Finite Group Databasebeta

← C2×#22592612 #32167215

Subgroups — C2×#22592612 #32167215

Order 18176.

4166 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556085C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D71C211yesmaximal, characteristic
3#22592612C2116yesmaximal, direct product factor
4C2×#17985935C211yesmaximal, characteristic, complemented
5C2×#17985934C211yesmaximal, characteristic, complemented
6C2×#17985928C211yesmaximal, characteristic, complemented
7C2×#17985927C211yesmaximal, characteristic, complemented
8C2×#17985891C211yesmaximal, characteristic, complemented
9C2×#17985890C211yesmaximal, characteristic, complemented
10C2×#17985887C211yesmaximal, characteristic, complemented
11C2×#17985873C211yesmaximal, characteristic, complemented
12C2×#17985870C211yesmaximal, characteristic, complemented
13C2×#17985861C211yesmaximal, characteristic, complemented
14C2×#17985854C211yesmaximal, characteristic
15C2×#17985854C211yesmaximal, characteristic
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556085—28no—
21C2×#14556085C2218yescomplemented
22C22×C4⋊Dic71C2211yescharacteristic, complemented
23C22×Dic71⋊C4C2211yescharacteristic, complemented
24C22×Dic71⋊C4C2211yescharacteristic, complemented
25C22×Dic71⋊C4C2211yescharacteristic, complemented
26C22×Dic71⋊C4C2211yescharacteristic, complemented
27C22×C22⋊Dic71C2211yescharacteristic
28C22×C22⋊Dic71C2211yescharacteristic
29C22×C22⋊Dic71C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C2×C22⋊C4×D71—28no—
41C2×C22⋊C4×D71C2218yes—
42C22×C4×Dic71C2211yescharacteristic, complemented
43#17985935C2218yescomplemented
44#17985934C2218yescomplemented
45#17985928C2218yescomplemented
46#17985927C2218yescomplemented
47#17985891C2218yescomplemented
48#17985890C2218yescomplemented
49#17985887C2218yescomplemented
50#17985873C2218yescomplemented
51#17985870C2218yescomplemented
52#17985861C2218yescomplemented
53#17985854C2218yes—
54#17985854C2218yes—
55C2×C71⋊#95C2211yescharacteristic, complemented
56C2×C71⋊#95C2211yescharacteristic, complemented
57C2×C71⋊#95C2211yescharacteristic, complemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C22×C4⋊C4×C71C2211yescharacteristic, complemented
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic, complemented
66#388×C71C2218yescomplemented
67C2×#95×C71C2211yescharacteristic, complemented
68C2×#95×C71C2211yescharacteristic, complemented
69C24×D71—24no—
70C24×D71—24no—
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—42no—
75C24×D71—42no—
76C24×D71C2311yescharacteristic
77C24×D71C2314yes—
78C24×D71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C22×C4×D71—24no—
86C22×C4×D71—24no—
87C22×C4×D71—24no—
88C22×C4×D71—42no—
89C22×C4×D71—42no—
