Finite Group Databasebeta

← C2×#22591718 #32166067

Subgroups — C2×#22591718 #32166067

Order 18176.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic, complemented
2C22×#14556096C211yesmaximal, characteristic
3C22×#14556086C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D71C211yesmaximal, characteristic, complemented
5#22591718C2116yesmaximal, direct product factor
6C2×#17985922C211yesmaximal, characteristic, complemented
7C2×#17985921C211yesmaximal, characteristic, complemented
8C2×#17985915C211yesmaximal, characteristic, complemented
9C2×#17985902C211yesmaximal, characteristic, complemented
10C2×#17985899C211yesmaximal, characteristic, complemented
11C2×#17985892C211yesmaximal, characteristic, complemented
12C2×#17985891C211yesmaximal, characteristic, complemented
13C2×#17985875C211yesmaximal, characteristic, complemented
14C2×#17985873C211yesmaximal, characteristic, complemented
15C2×#17985854C211yesmaximal, characteristic, complemented
16C2×#394×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C2×#14556110—28no—
23C2×#14556110C2218yescomplemented
24C2×#14556096—28no—
25C2×#14556096C2218yes—
26C2×#14556086—28no—
27C2×#14556086C2218yescomplemented
28C22×C4⋊Dic71C2211yescharacteristic, complemented
29C22×C4⋊Dic71C2211yescharacteristic, complemented
30C22×C4⋊Dic71C2211yescharacteristic, complemented
31C22×Dic71⋊C4C2211yescharacteristic, complemented
32C22×Dic71⋊C4C2211yescharacteristic, complemented
33C22×C22⋊Dic71C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic, complemented
37C22×C22⋊Dic71C2211yescharacteristic, complemented
38C22×(C2×D71)⋊C4C2211yescharacteristic
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
46C2×C22⋊C4×D71—28no—
47C2×C22⋊C4×D71C2218yescomplemented
48C22×C4×Dic71C2211yescharacteristic, complemented
49C22×C4×Dic71C2211yescharacteristic, complemented
50#17985922C2218yescomplemented
51#17985921C2218yescomplemented
52#17985915C2218yescomplemented
53#17985902C2218yescomplemented
54#17985899C2218yescomplemented
55#17985892C2218yescomplemented
56#17985891C2218yescomplemented
57#17985875C2218yescomplemented
58#17985873C2218yescomplemented
59#17985854C2218yescomplemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C2×C71⋊#95C2211yescharacteristic, complemented
63C23×D4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic, complemented
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic, complemented
68C22×C22⋊C4×C71C2211yescharacteristic, complemented
69#394×C71C2218yescomplemented
70C2×#95×C71C2211yescharacteristic, complemented
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—24no—
75C24×D71—24no—
76C24×D71—42no—
