Finite Group Databasebeta

← C2×#22591786 #32165405

Subgroups — C2×#22591786 #32165405

Order 18176.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556106C211yesmaximal, characteristic, complemented
2C22×#14556106C211yesmaximal, characteristic, complemented
3C22×#14556090C211yesmaximal, characteristic
4C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
5#22591786C2116yesmaximal, direct product factor
6C2×#17985932C211yesmaximal, characteristic, complemented
7C2×#17985921C211yesmaximal, characteristic, complemented
8C2×#17985921C211yesmaximal, characteristic, complemented
9C2×#17985903C211yesmaximal, characteristic, complemented
10C2×#17985896C211yesmaximal, characteristic, complemented
11C2×#17985877C211yesmaximal, characteristic
12C2×#17985877C211yesmaximal, characteristic
13C2×#17985858C211yesmaximal, characteristic, complemented
14C2×#17985858C211yesmaximal, characteristic, complemented
15C2×#17985856C211yesmaximal, characteristic, complemented
16C2×#398×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C2×#14556106—28no—
24C2×#14556106—28no—
25C2×#14556106C2218yescomplemented
26C2×#14556106C2218yescomplemented
27C2×#14556090—28no—
28C2×#14556090C2218yes—
29C22×C4⋊Dic71C2211yescharacteristic
30C22×C4⋊Dic71C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×Dic71⋊C4C2211yescharacteristic
36C22×Dic71⋊C4C2211yescharacteristic
37C2×C4⋊C4×D71—28no—
38C2×C4⋊C4×D71C2218yescomplemented
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×(C2×D71)⋊C4C2211yescharacteristic
43C22×(C2×D71)⋊C4C2211yescharacteristic
44C22×(C2×D71)⋊C4C2211yescharacteristic
45C22×(C2×D71)⋊C4C2211yescharacteristic
46C22×(C2×D71)⋊C4C2211yescharacteristic
47C22×C4×Dic71C2211yescharacteristic
48#17985932C2218yescomplemented
49#17985921C2218yescomplemented
50#17985921C2218yescomplemented
51#17985903C2218yescomplemented
52#17985896C2218yescomplemented
53#17985877C2218yes—
54#17985877C2218yes—
55#17985858C2218yescomplemented
56#17985858C2218yescomplemented
57#17985856C2218yescomplemented
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C2×C71⋊#95C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C4⋊C4×C71C2211yescharacteristic
67#398×C71C2218yescomplemented
68C2×#95×C71C2211yescharacteristic
69C2×#95×C71C2211yescharacteristic
70C2×#95×C71C2211yescharacteristic
71C24×D71C2311yescharacteristic
72C24×D71C2311yescharacteristic
73C22×Dic142—24no—
74C22×Dic142—24no—
75C22×Dic142—24no—
76C22×Dic142C2314yes—
77C22×D284—24no—
78C22×D284—24no—
79C22×D284Q818yescomplemented
80C22×D284C2314yes—
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C22×C4×D71—24no—
88C22×C4×D71—24no—
89C22×C4×D71—24no—
90C22×C4×D71—24no—
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—24no—
94C22×C4×D71—24no—
95C22×C4×D71—24no—
96C22×C4×D71—42no—
97C22×C4×D71—42no—
98C22×C4×D71D418yes—
99C22×C4×D71C2314yes—
100C22×C4×D71C2314yes—
101C22×C4×D71C2314yes—
102C22×C4×D71C2314yes—
103#14556106—232no—
104#14556106—232no—