90C22×C4×D71D418yes—
91C22×C4×D71C2314yes—
92C22×C4×D71C2314yes—
93#14556085—232no—
94C2×C4⋊Dic71—42no—
95C2×C4⋊Dic71C2314yescomplemented
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—42no—
99C2×Dic71⋊C4—42no—
100C2×Dic71⋊C4C2314yescomplemented
101C2×Dic71⋊C4C2314yescomplemented
102C2×Dic71⋊C4C2314yescomplemented
103C2×Dic71⋊C4C2314yescomplemented
104C2×C22⋊Dic71—24no—
105C2×C22⋊Dic71—24no—
106C2×C22⋊Dic71—42no—
107C2×C22⋊Dic71C2314yes—
108C2×C22⋊Dic71C2314yes—
109C2×C22⋊Dic71C2314yes—
110C2×(C2×D71)⋊C4—24no—
111C2×(C2×D71)⋊C4—24no—
112C2×(C2×D71)⋊C4—24no—
113C2×(C2×D71)⋊C4—24no—
114C2×(C2×D71)⋊C4—24no—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—42no—
119C2×(C2×D71)⋊C4—42no—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C22⋊C4×D71—232no—
131C2×C4×Dic71—24no—
132C2×C4×Dic71C2314yescomplemented
133C71⋊#95C2314yescomplemented
134C71⋊#95C2314yescomplemented
135C71⋊#95C2314yescomplemented
136C71⋊#95C2314yescomplemented
137C71⋊#95C2314yescomplemented
138C71⋊#95C2314yescomplemented
139C25×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C2×C4⋊C4×C71—42no—
147C2×C4⋊C4×C71C2314yescomplemented
148C2×C22⋊C4×C71—24no—
149C2×C22⋊C4×C71—24no—
150C2×C22⋊C4×C71—42no—
151C2×C22⋊C4×C71C2314yes—
152C2×C22⋊C4×C71C2314yes—
153C2×C22⋊C4×C71C2314yes—
154C2×C42×C71—24no—
155C2×C42×C71C2314yescomplemented
156#95×C71C2314yescomplemented
157#95×C71C2314yescomplemented
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71—232no—
163C23×D71—22no—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71—28no—
167C23×D71—22no—
168C23×D71—22no—
169C23×D71—22no—
170C23×D71—28no—
171C23×D71—28no—
172C23×D71—28no—
173C23×D71—28no—
174C23×D71—44no—
175C23×D71—44no—
176C23×D71—416no—
177C23×D71—416no—
178C23×D71—416no—
179C23×D71—416no—
180C23×D71—416no—
181C23×D71—416no—
182C23×D71C2×D414yes—
183C23×D71#4114yes—
184C23×D71#4114yes—
185C23×D71#4114yes—
186C23×D71C2412yes—
187C23×D71C2412yes—
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×Dic71—22no—
203C22×Dic71—22no—
204C22×Dic71—22no—
205C22×Dic71C2×D414yes—
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—44no—
217C2×C4×D71—44no—
218C2×C4×D71—416no—
219C2×C4×D71C2×D4116yes—
220C4⋊Dic71—44no—
221Dic71⋊C4—28no—
222Dic71⋊C4—28no—
223Dic71⋊C4—44no—
224Dic71⋊C4—44no—
225C22⋊Dic71—28no—
226C22⋊Dic71—28no—
227C22⋊Dic71—44no—
228(C2×D71)⋊C4—28no—
229(C2×D71)⋊C4—28no—
230(C2×D71)⋊C4—28no—
231(C2×D71)⋊C4—28no—
232(C2×D71)⋊C4—28no—
233(C2×D71)⋊C4—28no—
234(C2×D71)⋊C4—28no—
235(C2×D71)⋊C4—28no—
236(C2×D71)⋊C4—44no—
237(C2×D71)⋊C4—44no—
238C4×Dic71—28no—
239C24×C71—22no—
240C24×C71—22no—
241C24×C71—22no—
242C24×C71—22no—
243C24×C71—22no—
244C24×C71—22no—
245C24×C71#4114yes—
246C24×C71C2412yes—
247C24×C71C2411yescharacteristic
