Finite Group Databasebeta

← C2×#22594150 #32163796

Subgroups — C2×#22594150 #32163796

Order 18176.

4142 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556106C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D71C211yesmaximal, characteristic
3#22594150C2116yesmaximal, direct product factor
4C2×#17985935C211yesmaximal, characteristic, complemented
5C2×#17985934C211yesmaximal, characteristic, complemented
6C2×#17985922C211yesmaximal, characteristic, complemented
7C2×#17985921C211yesmaximal, characteristic, complemented
8C2×#17985921C211yesmaximal, characteristic, complemented
9C2×#17985912C211yesmaximal, characteristic, complemented
10C2×#17985911C211yesmaximal, characteristic, complemented
11C2×#17985873C211yesmaximal, characteristic, complemented
12C2×#17985870C211yesmaximal, characteristic, complemented
13C2×#17985856C211yesmaximal, characteristic, complemented
14C2×#17985854C211yesmaximal, characteristic
15C2×#17985854C211yesmaximal, characteristic
16C2×#396×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×Dic142C2211yescharacteristic, complemented
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556106—28no—
22C2×#14556106C2218yescomplemented
23C22×C4⋊Dic71C2211yescharacteristic, complemented
24C22×C4⋊Dic71C2211yescharacteristic, complemented
25C22×Dic71⋊C4C2211yescharacteristic, complemented
26C22×Dic71⋊C4C2211yescharacteristic, complemented
27C22×Dic71⋊C4C2211yescharacteristic, complemented
28C22×Dic71⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic71C2211yescharacteristic
30C22×C22⋊Dic71C2211yescharacteristic
31C22×C22⋊Dic71C2211yescharacteristic
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
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C2×C22⋊C4×D71—28no—
43C2×C22⋊C4×D71C2218yes—
44#17985935C2218yescomplemented
45#17985934C2218yescomplemented
46#17985922C2218yescomplemented
47#17985921C2218yescomplemented
48#17985921C2218yescomplemented
49#17985912C2218yescomplemented
50#17985911C2218yescomplemented
51#17985873C2218yescomplemented
52#17985870C2218yescomplemented
53#17985856C2218yescomplemented
54#17985854C2218yes—
55#17985854C2218yes—
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×C4⋊C4×C71C2211yescharacteristic, complemented
63C22×C4⋊C4×C71C2211yescharacteristic, complemented
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67#396×C71C2218yescomplemented
68C2×#95×C71C2211yescharacteristic, complemented
69C24×D71—24no—
70C24×D71—24no—
71C24×D71—42no—
72C24×D71—42no—
73C24×D71—42no—
74C24×D71—42no—
75C24×D71Q818yescomplemented
76C24×D71C2311yescharacteristic
77C24×D71C2311yescharacteristic
78C24×D71C2314yes—
79C22×Dic142—24no—
80C22×Dic142—42no—
81C22×Dic142—42no—
82C22×Dic142C2314yescomplemented
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C22×C4×D71—24no—
90C22×C4×D71—42no—
91C22×C4×D71—42no—
92C22×C4×D71—42no—