105#14556090—232no—
106C2×C4⋊Dic71—24no—
107C2×C4⋊Dic71—42no—
108C2×C4⋊Dic71C2314yes—
109C2×C4⋊Dic71C2314yes—
110C2×Dic71⋊C4—24no—
111C2×Dic71⋊C4—24no—
112C2×Dic71⋊C4—24no—
113C2×Dic71⋊C4—24no—
114C2×Dic71⋊C4—42no—
115C2×Dic71⋊C4D418yescomplemented
116C2×Dic71⋊C4C2314yes—
117C2×Dic71⋊C4C2314yes—
118C2×Dic71⋊C4C2314yes—
119C2×Dic71⋊C4C2314yes—
120C2×Dic71⋊C4C2314yes—
121C2×Dic71⋊C4C2314yes—
122C4⋊C4×D71—232no—
123C2×(C2×D71)⋊C4—24no—
124C2×(C2×D71)⋊C4—24no—
125C2×(C2×D71)⋊C4—24no—
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—24no—
129C2×(C2×D71)⋊C4—42no—
130C2×(C2×D71)⋊C4—42no—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yes—
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×(C2×D71)⋊C4C2314yes—
136C2×(C2×D71)⋊C4C2314yes—
137C2×(C2×D71)⋊C4C2314yes—
138C2×(C2×D71)⋊C4C2314yes—
139C2×C4×Dic71—24no—
140C2×C4×Dic71C2314yes—
141C71⋊#95C2314yes—
142C71⋊#95C2314yes—
143C71⋊#95C2314yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C23×C4×C71C2311yescharacteristic
152C23×C4×C71C2311yescharacteristic
153C2×C4⋊C4×C71—24no—
154C2×C4⋊C4×C71—24no—
155C2×C4⋊C4×C71—24no—
156C2×C4⋊C4×C71—24no—
157C2×C4⋊C4×C71C2314yes—
158C2×C4⋊C4×C71C2314yes—
159C2×C4⋊C4×C71C2314yes—
160C2×C4⋊C4×C71C2314yes—
161#95×C71C2314yes—
162#95×C71C2314yes—
163#95×C71C2314yes—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71—22no—
171C23×D71—22no—
172C23×D71—22no—
173C23×D71—22no—
174C23×D71C2×D414yes—
175C23×D71C2×Q814yes—
176C23×D71C2×Q814yes—
177C23×D71#4114yes—
178C23×D71C2412yes—
179C23×D71C2412yes—
180C2×Dic142—28no—
181C2×Dic142—28no—
182C2×Dic142—28no—
183C2×Dic142—416no—
184C2×D284—232no—
185C2×D284—28no—
186C2×D284—28no—
187C2×D284C2×Q8116yescomplemented
188C22×Dic71—22no—
189C22×Dic71—22no—
190C22×Dic71—22no—
191C22×Dic71—22no—
192C22×Dic71—22no—
193C22×Dic71—22no—
194C22×Dic71—22no—
195C22×Dic71—22no—
196C22×Dic71—22no—
197C22×Dic71—22no—
198C22×Dic71—22no—
199C22×Dic71—22no—
200C22×Dic71—22no—
201C22×Dic71—22no—
202C22×Dic71C2×D414yes—
203C22×Dic71C2×D414yes—
204C22×Dic71C2×D414yes—
205C22×Dic71#4114yes—
206C22×Dic71C2412yes—
207C22×Dic71C2412yes—
208C22×Dic71C2412yes—
209C22×Dic71C2412yes—
210C22×Dic71C2412yes—
211C22×Dic71C2412yes—
212C2×C4×D71—232no—
213C2×C4×D71—28no—
214C2×C4×D71—28no—
215C2×C4×D71—28no—
216C2×C4×D71—28no—
217C2×C4×D71—28no—
218C2×C4×D71—28no—
219C2×C4×D71—28no—
220C2×C4×D71—28no—
221C2×C4×D71—28no—
222C2×C4×D71—44no—
223C2×C4×D71—44no—
224C2×C4×D71—416no—
225C2×C4×D71—416no—
226C2×C4×D71—416no—
227C2×C4×D71C2×D4116yes—
228C4⋊Dic71—28no—
229C4⋊Dic71—44no—
230Dic71⋊C4—28no—
231Dic71⋊C4—28no—
232Dic71⋊C4—28no—
233Dic71⋊C4—28no—
234Dic71⋊C4—44no—
235Dic71⋊C4C2×D4116yescomplemented
236(C2×D71)⋊C4—28no—
237(C2×D71)⋊C4—28no—
238(C2×D71)⋊C4—28no—
239(C2×D71)⋊C4—28no—
240(C2×D71)⋊C4—28no—
241(C2×D71)⋊C4—28no—
242(C2×D71)⋊C4—44no—
243(C2×D71)⋊C4—44no—
244C4×Dic71—28no—
245C24×C71C2411yescharacteristic
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—22no—