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×C71—22no—
265C22×C4×C71C2×D414yes—
266C22×C4×C71C2412yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C22×C4×C71C2412yes—
270C22×C4×C71C2412yes—
271C22×C4×C71C2412yes—
272C4⋊C4×C71—44no—
273C22⋊C4×C71—28no—
274C22⋊C4×C71—28no—
275C22⋊C4×C71—44no—
276C42×C71—28no—
277C23×C71—28no—
278C23×C71—28no—
279C23×C71—28no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—44no—
287C23×C71—44no—
288C23×C71—44no—
289C23×C71—44no—
290C23×C71C22×D412yes—
291C23×C71C2×#4112yes—
292C23×C71C2×#4112yes—
293C23×C71C2×#4112yes—
294C23×C71C2×#4114yes—
295C23×C71C2×#4112yes—
296C23×C71H(5,𝔽2)12yes—
297C23×C71H(5,𝔽2)12yes—
298C23×C71C2511yescharacteristic
299C22×D71—28no—
300C22×D71—28no—
301C22×D71—28no—
302C22×D71—28no—
303C22×D71—28no—
304C22×D71—28no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—22no—
309C22×D71—232no—
310C22×D71—28no—
311C22×D71—28no—
312C22×D71—28no—
313C22×D71—22no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—22no—
319C22×D71—416no—
320C22×D71—416no—
321C22×D71—416no—
322C22×D71—416no—
323C22×D71—416no—
324C22×D71—4128no—
325C22×D71—44no—
326C22×D71—44no—
327C22×D71—44no—
328C22×D71—44no—
329C22×D71—416no—
330C22×D71#123116yes—
331C22×D71C22×D414yes—
332C22×D71C2×#4114yes—
333C22×D71C2×#4114yes—
334C22×D71C2×#4114yes—
335C2×C4×C71—28no—
336C2×C4×C71—22no—
337C2×C4×C71—22no—
338C2×C4×C71—22no—
339C2×C4×C71—22no—
340C2×C4×C71—22no—
341C2×C4×C71—22no—
342C2×C4×C71—22no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—22no—
346C2×C4×C71—22no—
347C2×C4×C71—22no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—44no—
354C2×C4×C71—44no—
355C2×C4×C71—44no—
356C2×C4×C71—44no—
357C2×C4×C71—44no—
358C2×C4×C71C22×D414yes—
359C2×Dic71—28no—
360C2×Dic71—22no—
361C2×Dic71—22no—
362C2×Dic71—22no—
363C2×Dic71—22no—
364C2×Dic71—22no—
365C2×Dic71—22no—
366C2×Dic71—22no—
367C2×Dic71—22no—
368C2×Dic71—22no—
369C2×Dic71—22no—
370C2×Dic71—22no—
371C2×Dic71—22no—
372C2×Dic71—22no—
373C2×Dic71—22no—
374C2×Dic71—22no—
375C2×Dic71—22no—
376C2×Dic71—22no—
377C2×Dic71—44no—
378C2×Dic71—44no—
379C2×Dic71—44no—
380C2×Dic71—44no—
381C2×Dic71—44no—
382C2×Dic71C22×D414yes—
383C4×D71—232no—
384C4×D71—416no—
385C22×C71—24no—
386C22×C71—24no—
387C22×C71—24no—
388C22×C71—42no—
389C22×C71—42no—
390C22×C71—42no—
391C22×C71—42no—
392C22×C71—416no—
393C22×C71C2×#12314yes—
394C22×C71#52514yes—
395C22×C71#53514yes—
396C22×C71#55114yes—
397C22×C71#55114yes—
398C22×C71#55114yes—
399C22×C71#55114yes—
400C22×C71C23×D411yescharacteristic
401C22×C71C22×#4111yescharacteristic
402C22×C71C22×#4111yescharacteristic
403C22×C71C22×#4111yescharacteristic
404C22×C71C22×#4111yescharacteristic
405C22×C71C2×H(5,𝔽2)11yescharacteristic