77C24×D71—42no—
78C24×D71C2311yescharacteristic
79C24×D71C2314yes—
80C24×D71C2311yescharacteristic
81C22×C22⋊D71—24no—
82C22×C22⋊D71—24no—
83C22×C22⋊D71—24no—
84C22×C22⋊D71—24no—
85C22×C22⋊D71—24no—
86C22×C22⋊D71—42no—
87C22×C22⋊D71C2314yes—
88C22×C22⋊D71C2314yes—
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2311yescharacteristic
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2311yescharacteristic
95C22×C4×D71—24no—
96C22×C4×D71—24no—
97C22×C4×D71—24no—
98C22×C4×D71—42no—
99C22×C4×D71—42no—
100C22×C4×D71D418yescomplemented
101C22×C4×D71C2314yes—
102C22×C4×D71C2314yes—
103#14556110—232no—
104#14556096—232no—
105#14556086—232no—
106C2×C4⋊Dic71—24no—
107C2×C4⋊Dic71—24no—
108C2×C4⋊Dic71—42no—
109C2×C4⋊Dic71C2314yescomplemented
110C2×C4⋊Dic71C2314yescomplemented
111C2×C4⋊Dic71C2314yescomplemented
112C2×Dic71⋊C4—24no—
113C2×Dic71⋊C4—42no—
114C2×Dic71⋊C4C2314yescomplemented
115C2×Dic71⋊C4C2314yescomplemented
116C2×C22⋊Dic71—24no—
117C2×C22⋊Dic71—24no—
118C2×C22⋊Dic71—24no—
119C2×C22⋊Dic71—42no—
120C2×C22⋊Dic71—42no—
121C2×C22⋊Dic71C2314yes—
122C2×C22⋊Dic71C2314yes—
123C2×C22⋊Dic71C2314yes—
124C2×C22⋊Dic71C2314yescomplemented
125C2×C22⋊Dic71C2314yescomplemented
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—24no—
129C2×(C2×D71)⋊C4—24no—
130C2×(C2×D71)⋊C4—24no—
131C2×(C2×D71)⋊C4—24no—
132C2×(C2×D71)⋊C4—42no—
133C2×(C2×D71)⋊C4D418yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×(C2×D71)⋊C4C2314yes—
136C2×(C2×D71)⋊C4C2314yes—
137C2×(C2×D71)⋊C4C2314yes—
138C2×(C2×D71)⋊C4C2314yes—
139C2×(C2×D71)⋊C4C2314yes—
140C2×(C2×D71)⋊C4C2314yes—
141C2×(C2×D71)⋊C4C2314yes—
142C22⋊C4×D71—232no—
143C2×C4×Dic71—24no—
144C2×C4×Dic71—24no—
145C2×C4×Dic71C2314yescomplemented
146C2×C4×Dic71C2314yescomplemented
147C71⋊#95C2314yescomplemented
148C71⋊#95C2314yescomplemented
149C71⋊#95C2314yescomplemented
150C25×C71C2311yescharacteristic
151C25×C71C2311yescharacteristic
152C22×D4×C71—24no—
153C22×D4×C71—24no—
154C22×D4×C71—42no—
155C22×D4×C71C2314yes—
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C2×C4⋊C4×C71—24no—
162C2×C4⋊C4×C71C2314yescomplemented
163C2×C22⋊C4×C71—24no—
164C2×C22⋊C4×C71—24no—
165C2×C22⋊C4×C71—24no—
166C2×C22⋊C4×C71—42no—
167C2×C22⋊C4×C71C2314yes—
168C2×C22⋊C4×C71C2314yes—
169C2×C22⋊C4×C71C2314yescomplemented
170C2×C22⋊C4×C71C2314yescomplemented
171#95×C71C2314yescomplemented
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—232no—
177C23×D71—22no—
178C23×D71—22no—
179C23×D71—22no—
180C23×D71—28no—
181C23×D71—22no—
182C23×D71—22no—
183C23×D71—22no—
184C23×D71—28no—
185C23×D71—28no—
186C23×D71—28no—
187C23×D71—28no—
188C23×D71—44no—
189C23×D71—44no—