262C22×C4×C71—22no—
263C22×C4×C71—22no—
264C22×C4×C71C2×D414yes—
265C22×C4×C71C2×D414yes—
266C22×C4×C71C2×Q814yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C22×C4×C71C2412yes—
270C22×C4×C71C2412yes—
271C22×C4×C71C2412yes—
272C22×C4×C71C2412yes—
273C22×C4×C71C2412yes—
274C4⋊C4×C71—28no—
275C4⋊C4×C71—28no—
276C4⋊C4×C71—28no—
277C4⋊C4×C71—28no—
278C23×C71C22×D412yes—
279C23×C71C22×D412yes—
280C23×C71C22×Q812yes—
281C23×C71C2×#4112yes—
282C23×C71C2×#4112yes—
283C23×C71H(5,𝔽2)12yes—
284C23×C712−1+412yes—
285C23×C71C2511yescharacteristic
286C22×D71—28no—
287C22×D71—28no—
288C22×D71—28no—
289C22×D71—28no—
290C22×D71—28no—
291C22×D71—28no—
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—28no—
297C22×D71—28no—
298C22×D71—28no—
299C22×D71—22no—
300C22×D71—22no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—44no—
306C22×D71—44no—
307C22×D71—44no—
308C22×D71—44no—
309C22×D71C22⋊Q8116yescomplemented
310C22×D71C22×D414yes—
311C22×D71C22×Q814yes—
312C22×D71C22×Q814yes—
313C22×D71C2×#4114yes—
314C2×C4×C71—28no—
315C2×C4×C71—28no—
316C2×C4×C71—28no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—44no—
336C2×C4×C71—44no—
337C2×C4×C71—44no—
338C2×C4×C71—44no—
339C2×C4×C71C22×D414yes—
340C2×C4×C71C22×D414yes—
341C2×C4×C71C22×Q814yes—
342C2×Dic71—28no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—22no—
353C2×Dic71—22no—
354C2×Dic71—22no—
355C2×Dic71—22no—
356C2×Dic71—22no—
357C2×Dic71—44no—
358C2×Dic71—44no—
359C2×Dic71—44no—
360C2×Dic71—44no—
361C2×Dic71#121116yes—
362C2×Dic71C22×D414yes—
363C2×Dic71C22×D414yes—
364C2×Dic71C22×D414yes—
365C2×Dic71C2×#4114yes—
366D284—232no—
367C4×D71—232no—
368C4×D71—416no—
369C4×D71—416no—
370C4×D71—416no—
371Dic142—416no—
372C22×C71C2×#12114yes—
373C22×C71C2×C22⋊Q814yes—
374C22×C71#53714yes—
375C22×C71#54614yes—
376C22×C71D4×Q814yes—
377C22×C71#55214yes—
378C22×C71#55414yes—
379C22×C71C23×D411yescharacteristic
380C22×C71C23×D411yescharacteristic
381C22×C71C23×Q811yescharacteristic
382C22×C71C22×#4111yescharacteristic
383C22×C71C22×#4111yescharacteristic
384C22×C71C2×H(5,𝔽2)11yescharacteristic
385C22×C71C2×2−1+411yescharacteristic
386C2×D71—24no—
387C2×D71—232no—
388C2×D71—24no—
389C2×D71—24no—
390C2×D71—24no—
391C2×D71—24no—
392C2×D71—24no—
393C2×D71—24no—
394C2×D71—24no—
395C2×D71—24no—
396C2×D71—42no—
397C2×D71—416no—
398C2×D71—42no—
399C2×D71—42no—
400C2×D71—42no—
401C2×D71C2×C22⋊Q818yescomplemented
402C4×C71—24no—
403C4×C71—24no—
404C4×C71—24no—
405C4×C71—42no—
406C4×C71—42no—
407C4×C71—42no—
408C4×C71—42no—
409Dic71—24no—
410Dic71—42no—
411Dic71—42no—
412Dic71—42no—
413Dic71—42no—
414Dic71C2×#12118yes—
415C2×#2417—711nomaximal, Sylow
416C2×C71#241718yescomplemented
417C2×C71C22×#12111yescharacteristic
418C2×C71C22×C22⋊Q811yescharacteristic
419C2×C71C2×#53711yescharacteristic
420C2×C71C2×#54611yescharacteristic
421C2×C71C2×D4×Q811yescharacteristic
422C2×C71C2×#55211yescharacteristic
423C2×C71C2×#55411yescharacteristic
424D71—28no—