406C22×C71C2×H(5,𝔽2)11yescharacteristic
407C2×D71—24no—
408C2×D71—24no—
409C2×D71—24no—
410C2×D71—24no—
411C2×D71—24no—
412C2×D71—24no—
413C2×D71—232no—
414C2×D71—24no—
415C2×D71—24no—
416C2×D71—24no—
417C2×D71—464no—
418C2×D71—42no—
419C2×D71—42no—
420C2×D71—42no—
421C2×D71—42no—
422C2×D71—416no—
423C2×D71C2×#12318yes—
424C4×C71—24no—
425C4×C71—42no—
426C4×C71—42no—
427C4×C71—42no—
428C4×C71—42no—
429C4×C71—42no—
430Dic71—24no—
431Dic71—42no—
432Dic71—42no—
433Dic71—42no—
434Dic71—42no—
435Dic71—42no—
436C2×#2482—711nomaximal, Sylow
437C2×C71—44no—
438C2×C71#248218yescomplemented
439C2×C71C22×#12311yescharacteristic
440C2×C71C2×#52511yescharacteristic
441C2×C71C2×#53511yescharacteristic
442C2×C71C2×#55111yescharacteristic
443C2×C71C2×#55111yescharacteristic
444C2×C71C2×#55111yescharacteristic
445C2×C71C2×#55111yescharacteristic
446D71—28no—
447D71—44no—
448C22×#117—711no—
449C23×C22⋊C4—711no—
450#2482—7116no—
451C2×#399—711no—
452C2×#399—711no—
453C2×#397—711no—
454C2×#397—711no—
455C2×#388—711no—
456C2×#388—711no—
457C2×#388—711no—
458C2×#388D7111yescharacteristic, complemented
459C2×#385—711no—
460C2×#385—711no—
461C2×#381—711no—
462C2×#379—711no—
463C2×#379—711no—
464C71C2×#248211yescharacteristic, complemented, Sylow
465C26—711no—
466C24×C4—711no—
467C24×C4—711no—
468C2×#117—718no—
469C2×#117—1428no—
470C22×C4⋊C4—711no—
471C22×C4⋊C4—711no—
472C22×C4⋊C4—711no—
473C22×C4⋊C4—711no—
474C22×C4⋊C4—711no—
475C22×C4⋊C4C2×D7111yescharacteristic, complemented
476C22×C22⋊C4—711no—
477C22×C22⋊C4—711no—
478C22×C22⋊C4—711no—
479C22×C22⋊C4—711no—
480C22×C22⋊C4—711no—
481C22×C22⋊C4—711no—
482C22×C22⋊C4—711no—
483C22×C22⋊C4—711no—
484C22×C22⋊C4—711no—
485C22×C22⋊C4—711no—
486C22×C22⋊C4—711no—
487C22×C22⋊C4—711no—
488C22×C22⋊C4—711no—
489C22×C22⋊C4—718no—
490C22×C22⋊C4—1428no—
491C22×C22⋊C4C2×D7111yescharacteristic
492C22×C22⋊C4C2×D7111yescharacteristic
493C22×C22⋊C4C2×D7111yescharacteristic
494C22×C42—711no—
495C22×C42C2×D7111yescharacteristic, complemented
496#399—718no—
497#399—718no—
498#397—718no—
499#397—718no—
500#388—718no—
501#388—718no—
502#388—718no—
503#388C2×D7118yescomplemented
504#385—718no—
505#385—718no—
506#381—718no—
507#379—718no—
508#379—718no—
509C2×#95—711no—
510C2×#95—711no—
511C2×#95—711no—
512C2×#95—711no—
513C2×#95—711no—
514C2×#95—711no—
515C2×#95C2×D7111yescharacteristic, complemented
516C2×#95C2×D7111yescharacteristic, complemented
517C25—2842no—
518C25—2842no—
519C25—714no—
520C25—711no—
521C25—711no—
522C25—1424no—
523C25—1424no—
524C25—1424no—
525C25—1424no—
526C25—1424no—
527C25C22×D7111yescharacteristic
528C23×C4—2842no—
529C23×C4—2842no—
530C23×C4—714no—
531C23×C4—711no—
532C23×C4—718no—
533C23×C4—714no—
534C23×C4—711no—