190C23×D71—416no—
191C23×D71—416no—
192C23×D71—416no—
193C23×D71—416no—
194C23×D71—416no—
195C23×D71—416no—
196C23×D71C2×D414yes—
197C23×D71C2×D414yes—
198C23×D71#4114yes—
199C23×D71#4114yes—
200C23×D71C2412yes—
201C23×D71C2412yes—
202C2×C22⋊D71—28no—
203C2×C22⋊D71—28no—
204C2×C22⋊D71—28no—
205C2×C22⋊D71—28no—
206C2×C22⋊D71—28no—
207C2×C22⋊D71—44no—
208C2×C22⋊D71—416no—
209C2×C22⋊D71—416no—
210C22×Dic71—22no—
211C22×Dic71—22no—
212C22×Dic71—22no—
213C22×Dic71—22no—
214C22×Dic71—22no—
215C22×Dic71—22no—
216C22×Dic71—22no—
217C22×Dic71—22no—
218C22×Dic71—22no—
219C22×Dic71—22no—
220C22×Dic71—22no—
221C22×Dic71—22no—
222C22×Dic71—22no—
223C22×Dic71—22no—
224C22×Dic71—22no—
225C22×Dic71—22no—
226C22×Dic71C2×D414yes—
227C22×Dic71C2×D414yes—
228C22×Dic71C2412yes—
229C22×Dic71C2412yes—
230C22×Dic71C2412yes—
231C22×Dic71C2412yes—
232C22×Dic71C2412yes—
233C22×Dic71C2412yes—
234C2×C4×D71—232no—
235C2×C4×D71—28no—
236C2×C4×D71—28no—
237C2×C4×D71—28no—
238C2×C4×D71—44no—
239C2×C4×D71—44no—
240C2×C4×D71—416no—
241C2×C4×D71C2×D4116yescomplemented
242C4⋊Dic71—28no—
243C4⋊Dic71—28no—
244C4⋊Dic71—44no—
245Dic71⋊C4—28no—
246Dic71⋊C4—44no—
247C22⋊Dic71—28no—
248C22⋊Dic71—28no—
249C22⋊Dic71—28no—
250C22⋊Dic71—44no—
251C22⋊Dic71—44no—
252(C2×D71)⋊C4—28no—
253(C2×D71)⋊C4—28no—
254(C2×D71)⋊C4—28no—
255(C2×D71)⋊C4—28no—
256(C2×D71)⋊C4—28no—
257(C2×D71)⋊C4—28no—
258(C2×D71)⋊C4—44no—
259(C2×D71)⋊C4C2×D4116yes—
260C4×Dic71—28no—
261C4×Dic71—28no—
262C24×C71—22no—
263C24×C71—22no—
264C24×C71—22no—
265C24×C71—22no—
266C24×C71—22no—
267C24×C71—22no—
268C24×C71—22no—
269C24×C71—22no—
270C24×C71—22no—
271C24×C71—22no—
272C24×C71—22no—
273C24×C71—22no—
274C24×C71—22no—
275C24×C71#4114yes—
276C24×C71C2412yes—
277C24×C71C2412yes—
278C24×C71C2411yescharacteristic
279C2×D4×C71—28no—
280C2×D4×C71—28no—
281C2×D4×C71—44no—
282C2×D4×C71—416no—
283C22×C4×C71—22no—
284C22×C4×C71—22no—
285C22×C4×C71—22no—
286C22×C4×C71—22no—
287C22×C4×C71—22no—
288C22×C4×C71—22no—
289C22×C4×C71—22no—
290C22×C4×C71—22no—
291C22×C4×C71—22no—
292C22×C4×C71—22no—
293C22×C4×C71—22no—
294C22×C4×C71—22no—
295C22×C4×C71—22no—
296C22×C4×C71C2×D414yes—
297C22×C4×C71C2×D414yes—
298C22×C4×C71C2412yes—
299C22×C4×C71C2412yes—
300C22×C4×C71C2412yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2412yes—
303C4⋊C4×C71—28no—
304C22⋊C4×C71—28no—
305C22⋊C4×C71—28no—
306C22⋊C4×C71—28no—
307C22⋊C4×C71—44no—
308C23×C71—28no—
309C23×C71—28no—
310C23×C71—28no—
311C23×C71—22no—
312C23×C71—22no—
313C23×C71—22no—
314C23×C71—22no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71—22no—
320C23×C71—22no—
321C23×C71—22no—
322C23×C71—22no—
323C23×C71—22no—