425D71—44no—
426C22×C22⋊Q8—711no—
427C22×C22⋊Q8—711no—
428C22×C4×D4—711no—
429C23×C4⋊C4—711no—
430#2417—7116no—
431C2×#398—711no—
432C2×#398D7111yescharacteristic, complemented
433C2×#396—711no—
434C2×#396—711no—
435C2×#391—711no—
436C2×#389—711no—
437C2×#386—711no—
438C2×#386—711no—
439C2×#380—711no—
440C2×#380—711no—
441C2×#380—711no—
442C71C2×#241711yescharacteristic, complemented, Sylow
443C23×Q8—711no—
444C23×D4—711no—
445C24×C4—711no—
446C24×C4—711no—
447C24×C4—711no—
448C24×C4—711no—
449C2×C22⋊Q8—718no—
450C2×C22⋊Q8—718no—
451C2×C22⋊Q8—1428no—
452C2×C22⋊Q8—1428no—
453C2×C4×D4—718no—
454C2×C4×D4—1428no—
455C22×C4⋊C4—711no—
456C22×C4⋊C4—711no—
457C22×C4⋊C4—711no—
458C22×C4⋊C4—711no—
459C22×C4⋊C4—711no—
460C22×C4⋊C4—711no—
461C22×C4⋊C4—711no—
462C22×C4⋊C4—711no—
463C22×C4⋊C4—718no—
464C22×C4⋊C4—1428no—
465C22×C4⋊C4C2×D7111yescharacteristic
466C22×C4⋊C4C2×D7111yescharacteristic
467C22×C4⋊C4C2×D7111yescharacteristic
468C22×C4⋊C4C2×D7111yescharacteristic
469C22×C22⋊C4—711no—
470C22×C22⋊C4—711no—
471C22×C22⋊C4—711no—
472C22×C22⋊C4—711no—
473C22×C22⋊C4—711no—
474C22×C22⋊C4—711no—
475C22×C22⋊C4—711no—
476C22×C22⋊C4—711no—
477C22×C42—711no—
478#398—718no—
479#398C2×D7118yescomplemented
480#396—718no—
481#396—718no—
482#391—718no—
483#389—718no—
484#386—718no—
485#386—718no—
486#380—718no—
487#380—718no—
488#380—718no—
489C2×#95—711no—
490C2×#95—711no—
491C2×#95—711no—
492C2×#95—711no—
493C2×#95—711no—
494C2×#95C2×D7111yescharacteristic
495C2×#95C2×D7111yescharacteristic
496C2×#95C2×D7111yescharacteristic
497C25—711no—
498C25—711no—
499C22×Q8—714no—
500C22×Q8—1424no—
501C22×Q8—1424no—
502C22×Q8—1424no—
503C22×D4—718no—
504C22×D4—714no—
505C22×D4—1424no—
506C22×D4—1424no—
507C23×C4—2842no—
508C23×C4—2842no—
509C23×C4—714no—
510C23×C4—714no—
511C23×C4—711no—
512C23×C4—711no—
513C23×C4—718no—
514C23×C4—714no—
515C23×C4—711no—
516C23×C4—711no—
517C23×C4—711no—
518C23×C4—711no—
519C23×C4—714no—
520C23×C4—1424no—
521C23×C4—1424no—
522C23×C4—1424no—
523C23×C4—1424no—
524C23×C4—1424no—
525C23×C4—1424no—
526C23×C4—1424no—
527C23×C4—1424no—
528C23×C4—1424no—
529C23×C4C22×D7111yescharacteristic
530C23×C4C22×D7111yescharacteristic
531C23×C4C22×D7111yescharacteristic
532C23×C4C22×D7111yescharacteristic
533C23×C4C22×D7111yescharacteristic
534C23×C4C22×D7111yescharacteristic
535C23×C4C22×D7111yescharacteristic
536C22⋊Q8—14232no—
537C22⋊Q8—14232no—
538C4×D4—14232no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—2842no—
544C2×C4⋊C4—2842no—
545C2×C4⋊C4—714no—
546C2×C4⋊C4—714no—
547C2×C4⋊C4—718no—
548C2×C4⋊C4—714no—
549C2×C4⋊C4—714no—
550C2×C4⋊C4—714no—
551C2×C4⋊C4—714no—
552C2×C4⋊C4—714no—
553C2×C4⋊C4—714no—
554C2×C4⋊C4—14232no—
555C2×C4⋊C4—1424no—
556C2×C4⋊C4—1424no—
557C2×C4⋊C4—1424no—
558C2×C4⋊C4—1424no—
559C2×C4⋊C4—1424no—
560C2×C4⋊C4C22×D7114yes—
561C2×C4⋊C4C22×D7114yes—
562C2×C4⋊C4C22×D7114yes—
563C2×C4⋊C4C22×D7114yes—
564C2×C22⋊C4—2842no—
565C2×C22⋊C4—2842no—
566C2×C22⋊C4—714no—
567C2×C22⋊C4—714no—