535C23×C4—711no—
536C23×C4—711no—
537C23×C4—711no—
538C23×C4—711no—
539C23×C4—1424no—
540C23×C4—1424no—
541C23×C4—1424no—
542C23×C4C22×D7111yescharacteristic
543C23×C4C22×D7111yescharacteristic
544C23×C4C22×D7111yescharacteristic
545C23×C4C22×D7111yescharacteristic
546C23×C4C22×D7111yescharacteristic
547C23×C4C22×D7111yescharacteristic
548#117—14232no—
549C2×C4⋊C4—42no—
550C2×C4⋊C4—2842no—
551C2×C4⋊C4—2842no—
552C2×C4⋊C4—2842no—
553C2×C4⋊C4—714no—
554C2×C4⋊C4—714no—
555C2×C4⋊C4—714no—
556C2×C4⋊C4—714no—
557C2×C4⋊C4—714no—
558C2×C4⋊C4—1424no—
559C2×C4⋊C4—1424no—
560C2×C4⋊C4C22×D7114yescomplemented
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—2842no—
565C2×C22⋊C4—2842no—
566C2×C22⋊C4—2842no—
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—714no—
575C2×C22⋊C4—714no—
576C2×C22⋊C4—714no—
577C2×C22⋊C4—714no—
578C2×C22⋊C4—714no—
579C2×C22⋊C4—714no—
580C2×C22⋊C4—14232no—
581C2×C22⋊C4—1424no—
582C2×C22⋊C4—1424no—
583C2×C22⋊C4—1424no—
584C2×C22⋊C4—1424no—
585C2×C22⋊C4—1424no—
586C2×C22⋊C4—1424no—
587C2×C22⋊C4—1424no—
588C2×C22⋊C4—1424no—
589C2×C22⋊C4—1424no—
590C2×C22⋊C4—1424no—
591C2×C22⋊C4C22×D7114yes—
592C2×C22⋊C4C22×D7114yes—
593C2×C22⋊C4C22×D7114yes—
594C2×C42—24no—
595C2×C42—714no—
596C2×C42—1424no—
597C2×C42C22×D7114yescomplemented
598#95—714no—
599#95—714no—
600#95—714no—
601#95—714no—
602#95—714no—
603#95—714no—
604#95C22×D7114yescomplemented
605#95C22×D7114yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—28416no—
613C24—28416no—
614C24—2844no—
615C24—2844no—
616C24—28416no—
617C24—28416no—
618C24—28416no—
619C24—28416no—
620C24—714no—
621C24—714no—
622C24—714no—
623C24—712no—
624C24—714no—
625C24—712no—
626C24—1428no—
627C24—1428no—
628C24—1428no—
629C24—1428no—
630C24—14232no—
631C24—1422no—
632C24—1422no—
633C24—1422no—
634C24—1428no—
635C24—1422no—
636C24—1422no—
637C24—1422no—
638C24—1422no—
639C24—1422no—
640C24—1422no—
641C24—1422no—
642C24#1176586514yes—
643C24C23×D7112yes—
644C24C23×D7111yescharacteristic
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—2844no—
663C22×C4—2844no—
664C22×C4—28416no—
665C22×C4—714no—
666C22×C4—712no—
667C22×C4—7116no—
668C22×C4—712no—
669C22×C4—712no—
670C22×C4—712no—
671C22×C4—712no—
672C22×C4—712no—
673C22×C4—1428no—
674C22×C4—1428no—
675C22×C4—1428no—
676C22×C4—14232no—
677C22×C4—1422no—
678C22×C4—1422no—
679C22×C4—1422no—
680C22×C4—1422no—
681C22×C4—1422no—
682C22×C4—1422no—
683C22×C4—1422no—
684C22×C4—1422no—
685C22×C4—1422no—
686C22×C4—1422no—
687C22×C4—1422no—
688C22×C4—1422no—
689C22×C4—1422no—
690C22×C4—1422no—
691C22×C4—1422no—
692C22×C4—1422no—
693C22×C4—1422no—
694C22×C4D4×D7114yes—
695C22×C4C23×D7112yes—
696C22×C4C23×D7112yes—
697C22×C4C23×D7112yes—
698C22×C4C23×D7112yes—
