415C4×C71—22no—
416C4×C71—24no—
417C4×C71—22no—
418C4×C71—22no—
419C4×C71—42no—
420C4×C71—42no—
421C4×C71—42no—
422C4×C71D4212yes—
423C4×C71C23×D411yescharacteristic
424C4×C71C2×H(5,𝔽2)11yescharacteristic
425Dic71—24no—
426Dic71—42no—
427Dic71—42no—
428C2×#3270—711nomaximal, Sylow
429C2×C71—24no—
430C2×C71—42no—
431C2×C71#327014yescomplemented
432C2×C71C2×D4211yescharacteristic
433C2×C71C22×#13711yescharacteristic
434C2×C71C2×#57811yescharacteristic
435D71—82no—
436C22×#137—711no—
437C23×Q16—711no—
438C2×D4×Q8D7111yescharacteristic, complemented
439C2×#548—711no—
440#3270—7116no—
441C2×#497—711no—
442C2×#470—711no—
443C2×#465—711no—
444C2×#464—711no—
445C2×#462—711no—
446C2×#452—711no—
447C2×#451—711no—
448C2×#451—711no—
449C2×#448—711no—
450C2×#441—711no—
451C2×#435—711no—
452C71C2×#327011yescharacteristic, complemented, Sylow
453C22×#41—711no—
454C23×Q8—711no—
455C23×Q8C2×D7111yescharacteristic
456C23×Q8C2×D7111yescharacteristic
457C2×#137—718no—
458C2×#137—1428no—
459C22×Q16—711no—
460C22×Q16—711no—
461C22×Q16—711no—
462C22×Q16—711no—
463C22×Q16—711no—
464C22×Q16—711no—
465C22×Q16—718no—
466C22×Q16—1428no—
467C22×SD16—711no—
468C22×SD16—711no—
469C22×SD16—711no—
470C22×M16—711no—
471C23×C8—711no—
472D4×Q8—24no—
473D4×Q8C2×D7118yescomplemented
474#548—718no—
475#548—1424no—
476C2×C4⋊Q8—21no—
477C2×C4⋊Q8C2×D7111yescharacteristic
478C2×#124—711no—
479C2×#124—1421no—
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8—711no—
483C2×C22⋊Q8—1421no—
484C2×C22⋊Q8C2×D7111yescharacteristic
485C2×C22⋊Q8C2×D7111yescharacteristic
486C2×#121—711no—
487C2×#121—1421no—
488C2×C4×Q8—711no—
489C2×C4×Q8C2×D7111yescharacteristic
490C2×C4×D4—21no—
491C2×C4×D4—1421no—
492C2×C4×D4C2×D7111yescharacteristic
493#497—718no—
494#470—718no—
495#465—718no—
496#464—718no—
497#462—718no—
498#452—718no—
499#451—718no—
500#451—718no—
501#448—718no—
502#441—718no—
503#435—718no—
504C2×#106—711no—
505C2×C4⋊C8—711no—
506C2×#103—711no—
507C2×#103—711no—
508C2×#103—711no—
509C2×#103—711no—
510C2×#103—711no—
511C2×#102—711no—
512C2×C22⋊C8—711no—
513C2×C22⋊C8—711no—
514C2×#97—711no—
515C2×#41—2842no—
516C2×#41—714no—
517C2×#41—1424no—
518C2×#41—1422no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—22no—
522C22×Q8—22no—
523C22×Q8—24no—
524C22×Q8—24no—
525C22×Q8—42no—
526C22×Q8—42no—
527C22×Q8—2842no—
528C22×Q8—714no—
529C22×Q8—711no—
530C22×Q8—711no—
531C22×Q8—1424no—
532C22×Q8—1421no—
533C22×Q8—1422no—
534C22×Q8C22×D7111yescharacteristic
535C22×Q8C22×D7111yescharacteristic
536C22×Q8C22×D7114yes—
537C22×Q8C22×D7114yes—
538C22×Q8C22×D7111yescharacteristic
539C22×D4—711no—
540C22×D4—1421no—
541C22×D4—1421no—
542C22×D4C22⋊D7111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—1421no—
546C23×C4—1421no—
547C23×C4C22×D7111yescharacteristic
548C23×C4C22×D7111yescharacteristic
549#137—14232no—
550C2×Q16—2842no—
551C2×Q16—714no—
552C2×Q16—718no—
553C2×Q16—714no—
554C2×Q16—714no—
555C2×Q16—714no—
556C2×Q16—714no—
557C2×Q16—714no—
558C2×Q16—1424no—
559C2×Q16—14232no—
560C2×Q16—1424no—
561C2×Q16—1424no—
562C2×Q16—1424no—
563C2×SD16—2842no—
564C2×SD16—714no—
565C2×SD16—714no—
566C2×SD16—714no—
567C2×SD16—1424no—
568C2×SD16—1424no—
569C2×M16—714no—
570C2×M16—1424no—
571C22×C8—711no—
572C22×C8—711no—
573C22×C8—714no—