93C22×C4×D71—42no—
94C22×C4×D71D418yes—
95C22×C4×D71C2314yes—
96C22×C4×D71C2314yes—
97#14556106—232no—
98C2×C4⋊Dic71—42no—
99C2×C4⋊Dic71—42no—
100C2×C4⋊Dic71C2314yescomplemented
101C2×C4⋊Dic71C2314yescomplemented
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4—24no—
104C2×Dic71⋊C4—42no—
105C2×Dic71⋊C4—42no—
106C2×Dic71⋊C4C2314yescomplemented
107C2×Dic71⋊C4C2314yescomplemented
108C2×Dic71⋊C4C2314yescomplemented
109C2×Dic71⋊C4C2314yescomplemented
110C2×C22⋊Dic71—24no—
111C2×C22⋊Dic71—42no—
112C2×C22⋊Dic71—42no—
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2314yes—
115C2×C22⋊Dic71C2314yes—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4—24no—
120C2×(C2×D71)⋊C4—24no—
121C2×(C2×D71)⋊C4—24no—
122C2×(C2×D71)⋊C4—42no—
123C2×(C2×D71)⋊C4—42no—
124C2×(C2×D71)⋊C4—42no—
125C2×(C2×D71)⋊C4—42no—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2314yes—
130C2×(C2×D71)⋊C4C2314yes—
131C2×(C2×D71)⋊C4C2314yes—
132C2×(C2×D71)⋊C4C2314yes—
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×(C2×D71)⋊C4C2314yes—
136C22⋊C4×D71—232no—
137C71⋊#95C2314yescomplemented
138C71⋊#95C2314yescomplemented
139C71⋊#95C2314yescomplemented
140C71⋊#95C2314yescomplemented
141C71⋊#95C2314yescomplemented
142C25×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C2×C4⋊C4×C71—24no—
150C2×C4⋊C4×C71—42no—
151C2×C4⋊C4×C71—42no—
152C2×C4⋊C4×C71C2314yescomplemented
153C2×C4⋊C4×C71C2314yescomplemented
154C2×C4⋊C4×C71C2314yescomplemented
155C2×C22⋊C4×C71—24no—
156C2×C22⋊C4×C71—42no—
157C2×C22⋊C4×C71—42no—
158C2×C22⋊C4×C71C2314yes—
159C2×C22⋊C4×C71C2314yes—
160C2×C22⋊C4×C71C2314yes—
161#95×C71C2314yescomplemented
162C23×D71—22no—
163C23×D71—22no—
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—232no—
173C23×D71—28no—
174C23×D71—28no—
175C23×D71—416no—
176C23×D71—416no—
177C23×D71—44no—
178C23×D71—44no—
179C23×D71—44no—
180C23×D71—44no—
181C23×D71—416no—
182C23×D71—416no—
183C23×D71—416no—
184C23×D71—416no—
185C23×D71C2×D414yes—
186C23×D71C2×Q814yes—
187C23×D71C2×Q814yes—
188C23×D71C2×Q8116yescomplemented
189C23×D71#4114yes—
190C23×D71C2412yes—
191C23×D71C2412yes—
192C2×Dic142—28no—
193C2×Dic142—44no—
194C2×Dic142—44no—
195C2×Dic142—416no—
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×Dic71—22no—
206C22×Dic71—22no—
207C22×Dic71—22no—
208C22×Dic71—22no—
209C22×Dic71—22no—
210C22×Dic71—22no—
211C22×Dic71—22no—
212C22×Dic71—22no—
213C22×Dic71C2×D414yes—
214C22×Dic71C2412yes—
215C22×Dic71C2412yes—
216C22×Dic71C2412yes—
217C22×Dic71C2412yes—
218C22×Dic71C2412yes—
219C22×Dic71C2412yes—
220C2×C4×D71—28no—
221C2×C4×D71—416no—
222C2×C4×D71—44no—
223C2×C4×D71—44no—
224C2×C4×D71—44no—
225C2×C4×D71—44no—
226C2×C4×D71—416no—
227C2×C4×D71C2×D4116yes—
228C4⋊Dic71—44no—
229C4⋊Dic71—44no—
230Dic71⋊C4—28no—
231Dic71⋊C4—28no—
232Dic71⋊C4—44no—
233Dic71⋊C4—44no—
234C22⋊Dic71—28no—
235C22⋊Dic71—44no—
236C22⋊Dic71—44no—