324C23×C71—44no—
325C23×C71—44no—
326C23×C71—44no—
327C23×C71—44no—
328C23×C71—44no—
329C23×C71—44no—
330C23×C71—44no—
331C23×C71—44no—
332C23×C71—44no—
333C23×C71—44no—
334C23×C71—44no—
335C23×C71C22×D412yes—
336C23×C71C22×D412yes—
337C23×C71C2×#4112yes—
338C23×C71C2×#4112yes—
339C23×C71C2×#4114yes—
340C23×C71C2×#4112yes—
341C23×C71H(5,𝔽2)12yes—
342C23×C71H(5,𝔽2)12yes—
343C23×C71C2511yescharacteristic
344C22×D71—28no—
345C22×D71—28no—
346C22×D71—28no—
347C22×D71—28no—
348C22×D71—28no—
349C22×D71—28no—
350C22×D71—22no—
351C22×D71—22no—
352C22×D71—22no—
353C22×D71—22no—
354C22×D71—232no—
355C22×D71—28no—
356C22×D71—28no—
357C22×D71—28no—
358C22×D71—22no—
359C22×D71—22no—
360C22×D71—22no—
361C22×D71—22no—
362C22×D71—22no—
363C22×D71—22no—
364C22×D71—416no—
365C22×D71—416no—
366C22×D71—416no—
367C22×D71—416no—
368C22×D71—4128no—
369C22×D71—416no—
370C22×D71—44no—
371C22×D71—44no—
372C22×D71—44no—
373C22×D71—44no—
374C22×D71—416no—
375C22×D71#121116yes—
376C22×D71C22×D414yes—
377C22×D71C22×D414yes—
378C22×D71C2×#4114yes—
379C22×D71C2×#4114yes—
380D4×C71—416no—
381C2×C4×C71—28no—
382C2×C4×C71—28no—
383C2×C4×C71—22no—
384C2×C4×C71—22no—
385C2×C4×C71—22no—
386C2×C4×C71—22no—
387C2×C4×C71—22no—
388C2×C4×C71—22no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—22no—
396C2×C4×C71—44no—
397C2×C4×C71—44no—
398C2×C4×C71—44no—
399C2×C4×C71C22×D414yes—
400C2×C4×C71C22×D414yes—
401C22⋊D71—416no—
402C22⋊D71—416no—
403C2×Dic71—28no—
404C2×Dic71—28no—
405C2×Dic71—22no—
406C2×Dic71—22no—
407C2×Dic71—22no—
408C2×Dic71—22no—
409C2×Dic71—22no—
410C2×Dic71—22no—
411C2×Dic71—22no—
412C2×Dic71—22no—
413C2×Dic71—22no—
414C2×Dic71—22no—
415C2×Dic71—22no—
416C2×Dic71—22no—
417C2×Dic71—22no—
418C2×Dic71—22no—
419C2×Dic71—22no—
420C2×Dic71—22no—
421C2×Dic71—44no—
422C2×Dic71—44no—
423C2×Dic71—44no—
424C2×Dic71—44no—
425C2×Dic71C22×D414yes—
426C2×Dic71C22×D414yes—
427C4×D71—232no—
428C4×D71—416no—
429C22×C71—24no—
430C22×C71—24no—
431C22×C71—24no—
432C22×C71—42no—
433C22×C71—416no—
434C22×C71—42no—
435C22×C71—42no—
436C22×C71—42no—
437C22×C71—42no—
438C22×C71—42no—
439C22×C71—42no—
440C22×C71—42no—
441C22×C71—42no—
442C22×C71—42no—
443C22×C71—42no—
444C22×C71—88no—
445C22×C71C2×#12114yes—
446C22×C71#52514yes—
447C22×C71#53514yes—
448C22×C71#54614yes—
449C22×C71#54614yes—
450C22×C71#55114yes—
451C22×C71#55114yes—
452C22×C71C23×D411yescharacteristic
453C22×C71C23×D411yescharacteristic
454C22×C71C22×#4111yescharacteristic
455C22×C71C22×#4111yescharacteristic
456C22×C71C22×#4111yescharacteristic
457C22×C71C2×H(5,𝔽2)11yescharacteristic
458C22×C71C2×H(5,𝔽2)11yescharacteristic
459C2×D71—232no—