574C22×C8—711no—
575C22×C8—711no—
576C22×C8—1424no—
577C4⋊Q8—28no—
578C4⋊Q8—22no—
579C4⋊Q8C22×D7114yes—
580#124—714no—
581#124—1428no—
582#124—1422no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—28no—
586C22⋊Q8—28no—
587C22⋊Q8—714no—
588C22⋊Q8—1422no—
589C22⋊Q8—1428no—
590C22⋊Q8C22×D7114yes—
591C22⋊Q8C22×D7114yes—
592#121—714no—
593#121—1428no—
594#121—1422no—
595C4×Q8—22no—
596C4×Q8—714no—
597C4×Q8—1422no—
598C4×Q8C22×D7114yes—
599C4×D4—28no—
600C4×D4—1428no—
601C4×D4C22⋊D7114yes—
602C4×D4C22×D7114yes—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—711no—
609C2×C4⋊C4—1421no—
610C2×C4⋊C4—1421no—
611C2×C4⋊C4C22⋊D7111yescharacteristic
612C2×C4⋊C4C22×D7111yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—1421no—
616C2×C22⋊C4—1421no—
617C2×C22⋊C4—1421no—
618C2×C22⋊C4—1421no—
619C2×C22⋊C4C22⋊D7111yescharacteristic
620C2×C22⋊C4C22⋊D7111yescharacteristic
621C2×C42—21no—
622C2×C42—1421no—
623C2×C42C22×D7111yescharacteristic
624#106—714no—
625C4⋊C8—714no—
626#103—714no—
627#103—714no—
628#103—714no—
629#103—714no—
630#103—714no—
631#102—714no—
632C22⋊C8—714no—
633C22⋊C8—714no—
634#97—714no—
635C24—1421no—
636C24C2×C22⋊D7111yescharacteristic
637C24C2×C22⋊D7111yescharacteristic
638#41—2848no—
639#41—2844no—
640#41—1428no—
641C2×Q8—21no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—22no—
647C2×Q8—28no—
648C2×Q8—28no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—44no—
654C2×Q8—44no—
655C2×Q8—44no—
656C2×Q8—44no—
657C2×Q8—48no—
658C2×Q8—48no—
659C2×Q8—2848no—
660C2×Q8—2844no—
661C2×Q8—2844no—
662C2×Q8—714no—
663C2×Q8—712no—
664C2×Q8—712no—
665C2×Q8—1428no—
666C2×Q8—1422no—
667C2×Q8—1422no—
668C2×Q8—1421no—
669C2×Q8—1424no—
670C2×Q8—1421no—
671C2×Q8—1422no—
672C2×Q8D4×D7114yes—
673C2×Q8C23×D7112yes—
674C2×Q8C23×D7112yes—
675C2×Q8C23×D7112yes—
676C2×D4—24no—
677C2×D4—2844no—
678C2×D4—2844no—
679C2×D4—712no—
680C2×D4—1424no—
681C2×D4—1424no—
682C2×D4—1422no—
683C2×D4—1421no—
684C2×D4—1422no—
685C2×D4C2×C22⋊D7114yes—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—2844no—
699C22×C4—2844no—
700C22×C4—1424no—
701C22×C4—1421no—
702C22×C4—1421no—
703C22×C4—1424no—
704C22×C4—1421no—
705C22×C4C2×C22⋊D7112yes—
706C22×C4C2×C22⋊D7112yes—
707C22×C4C2×C22⋊D7111yescharacteristic
708C22×C4C2×C22⋊D7111yescharacteristic
709C22×C4C2×C22⋊D7111yescharacteristic
710C22×C4C2×C22⋊D7111yescharacteristic
711C22×C4C23×D7112yes—
712C22×C4C23×D7112yes—
713C22×C4C23×D7111yescharacteristic
714Q16—2844no—
715Q16—7116no—
716Q16—1428no—
717Q16—1428no—
718Q16—1428no—
719Q16—1428no—
720SD16—2844no—
721SD16—1428no—
722SD16—1428no—
723M16—1428no—
724C2×C8—714no—
725C2×C8—712no—
726C2×C8—712no—
727C2×C8—712no—
728C2×C8—712no—
729C2×C8—1428no—
730C2×C8—1422no—
731C2×C8—1422no—
732C2×C8—1422no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—21no—
739C4⋊C4—712no—
740C4⋊C4—1424no—
741C4⋊C4—1424no—
742C4⋊C4—1421no—
743C4⋊C4C2×C22⋊D7114yes—
744C4⋊C4C23×D7112yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—1424no—
748C22⋊C4—1424no—
749C22⋊C4—1424no—
750C22⋊C4—1424no—
751C22⋊C4C2×C22⋊D7114yes—
752C22⋊C4C2×C22⋊D7114yes—
753C42—24no—
754C42—1424no—
755C42C2×C22⋊D7112yes—
756C42C23×D7112yes—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—2842no—
763C23—2842no—
764C23—2842no—
765C23—1422no—