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—28no—
243(C2×D71)⋊C4—44no—
244(C2×D71)⋊C4—44no—
245(C2×D71)⋊C4—44no—
246(C2×D71)⋊C4—44no—
247C24×C71—22no—
248C24×C71—22no—
249C24×C71—22no—
250C24×C71—22no—
251C24×C71—22no—
252C24×C71—22no—
253C24×C71C2×Q814yes—
254C24×C71C2412yes—
255C24×C71C2411yescharacteristic
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×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—22no—
272C22×C4×C71—22no—
273C22×C4×C71C2×D414yes—
274C22×C4×C71C2412yes—
275C22×C4×C71C2412yes—
276C22×C4×C71C2412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2412yes—
280C4⋊C4×C71—28no—
281C4⋊C4×C71—44no—
282C4⋊C4×C71—44no—
283C22⋊C4×C71—28no—
284C22⋊C4×C71—44no—
285C22⋊C4×C71—44no—
286C23×C71—28no—
287C23×C71—28no—
288C23×C71—28no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—44no—
296C23×C71—44no—
297C23×C71—44no—
298C23×C71—44no—
299C23×C71C22×D412yes—
300C23×C71C22×Q814yes—
301C23×C71C22×Q812yes—
302C23×C71C2×#4112yes—
303C23×C71H(5,𝔽2)12yes—
304C23×C71H(5,𝔽2)12yes—
305C23×C71H(5,𝔽2)12yes—
306C23×C71H(5,𝔽2)12yes—
307C23×C71C2511yescharacteristic
308C22×D71—28no—
309C22×D71—28no—
310C22×D71—28no—
311C22×D71—28no—
312C22×D71—28no—
313C22×D71—28no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—28no—
319C22×D71—28no—
320C22×D71—28no—
321C22×D71—22no—
322C22×D71—22no—
323C22×D71—22no—
324C22×D71—22no—
325C22×D71—22no—
326C22×D71—22no—
327C22×D71—232no—
328C22×D71—416no—
329C22×D71—416no—
330C22×D71—4128no—
331C22×D71—416no—
332C22×D71—416no—
333C22×D71—416no—
334C22×D71—416no—
335C22×D71—44no—
336C22×D71—44no—
337C22×D71—44no—
338C22×D71—44no—
339C22×D71C22⋊Q8116yes—
340C22×D71C22×D414yes—
341C22×D71C22×Q814yes—
342C22×D71C22×Q814yes—
343C22×D71C2×#4114yes—
344C2×C4×C71—28no—
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—22no—
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—22no—
362C2×C4×C71—44no—
363C2×C4×C71—44no—
364C2×C4×C71—44no—
365C2×C4×C71—44no—
366C2×C4×C71—44no—
367C2×C4×C71C22×D414yes—
368C2×Dic71—28no—
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—22no—
378C2×Dic71—22no—
379C2×Dic71—22no—
380C2×Dic71—22no—
381C2×Dic71—22no—
382C2×Dic71—22no—
383C2×Dic71—22no—
384C2×Dic71—22no—
385C2×Dic71—22no—
386C2×Dic71—44no—
387C2×Dic71—44no—
388C2×Dic71—44no—
389C2×Dic71—44no—
390C2×Dic71—44no—
391C2×Dic71C22×D414yes—
392C4×D71—416no—
393C4×D71—416no—
394Dic142—416no—
395C22×C71—24no—
396C22×C71—24no—
397C22×C71—24no—
398C22×C71—416no—
399C22×C71—42no—
400C22×C71—42no—
401C22×C71—42no—
402C22×C71—42no—
403C22×C71C2×C22⋊Q814yes—
404C22×C71#53414yes—
405C22×C71#53514yes—
406C22×C71#53814yes—
407C22×C71#53814yes—
408C22×C71#54314yes—
409C22×C71#54314yes—
410C22×C71C23×D411yescharacteristic
411C22×C71C23×Q811yescharacteristic
412C22×C71C22×#4111yescharacteristic
413C22×C71C2×H(5,𝔽2)11yescharacteristic