699C22×C4C23×D7112yes—
700C22×C4C23×D7112yes—
701C4⋊C4—44no—
702C4⋊C4—2844no—
703C4⋊C4—2844no—
704C4⋊C4—2844no—
705C4⋊C4—1428no—
706C4⋊C4—1428no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—44no—
710C22⋊C4—2844no—
711C22⋊C4—2844no—
712C22⋊C4—2844no—
713C22⋊C4—1428no—
714C22⋊C4—1428no—
715C22⋊C4—1428no—
716C22⋊C4—1428no—
717C22⋊C4—1428no—
718C22⋊C4—1428no—
719C22⋊C4—1428no—
720C22⋊C4—1428no—
721C22⋊C4—1428no—
722C22⋊C4—1428no—
723C42—28no—
724C42—1428no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—28no—
732C23—28no—
733C23—28no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—28416no—
739C23—28416no—
740C23—28416no—
741C23—284128no—
742C23—28416no—
743C23—28416no—
744C23—28416no—
745C23—2844no—
746C23—2844no—
747C23—2844no—
748C23—2844no—
749C23—714no—
750C23—714no—
751C23—714no—
752C23—7116no—
753C23—714no—
754C23—14232no—
755C23—1422no—
756C23—1422no—
757C23—1422no—
758C23—1422no—
759C23—1422no—
760C23—1422no—
761C23—1428no—
762C23—1428no—
763C23—1428no—
764C23—1428no—
765C23—1422no—
766C23—1422no—
767C23—1422no—
768C23—1422no—
769C23—1428no—
770C23—1428no—
771C23—1428no—
772C23—1428no—
773C23—1428no—
774C23C2×D4×D7112yes—
775C23#41×D7112yes—
776C23#41×D7112yes—
777C23#41×D7112yes—
778C23C2×#1176586514yes—
779C23C2×#1176586512yes—
780C23#1455617312yes—
781C23#1455617412yes—
782C23C24×D7111yescharacteristic
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—28416no—
807C2×C4—2844no—
808C2×C4—2844no—
809C2×C4—2844no—
810C2×C4—2844no—
811C2×C4—2844no—
812C2×C4—714no—
813C2×C4—14232no—
814C2×C4—1422no—
815C2×C4—1422no—
816C2×C4—1422no—
817C2×C4—1422no—
818C2×C4—1422no—
819C2×C4—1422no—
820C2×C4—1422no—
821C2×C4—1422no—
822C2×C4—1422no—
823C2×C4—1422no—
824C2×C4—1422no—
825C2×C4—1422no—
826C2×C4—1422no—
827C2×C4—1422no—
828C2×C4—1422no—
829C2×C4—1422no—
830C2×C4—1422no—
831C2×C4—1428no—
832C2×C4C2×D4×D7114yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—42no—
837C22—416no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—28464no—
842C22—2842no—
843C22—28416no—
844C22—2842no—
845C22—2842no—
846C22—2842no—
847C22—718no—
848C22—1424no—
849C22—1424no—
850C22—1424no—
851C22—14232no—
852C22—1424no—
853C22—1424no—
854C22—1424no—
855C22—1424no—
856C22—1424no—
857C22—1424no—
858C22#123×D7114yes—
859C22#1798650814yes—
860C22#1798656514yes—
861C22#1798667314yes—
862C22#1798667414yes—
863C22#1798667814yes—
864C22#1798667914yes—
865C22C22×D4×D7111yescharacteristic
866C22C2×#41×D7111yescharacteristic
867C22C2×#41×D7111yescharacteristic
868C22C2×#41×D7111yescharacteristic
869C22C22×#1176586511yescharacteristic
870C22C2×#1455617311yescharacteristic
871C22C2×#1455617411yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—2842no—
879C4—2842no—
880C4—2842no—