568C2×C22⋊C4—714no—
569C2×C22⋊C4—714no—
570C2×C22⋊C4—714no—
571C2×C22⋊C4—714no—
572C2×C22⋊C4—714no—
573C2×C22⋊C4—714no—
574C2×C22⋊C4—1424no—
575C2×C22⋊C4—1424no—
576C2×C22⋊C4—1424no—
577C2×C22⋊C4—1424no—
578C2×C22⋊C4—1424no—
579C2×C22⋊C4—1424no—
580C2×C42—714no—
581C2×C42—1424no—
582#95—714no—
583#95—714no—
584#95—714no—
585#95—714no—
586#95—714no—
587#95C22×D7114yes—
588#95C22×D7114yes—
589#95C22×D7114yes—
590C24—714no—
591C24—714no—
592C24—714no—
593C24—712no—
594C24—714no—
595C24—712no—
596C24—1422no—
597C24—1422no—
598C24—1422no—
599C24—1422no—
600C24—1422no—
601C24—1422no—
602C24—1422no—
603C24—1422no—
604C24—1422no—
605C24—1422no—
606C24C23×D7111yescharacteristic
607C2×Q8—28416no—
608C2×Q8—1428no—
609C2×Q8—1428no—
610C2×Q8—1428no—
611C2×D4—7116no—
612C2×D4—1428no—
613C2×D4—1428no—
614C2×D4—14232no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—28416no—
634C22×C4—2844no—
635C22×C4—2844no—
636C22×C4—28416no—
637C22×C4—28416no—
638C22×C4—714no—
639C22×C4—714no—
640C22×C4—714no—
641C22×C4—712no—
642C22×C4—714no—
643C22×C4—712no—
644C22×C4—7116no—
645C22×C4—712no—
646C22×C4—712no—
647C22×C4—712no—
648C22×C4—712no—
649C22×C4—1428no—
650C22×C4—1428no—
651C22×C4—1428no—
652C22×C4—1428no—
653C22×C4—1428no—
654C22×C4—1428no—
655C22×C4—1428no—
656C22×C4—1428no—
657C22×C4—14232no—
658C22×C4—1422no—
659C22×C4—1422no—
660C22×C4—1422no—
661C22×C4—1422no—
662C22×C4—1422no—
663C22×C4—1422no—
664C22×C4—1422no—
665C22×C4—1422no—
666C22×C4—1422no—
667C22×C4—1422no—
668C22×C4—1422no—
669C22×C4—1422no—
670C22×C4—1428no—
671C22×C4—1422no—
672C22×C4—1422no—
673C22×C4D4×D7114yes—
674C22×C4D4×D7114yes—
675C22×C4Q8×D7114yes—
676C22×C4C23×D7112yes—
677C22×C4C23×D7112yes—
678C22×C4C23×D7112yes—
679C22×C4C23×D7112yes—
680C22×C4C23×D7112yes—
681C22×C4C23×D7112yes—
682C22×C4C23×D7112yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—2844no—
688C4⋊C4—2844no—
689C4⋊C4—7116no—
690C4⋊C4—1428no—
691C4⋊C4—1428no—
692C4⋊C4—1428no—
693C4⋊C4—1428no—
694C4⋊C4—1428no—
695C22⋊C4—2844no—
696C22⋊C4—2844no—
697C22⋊C4—1428no—
698C22⋊C4—1428no—
699C22⋊C4—1428no—
700C22⋊C4—1428no—
701C22⋊C4—1428no—
702C22⋊C4—1428no—
703C42—1428no—
704C23—2844no—
705C23—2844no—
706C23—2844no—
707C23—2844no—
708C23—714no—
709C23—714no—
710C23—714no—
711C23—7116no—
712C23—714no—
713C23—1422no—
714C23—1422no—
715C23—1422no—
716C23—1422no—
717C23—1422no—
718C23—1422no—
719C23—1428no—
720C23—1428no—
721C23—1428no—
722C23—1422no—
723C23—1422no—
724C23—1422no—
725C23—1422no—
726C23—1428no—
727C23—1428no—
728C23—1428no—
729C23—1428no—
730C23—1428no—
731C23—1428no—
732C23C2×D4×D7112yes—
733C23C2×D4×D7112yes—
734C23C2×Q8×D7112yes—
735C23#41×D7112yes—
736C23#41×D7112yes—
737C23#1455617412yes—
738C23#1455617612yes—
739C23C24×D7111yescharacteristic
740Q8—28416no—
741D4—14232no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—28416no—
768C2×C4—28416no—
769C2×C4—28416no—
770C2×C4—2844no—
771C2×C4—2844no—
772C2×C4—2844no—
773C2×C4—2844no—