414C22×C71C2×H(5,𝔽2)11yescharacteristic
415C22×C71C2×H(5,𝔽2)11yescharacteristic
416C22×C71C2×H(5,𝔽2)11yescharacteristic
417C2×D71—232no—
418C2×D71—24no—
419C2×D71—24no—
420C2×D71—24no—
421C2×D71—24no—
422C2×D71—24no—
423C2×D71—24no—
424C2×D71—24no—
425C2×D71—24no—
426C2×D71—24no—
427C2×D71—464no—
428C2×D71—416no—
429C2×D71—42no—
430C2×D71—42no—
431C2×D71—42no—
432C2×D71—42no—
433C2×D71C2×C22⋊Q818yes—
434C4×C71—24no—
435C4×C71—42no—
436C4×C71—42no—
437C4×C71—42no—
438C4×C71—42no—
439C4×C71—42no—
440Dic71—24no—
441Dic71—42no—
442Dic71—42no—
443Dic71—42no—
444Dic71—42no—
445Dic71—42no—
446C2×#2626—711nomaximal, Sylow
447C2×C71—44no—
448C2×C71#262618yescomplemented
449C2×C71C22×C22⋊Q811yescharacteristic
450C2×C71C2×#53411yescharacteristic
451C2×C71C2×#53511yescharacteristic
452C2×C71C2×#53811yescharacteristic
453C2×C71C2×#53811yescharacteristic
454C2×C71C2×#54311yescharacteristic
455C2×C71C2×#54311yescharacteristic
456D71—28no—
457D71—44no—
458C22×C22⋊Q8—711no—
459C23×C22⋊C4—711no—
460#2626—7116no—
461C2×#399—711no—
462C2×#399—711no—
463C2×#396—711no—
464C2×#396—711no—
465C2×#396—711no—
466C2×#396D7111yescharacteristic, complemented
467C2×#393—711no—
468C2×#393—711no—
469C2×#385—711no—
470C2×#385—711no—
471C2×#380—711no—
472C2×#379—711no—
473C2×#379—711no—
474C71C2×#262611yescharacteristic, complemented, Sylow
475C26—711no—
476C23×Q8—711no—
477C24×C4—711no—
478C24×C4—711no—
479C2×C22⋊Q8—718no—
480C2×C22⋊Q8—1428no—
481C22×C4⋊C4—711no—
482C22×C4⋊C4—711no—
483C22×C4⋊C4—711no—
484C22×C4⋊C4—711no—
485C22×C4⋊C4—711no—
486C22×C4⋊C4—711no—
487C22×C4⋊C4C2×D7111yescharacteristic, complemented
488C22×C4⋊C4C2×D7111yescharacteristic, complemented
489C22×C4⋊C4C2×D7111yescharacteristic, complemented
490C22×C22⋊C4—711no—
491C22×C22⋊C4—711no—
492C22×C22⋊C4—711no—
493C22×C22⋊C4—711no—
494C22×C22⋊C4—711no—
495C22×C22⋊C4—711no—
496C22×C22⋊C4—711no—
497C22×C22⋊C4—711no—
498C22×C22⋊C4—711no—
499C22×C22⋊C4—711no—
500C22×C22⋊C4—711no—
501C22×C22⋊C4—711no—
502C22×C22⋊C4—711no—
503C22×C22⋊C4—718no—
504C22×C22⋊C4—1428no—
505C22×C22⋊C4C2×D7111yescharacteristic
506C22×C22⋊C4C2×D7111yescharacteristic
507C22×C22⋊C4C2×D7111yescharacteristic
508#399—718no—
509#399—718no—
510#396—718no—
511#396—718no—
512#396—718no—
513#396C2×D7118yescomplemented
514#393—718no—
515#393—718no—
516#385—718no—
517#385—718no—
518#380—718no—
519#379—718no—
520#379—718no—
521C2×#95—711no—
522C2×#95—711no—
523C2×#95—711no—
524C2×#95—711no—
525C2×#95—711no—
526C2×#95C2×D7111yescharacteristic, complemented
527C25—2842no—
528C25—2842no—
529C25—2842no—
530C25—2842no—
531C25—718no—
532C25—714no—
533C25—711no—
534C25—711no—
535C25—1424no—
536C25—1424no—
537C25C22×D7111yescharacteristic
538C22×Q8—2842no—
539C22×Q8—2842no—
540C22×Q8—714no—
541C22×Q8—1424no—
542C23×C4—2842no—
543C23×C4—2842no—
544C23×C4—2842no—
545C23×C4—2842no—
546C23×C4—718no—
547C23×C4—714no—