460C2×D71—24no—
461C2×D71—24no—
462C2×D71—24no—
463C2×D71—24no—
464C2×D71—24no—
465C2×D71—24no—
466C2×D71—24no—
467C2×D71—24no—
468C2×D71—24no—
469C2×D71—464no—
470C2×D71—42no—
471C2×D71—416no—
472C2×D71—42no—
473C2×D71—42no—
474C2×D71—42no—
475C2×D71C2×#12118yes—
476C4×C71—24no—
477C4×C71—24no—
478C4×C71—42no—
479C4×C71—42no—
480C4×C71—42no—
481Dic71—24no—
482Dic71—24no—
483Dic71—42no—
484Dic71—42no—
485Dic71—42no—
486Dic71—42no—
487C2×#2411—711nomaximal, Sylow
488C2×C71—44no—
489C2×C71—82no—
490C2×C71#241118yescomplemented
491C2×C71C22×#12111yescharacteristic
492C2×C71C2×#52511yescharacteristic
493C2×C71C2×#53511yescharacteristic
494C2×C71C2×#54611yescharacteristic
495C2×C71C2×#54611yescharacteristic
496C2×C71C2×#55111yescharacteristic
497C2×C71C2×#55111yescharacteristic
498D71—28no—
499D71—44no—
500C22×#123—711no—
501C22×#120—711no—
502C22×#117—711no—
503C23×C22⋊C4—711no—
504#2411—7116no—
505C2×#396—711no—
506C2×#396—711no—
507C2×#394—711no—
508C2×#394D7111yescharacteristic, complemented
509C2×#390—711no—
510C2×#390—711no—
511C2×#388—711no—
512C2×#388—711no—
513C2×#386—711no—
514C2×#385—711no—
515C2×#379—711no—
516C71C2×#241111yescharacteristic, complemented, Sylow
517C26—711no—
518C23×D4—711no—
519C23×D4—711no—
520C23×D4C2×D7111yescharacteristic
521C24×C4—711no—
522C24×C4—711no—
523C2×#123—718no—
524C2×#123—1428no—
525C2×#120—718no—
526C2×#120—1428no—
527C2×#117—718no—
528C2×#117—1428no—
529C22×C4⋊C4—711no—
530C22×C4⋊C4—711no—
531C22×C4⋊C4—711no—
532C22×C4⋊C4—711no—
533C22×C4⋊C4—711no—
534C22×C4⋊C4C2×D7111yescharacteristic, complemented
535C22×C22⋊C4—711no—
536C22×C22⋊C4—711no—
537C22×C22⋊C4—711no—
538C22×C22⋊C4—711no—
539C22×C22⋊C4—711no—
540C22×C22⋊C4—711no—
541C22×C22⋊C4—711no—
542C22×C22⋊C4—711no—
543C22×C22⋊C4—711no—
544C22×C22⋊C4—711no—
545C22×C22⋊C4—711no—
546C22×C22⋊C4—711no—
547C22×C22⋊C4—711no—
548C22×C22⋊C4—718no—
549C22×C22⋊C4—1428no—
550C22×C22⋊C4C2×D7111yescharacteristic
551C22×C22⋊C4C2×D7111yescharacteristic
552C22×C22⋊C4C2×D7111yescharacteristic, complemented
553C22×C22⋊C4C2×D7111yescharacteristic, complemented
554C22×C42—711no—
555C22×C42—711no—
556#396—718no—
557#396—718no—
558#394—718no—
559#394C2×D7118yescomplemented
560#390—718no—
561#390—718no—
562#388—718no—
563#388—718no—
564#386—718no—
565#385—718no—
566#379—718no—
567C2×#95—711no—
568C2×#95—711no—
569C2×#95—711no—
570C2×#95C2×D7111yescharacteristic, complemented
571C25—2842no—
572C25—2842no—
573C25—714no—
574C25—711no—
575C25—711no—
576C25—1424no—
577C25—1424no—
578C25—1424no—
579C25—1424no—
580C25—1424no—
581C25C22×D7111yescharacteristic
582C25C22×D7111yescharacteristic
583C22×D4—24no—