774C2×C4—714no—
775C2×C4—714no—
776C2×C4—714no—
777C2×C4—7116no—
778C2×C4—714no—
779C2×C4—14232no—
780C2×C4—1422no—
781C2×C4—1422no—
782C2×C4—1422no—
783C2×C4—1422no—
784C2×C4—1422no—
785C2×C4—1422no—
786C2×C4—1422no—
787C2×C4—1422no—
788C2×C4—1422no—
789C2×C4—1422no—
790C2×C4—1422no—
791C2×C4—1422no—
792C2×C4—1422no—
793C2×C4—1422no—
794C2×C4—1428no—
795C2×C4C2×D4×D7114yes—
796C2×C4C2×D4×D7114yes—
797C2×C4C2×Q8×D7114yes—
798C22—28416no—
799C22—2842no—
800C22—2842no—
801C22—2842no—
802C22—2842no—
803C22—718no—
804C22—1424no—
805C22—1424no—
806C22—1424no—
807C22—14232no—
808C22—1424no—
809C22—1424no—
810C22—1424no—
811C22—1424no—
812C22—1424no—
813C22—1424no—
814C22#121×D7114yes—
815C22C22⋊Q8×D7114yes—
816C22#1798657914yes—
817C22#1798664114yes—
818C22#1798666414yes—
819C22#1798668114yes—
820C22#1798670514yes—
821C22C22×D4×D7111yescharacteristic
822C22C22×D4×D7111yescharacteristic
823C22C22×Q8×D7111yescharacteristic
824C22C2×#41×D7111yescharacteristic
825C22C2×#41×D7111yescharacteristic
826C22C2×#1455617411yescharacteristic
827C22C2×#1455617611yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—2842no—
836C4—2842no—
837C4—2842no—
838C4—2842no—
839C4—718no—
840C4—1424no—
841C2—2844no—
842C2—1428no—
843C2#2259178618yesdirect product factor
844C2C2×#121×D7111yescharacteristic
845C2C2×C22⋊Q8×D7111yescharacteristic
846C2C2×#1798657911yescharacteristic
847C2C2×#1798664111yescharacteristic
848C2C2×#1798666411yescharacteristic
849C2C2×#1798668111yescharacteristic
850C2C2×#1798670511yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#398×C71C2
socleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×#398D71
hypocenterC71C2×#2417
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#14556106C2semidirect
2. C22×#14556106C2semidirect
4. C22×C4⋊C4×D71C2semidirect
5. #22591786C2direct (N × H)
6. C2×#17985932C2semidirect
7. C2×#17985921C2semidirect
8. C2×#17985921C2semidirect
9. C2×#17985903C2semidirect
10. C2×#17985896C2semidirect
13. C2×#17985858C2semidirect
14. C2×#17985858C2semidirect
15. C2×#17985856C2semidirect
16. C2×#398×C71C2semidirect
25. C2×#14556106C22semidirect
26. C2×#14556106C22semidirect
38. C2×C4⋊C4×D71C22semidirect
48. #17985932C22semidirect
49. #17985921C22semidirect
50. #17985921C22semidirect
51. #17985903C22semidirect
52. #17985896C22semidirect
55. #17985858C22semidirect
56. #17985858C22semidirect
57. #17985856C22semidirect
67. #398×C71C22semidirect
79. C22×D284Q8semidirect
115. C2×Dic71⋊C4D4semidirect
187. C2×D284C2×Q8semidirect
235. Dic71⋊C4C2×D4semidirect
309. C22×D71C22⋊Q8semidirect
401. C2×D71C2×C22⋊Q8semidirect
416. C2×C71#2417semidirect
432. C2×#398D71semidirect
442. C71C2×#2417semidirect
479. #398C2×D71semidirect
843. C2#22591786direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561062
C22×#145560902
C22×C4⋊C4×D712
#225917862
C2×#179859322
C2×#179859212
C2×#179859032
C2×#179858962
C2×#179858772
C2×#179858582
C2×#179858562
C2×#398×C712
C2×#241771