548C23×C4—714no—
549C23×C4—711no—
550C23×C4—711no—
551C23×C4—711no—
552C23×C4—711no—
553C23×C4—711no—
554C23×C4—711no—
555C23×C4—1424no—
556C23×C4C22×D7111yescharacteristic
557C23×C4C22×D7111yescharacteristic
558C23×C4C22×D7111yescharacteristic
559C23×C4C22×D7111yescharacteristic
560C23×C4C22×D7111yescharacteristic
561C23×C4C22×D7111yescharacteristic
562C22⋊Q8—14232no—
563C2×C4⋊C4—24no—
564C2×C4⋊C4—42no—
565C2×C4⋊C4—42no—
566C2×C4⋊C4—2842no—
567C2×C4⋊C4—2842no—
568C2×C4⋊C4—2842no—
569C2×C4⋊C4—2842no—
570C2×C4⋊C4—714no—
571C2×C4⋊C4—714no—
572C2×C4⋊C4—714no—
573C2×C4⋊C4—714no—
574C2×C4⋊C4—714no—
575C2×C4⋊C4—714no—
576C2×C4⋊C4—1424no—
577C2×C4⋊C4—1424no—
578C2×C4⋊C4C22×D7114yescomplemented
579C2×C4⋊C4C22×D7114yescomplemented
580C2×C4⋊C4C22×D7114yescomplemented
581C2×C22⋊C4—24no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—2842no—
585C2×C22⋊C4—2842no—
586C2×C22⋊C4—2842no—
587C2×C22⋊C4—2842no—
588C2×C22⋊C4—2842no—
589C2×C22⋊C4—2842no—
590C2×C22⋊C4—714no—
591C2×C22⋊C4—714no—
592C2×C22⋊C4—714no—
593C2×C22⋊C4—714no—
594C2×C22⋊C4—714no—
595C2×C22⋊C4—714no—
596C2×C22⋊C4—714no—
597C2×C22⋊C4—714no—
598C2×C22⋊C4—714no—
599C2×C22⋊C4—714no—
600C2×C22⋊C4—714no—
601C2×C22⋊C4—714no—
602C2×C22⋊C4—714no—
603C2×C22⋊C4—14232no—
604C2×C22⋊C4—1424no—
605C2×C22⋊C4—1424no—
606C2×C22⋊C4—1424no—
607C2×C22⋊C4—1424no—
608C2×C22⋊C4—1424no—
609C2×C22⋊C4—1424no—
610C2×C22⋊C4—1424no—
611C2×C22⋊C4C22×D7114yes—
612C2×C22⋊C4C22×D7114yes—
613C2×C22⋊C4C22×D7114yes—
614#95—714no—
615#95—714no—
616#95—714no—
617#95—714no—
618#95—714no—
619#95C22×D7114yescomplemented
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—2844no—
627C24—2844no—
628C24—2844no—
629C24—2844no—
630C24—28416no—
631C24—28416no—
632C24—28416no—
633C24—28416no—
634C24—28416no—
635C24—28416no—
636C24—7116no—
637C24—714no—
638C24—714no—
639C24—714no—
640C24—712no—
641C24—714no—
642C24—712no—
643C24—1428no—
644C24—1428no—
645C24—14232no—
646C24—1422no—
647C24—1422no—
648C24—1422no—
649C24—1422no—
650C24—1422no—
651C24—1422no—
652C24—1422no—
653C24—1422no—
654C24—1422no—
655C24—1422no—
656C24Q8×D7114yes—
657C24C23×D7112yes—
658C24C23×D7111yescharacteristic
659C2×Q8—2844no—
660C2×Q8—2844no—
661C2×Q8—28416no—
662C2×Q8—1428no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—2844no—
681C22×C4—2844no—
682C22×C4—28416no—
683C22×C4—2844no—
684C22×C4—2844no—
685C22×C4—28416no—
686C22×C4—7116no—
687C22×C4—714no—
688C22×C4—712no—
689C22×C4—712no—
690C22×C4—712no—
691C22×C4—712no—
692C22×C4—712no—
693C22×C4—712no—
694C22×C4—1428no—
695C22×C4—1422no—
696C22×C4—1422no—
697C22×C4—1422no—
698C22×C4—1422no—
699C22×C4—1422no—
700C22×C4—1422no—
701C22×C4—1422no—
702C22×C4—1422no—
703C22×C4—1422no—
704C22×C4—1422no—
705C22×C4—1422no—
706C22×C4—1422no—
707C22×C4—1422no—
708C22×C4—1422no—
709C22×C4—1422no—
710C22×C4—1422no—
711C22×C4—1422no—
712C22×C4D4×D7114yes—