881C4—2842no—
882C4—2842no—
883C4—1424no—
884C2—44no—
885C2—2844no—
886C2—1428no—
887C2#2259261218yesdirect product factor
888C2C2×#123×D7111yescharacteristic
889C2C2×#1798650811yescharacteristic
890C2C2×#1798656511yescharacteristic
891C2C2×#1798667311yescharacteristic
892C2C2×#1798667411yescharacteristic
893C2C2×#1798667811yescharacteristic
894C2C2×#1798667911yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC25×D71C22
hypercenterC2×#388D71
hypocenterC71C2×#2482
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#14556085C2semidirect
3. #22592612C2direct (N × H)
4. C2×#17985935C2semidirect
5. C2×#17985934C2semidirect
6. C2×#17985928C2semidirect
7. C2×#17985927C2semidirect
8. C2×#17985891C2semidirect
9. C2×#17985890C2semidirect
10. C2×#17985887C2semidirect
11. C2×#17985873C2semidirect
12. C2×#17985870C2semidirect
13. C2×#17985861C2semidirect
16. C2×#388×C71C2semidirect
21. C2×#14556085C22semidirect
22. C22×C4⋊Dic71C22semidirect
23. C22×Dic71⋊C4C22semidirect
24. C22×Dic71⋊C4C22semidirect
25. C22×Dic71⋊C4C22semidirect
26. C22×Dic71⋊C4C22semidirect
42. C22×C4×Dic71C22semidirect
43. #17985935C22semidirect
44. #17985934C22semidirect
45. #17985928C22semidirect
46. #17985927C22semidirect
47. #17985891C22semidirect
48. #17985890C22semidirect
49. #17985887C22semidirect
50. #17985873C22semidirect
51. #17985870C22semidirect
52. #17985861C22semidirect
55. C2×C71⋊#95C22semidirect
56. C2×C71⋊#95C22semidirect
57. C2×C71⋊#95C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C22×C4⋊C4×C71C22semidirect
65. C22×C42×C71C22semidirect
66. #388×C71C22semidirect
67. C2×#95×C71C22semidirect
68. C2×#95×C71C22semidirect
95. C2×C4⋊Dic71C23semidirect
100. C2×Dic71⋊C4C23semidirect
101. C2×Dic71⋊C4C23semidirect
102. C2×Dic71⋊C4C23semidirect
103. C2×Dic71⋊C4C23semidirect
132. C2×C4×Dic71C23semidirect
133. C71⋊#95C23semidirect
134. C71⋊#95C23semidirect
135. C71⋊#95C23semidirect
136. C71⋊#95C23semidirect
137. C71⋊#95C23semidirect
138. C71⋊#95C23semidirect
147. C2×C4⋊C4×C71C23semidirect
155. C2×C42×C71C23semidirect
156. #95×C71C23semidirect
157. #95×C71C23semidirect
438. C2×C71#2482semidirect
458. C2×#388D71semidirect
464. C71C2×#2482semidirect
475. C22×C4⋊C4C2×D71semidirect
495. C22×C42C2×D71semidirect
503. #388C2×D71semidirect
515. C2×#95C2×D71semidirect
516. C2×#95C2×D71semidirect
560. C2×C4⋊C4C22×D71semidirect
597. C2×C42C22×D71semidirect
604. #95C22×D71semidirect
605. #95C22×D71semidirect
887. C2#22592612direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145560852
C22×C22⋊C4×D712
#225926122
C2×#179859352
C2×#179859342
C2×#179859282
C2×#179859272
C2×#179858912
C2×#179858902
C2×#179858872
C2×#179858732
C2×#179858702
C2×#179858612
C2×#179858542
C2×#388×C712
C2×#248271