766C23#1455615914yescomplemented
767C23C22×C22⋊D7112yes—
768C23C22×C22⋊D7112yes—
769C23C22×C22⋊D7111yescharacteristic
770Q8—22no—
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—22no—
776Q8—48no—
777Q8—48no—
778Q8—42no—
779Q8—42no—
780Q8—2848no—
781Q8—2842no—
782Q8—714no—
783Q8—1422no—
784Q8—1422no—
785Q8—1422no—
786Q8—1424no—
787Q8C2×D4×D7114yes—
788D4—28no—
789D4—2848no—
790D4—2848no—
791D4—2842no—
792D4—1422no—
793D4—1422no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—48no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—2848no—
815C2×C4—2842no—
816C2×C4—2842no—
817C2×C4—2848no—
818C2×C4—1422no—
819C2×C4—1422no—
820C2×C4—1422no—
821C2×C4—1424no—
822C2×C4C2×D4×D7112yes—
823C2×C4C22×C22⋊D7112yes—
824C2×C4C22×C22⋊D7112yes—
825C2×C4C22×C22⋊D7112yes—
826C2×C4C22×C22⋊D7112yes—
827C2×C4C22×C22⋊D7111yescharacteristic
828C2×C4#1455617312yes—
829C2×C4C24×D7111yescharacteristic
830C8—714no—
831C8—1422no—
832C8—1422no—
833C8—1422no—
834C22—22no—
835C22—22no—
836C22—28no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—44no—
841C22—2842no—
842C22—2842no—
843C22—2842no—
844C22—5684no—
845C22D4×C22⋊D7112yes—
846C22C2×#1455615912yes—
847C22C2×#1455615914yescomplemented
848C22#1798681412yes—
849C22C23×C22⋊D7111yescharacteristic
850C4—22no—
851C4—22no—
852C4—24no—
853C4—22no—
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—2842no—
859C4—2842no—
860C4—1424no—
861C4D4×C22⋊D7112yes—
862C4C22×D4×D7111yescharacteristic
863C4C2×#1455617311yescharacteristic
864C2—24no—
865C2—42no—
866C2—5682no—
867C2#2259991114yesdirect product factor
868C2C2×D4×C22⋊D7111yescharacteristic
869C2C22×#1455615911yescharacteristic
870C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×D4×Q8×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986658C2
hypercenterC2×D4×Q8D71
hypocenterC71C2×#3270
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556159C2semidirect
2. C23×#11765855C2semidirect
4. #22599911C2direct (N × H)
5. C2×#17986391C2semidirect
6. C2×#17986255C2semidirect
7. C2×#17986230C2semidirect
8. C2×#17986221C2semidirect
9. C2×#17986206C2semidirect
10. C2×#17986159C2semidirect
11. C2×#17986155C2semidirect
12. C2×#17986154C2semidirect
13. C2×#17986138C2semidirect
14. C2×#17986104C2semidirect
15. C2×#17986071C2semidirect
16. C2×D4×Q8×C71C2semidirect
20. C2×#14556159C22semidirect
28. C22×#11765855C22semidirect
44. #17986391C22semidirect
45. #17986255C22semidirect
46. #17986230C22semidirect
47. #17986221C22semidirect
48. #17986206C22semidirect
49. #17986159C22semidirect
50. #17986155C22semidirect
51. #17986154C22semidirect
52. #17986138C22semidirect
53. #17986104C22semidirect
54. #17986071C22semidirect
69. D4×Q8×C71C22semidirect
102. C2×#11765855D4semidirect
236. #11765855C2×D4semidirect
326. C23×C71#137semidirect
407. C22×C71C2×#137semidirect
431. C2×C71#3270semidirect
438. C2×D4×Q8D71semidirect
452. C71C2×#3270semidirect
473. D4×Q8C2×D71semidirect
766. C23#14556159semidirect
847. C22C2×#14556159semidirect
867. C2#22599911direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561592
C23×#117658552
C2×#179866582
#225999112
C2×#179863912
C2×#179862552
C2×#179862302
C2×#179862212
C2×#179862062
C2×#179861592
C2×#179861552
C2×#179861542
C2×#179861382
C2×#179861042
C2×#179860712
C2×D4×Q8×C712
C2×#327071