713C22×C4C23×D7112yes—
714C22×C4C23×D7112yes—
715C22×C4C23×D7112yes—
716C22×C4C23×D7112yes—
717C22×C4C23×D7112yes—
718C22×C4C23×D7112yes—
719C4⋊C4—28no—
720C4⋊C4—44no—
721C4⋊C4—44no—
722C4⋊C4—2844no—
723C4⋊C4—2844no—
724C4⋊C4—2844no—
725C4⋊C4—2844no—
726C4⋊C4—1428no—
727C4⋊C4—1428no—
728C22⋊C4—28no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—2844no—
732C22⋊C4—2844no—
733C22⋊C4—2844no—
734C22⋊C4—2844no—
735C22⋊C4—2844no—
736C22⋊C4—2844no—
737C22⋊C4—1428no—
738C22⋊C4—1428no—
739C22⋊C4—1428no—
740C22⋊C4—1428no—
741C22⋊C4—1428no—
742C22⋊C4—1428no—
743C22⋊C4—1428no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—28no—
751C23—28no—
752C23—28no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—28416no—
758C23—28416no—
759C23—284128no—
760C23—28416no—
761C23—28416no—
762C23—28416no—
763C23—28416no—
764C23—2844no—
765C23—2844no—
766C23—2844no—
767C23—2844no—
768C23—714no—
769C23—714no—
770C23—714no—
771C23—7116no—
772C23—714no—
773C23—14232no—
774C23—1422no—
775C23—1422no—
776C23—1422no—
777C23—1422no—
778C23—1422no—
779C23—1422no—
780C23—1428no—
781C23—1428no—
782C23—1428no—
783C23—1428no—
784C23—1422no—
785C23—1422no—
786C23—1422no—
787C23—1422no—
788C23—1428no—
789C23—1428no—
790C23—1428no—
791C23—1428no—
792C23—1428no—
793C23C2×D4×D7112yes—
794C23C2×Q8×D7114yes—
795C23C2×Q8×D7112yes—
796C23#41×D7112yes—
797C23#1455617312yes—
798C23#1455617312yes—
799C23#1455617412yes—
800C23#1455617412yes—
801C23C24×D7111yescharacteristic
802Q8—28416no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—28no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—28416no—
827C2×C4—28416no—
828C2×C4—2844no—
829C2×C4—2844no—
830C2×C4—2844no—
831C2×C4—2844no—
832C2×C4—2844no—
833C2×C4—714no—
834C2×C4—1422no—
835C2×C4—1422no—
836C2×C4—1422no—
837C2×C4—1422no—
838C2×C4—1422no—
839C2×C4—1422no—
840C2×C4—1422no—
841C2×C4—1422no—
842C2×C4—1422no—
843C2×C4—1422no—
844C2×C4—1422no—
845C2×C4—1422no—
846C2×C4—1422no—
847C2×C4—1422no—
848C2×C4—1422no—
849C2×C4—1422no—
850C2×C4—1422no—
851C2×C4—1428no—
852C2×C4C2×D4×D7114yes—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—416no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—28464no—
862C22—28416no—
863C22—2842no—
864C22—2842no—
865C22—2842no—
866C22—2842no—
867C22—718no—
868C22—1424no—
869C22—1424no—
870C22—1424no—
871C22—1424no—
872C22—1424no—
873C22—14232no—
874C22—1424no—
875C22—1424no—
876C22—1424no—
877C22—1424no—
878C22C22⋊Q8×D7114yes—
879C22#1798655714yes—
880C22#1798656514yes—
881C22#1798658114yes—
882C22#1798658814yes—
883C22#1798662414yes—
884C22#1798662414yes—
885C22C22×D4×D7111yescharacteristic
886C22C22×Q8×D7111yescharacteristic
887C22C2×#41×D7111yescharacteristic
888C22C2×#1455617311yescharacteristic
889C22C2×#1455617311yescharacteristic
890C22C2×#1455617411yescharacteristic
891C22C2×#1455617411yescharacteristic
892C4—24no—
893C4—42no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—2842no—
899C4—2842no—
900C4—2842no—
901C4—2842no—
902C4—2842no—
903C4—1424no—
904C2—44no—
905C2—2844no—
906C2—1428no—
907C2#2259415018yesdirect product factor
908C2C2×C22⋊Q8×D7111yescharacteristic
909C2C2×#1798655711yescharacteristic
910C2C2×#1798656511yescharacteristic
911C2C2×#1798658111yescharacteristic
912C2C2×#1798658811yescharacteristic
913C2C2×#1798662411yescharacteristic
914C2C2×#1798662411yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#396×C71C2
socleC24×C71C24
prime radicalC25×D71C22
hypercenterC2×#396D71
hypocenterC71C2×#2626
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14556106C2semidirect
3. #22594150C2direct (N × H)
4. C2×#17985935C2semidirect
5. C2×#17985934C2semidirect
6. C2×#17985922C2semidirect
7. C2×#17985921C2semidirect
8. C2×#17985921C2semidirect
9. C2×#17985912C2semidirect
10. C2×#17985911C2semidirect
11. C2×#17985873C2semidirect
12. C2×#17985870C2semidirect
13. C2×#17985856C2semidirect
16. C2×#396×C71C2semidirect
18. C23×Dic142C22semidirect
22. C2×#14556106C22semidirect
23. C22×C4⋊Dic71C22semidirect
24. C22×C4⋊Dic71C22semidirect
25. C22×Dic71⋊C4C22semidirect
26. C22×Dic71⋊C4C22semidirect
27. C22×Dic71⋊C4C22semidirect
28. C22×Dic71⋊C4C22semidirect
44. #17985935C22semidirect
45. #17985934C22semidirect
46. #17985922C22semidirect
47. #17985921C22semidirect
48. #17985921C22semidirect
49. #17985912C22semidirect
50. #17985911C22semidirect
51. #17985873C22semidirect
52. #17985870C22semidirect
53. #17985856C22semidirect
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
62. C22×C4⋊C4×C71C22semidirect
63. C22×C4⋊C4×C71C22semidirect
67. #396×C71C22semidirect
68. C2×#95×C71C22semidirect
75. C24×D71Q8semidirect
82. C22×Dic142C23semidirect
100. C2×C4⋊Dic71C23semidirect
101. C2×C4⋊Dic71C23semidirect
106. C2×Dic71⋊C4C23semidirect
107. C2×Dic71⋊C4C23semidirect
108. C2×Dic71⋊C4C23semidirect
109. C2×Dic71⋊C4C23semidirect
137. C71⋊#95C23semidirect
138. C71⋊#95C23semidirect
139. C71⋊#95C23semidirect
140. C71⋊#95C23semidirect
141. C71⋊#95C23semidirect
152. C2×C4⋊C4×C71C23semidirect
153. C2×C4⋊C4×C71C23semidirect
154. C2×C4⋊C4×C71C23semidirect
161. #95×C71C23semidirect
188. C23×D71C2×Q8semidirect
448. C2×C71#2626semidirect
466. C2×#396D71semidirect
474. C71C2×#2626semidirect
487. C22×C4⋊C4C2×D71semidirect
488. C22×C4⋊C4C2×D71semidirect
489. C22×C4⋊C4C2×D71semidirect
513. #396C2×D71semidirect
526. C2×#95C2×D71semidirect
578. C2×C4⋊C4C22×D71semidirect
579. C2×C4⋊C4C22×D71semidirect
580. C2×C4⋊C4C22×D71semidirect
619. #95C22×D71semidirect
907. C2#22594150direct (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×C22⋊C4×D712
#225941502
C2×#179859352
C2×#179859342
C2×#179859222
C2×#179859212
C2×#179859122
C2×#179859112
C2×#179858732
C2×#179858702
C2×#179858562
C2×#179858542
C2×#396×C712
C2×#262671