584C22×D4—24no—
585C22×D4—42no—
586C22×D4—2842no—
587C22×D4—714no—
588C22×D4—714no—
589C22×D4—1424no—
590C22×D4—1424no—
591C22×D4—1424no—
592C22×D4—1424no—
593C22×D4—1424no—
594C22×D4C22×D7114yes—
595C23×C4—2842no—
596C23×C4—2842no—
597C23×C4—714no—
598C23×C4—711no—
599C23×C4—711no—
600C23×C4—718no—
601C23×C4—714no—
602C23×C4—711no—
603C23×C4—711no—
604C23×C4—711no—
605C23×C4—711no—
606C23×C4—1424no—
607C23×C4—1424no—
608C23×C4—1424no—
609C23×C4C22×D7111yescharacteristic
610C23×C4C22×D7111yescharacteristic
611C23×C4C22×D7111yescharacteristic
612C23×C4C22×D7111yescharacteristic
613C23×C4C22×D7111yescharacteristic
614#123—14232no—
615#120—14232no—
616#117—14232no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—2842no—
619C2×C4⋊C4—2842no—
620C2×C4⋊C4—714no—
621C2×C4⋊C4—714no—
622C2×C4⋊C4—714no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—714no—
625C2×C4⋊C4—1424no—
626C2×C4⋊C4—1424no—
627C2×C4⋊C4—1424no—
628C2×C4⋊C4C22×D7114yescomplemented
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—42no—
633C2×C22⋊C4—2842no—
634C2×C22⋊C4—2842no—
635C2×C22⋊C4—2842no—
636C2×C22⋊C4—714no—
637C2×C22⋊C4—714no—
638C2×C22⋊C4—714no—
639C2×C22⋊C4—718no—
640C2×C22⋊C4—714no—
641C2×C22⋊C4—714no—
642C2×C22⋊C4—714no—
643C2×C22⋊C4—714no—
644C2×C22⋊C4—714no—
645C2×C22⋊C4—714no—
646C2×C22⋊C4—714no—
647C2×C22⋊C4—714no—
648C2×C22⋊C4—714no—
649C2×C22⋊C4—714no—
650C2×C22⋊C4—14232no—
651C2×C22⋊C4—1424no—
652C2×C22⋊C4—1424no—
653C2×C22⋊C4—1424no—
654C2×C22⋊C4—1424no—
655C2×C22⋊C4—1424no—
656C2×C22⋊C4—1424no—
657C2×C22⋊C4—1424no—
658C2×C22⋊C4—1424no—
659C2×C22⋊C4—1424no—
660C2×C22⋊C4C22×D7114yes—
661C2×C22⋊C4C22×D7114yes—
662C2×C22⋊C4C22×D7114yescomplemented
663C2×C22⋊C4C22×D7114yescomplemented
664C2×C42—714no—
665C2×C42—714no—
666C2×C42—1424no—
667C2×C42—1424no—
668#95—714no—
669#95—714no—
670#95—714no—
671#95C22×D7114yescomplemented
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—28416no—
686C24—28416no—
687C24—2844no—
688C24—2844no—
689C24—28416no—
690C24—28416no—
691C24—28416no—
692C24—28416no—
693C24—714no—
694C24—714no—
695C24—714no—
696C24—712no—
697C24—714no—
698C24—712no—
699C24—1428no—
700C24—1428no—
701C24—1428no—
702C24—1428no—
703C24—14232no—
704C24—1422no—
705C24—1422no—
706C24—1422no—
707C24—1428no—
708C24—1422no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24—1422no—
713C24—1422no—
714C24—1422no—
715C24#1176586414yes—
716C24C23×D7112yes—
717C24C23×D7112yes—
718C24C23×D7111yescharacteristic
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—44no—
722C2×D4—416no—
723C2×D4—28416no—
724C2×D4—2844no—
725C2×D4—28416no—
726C2×D4—1428no—
727C2×D4—1428no—
728C2×D4—1428no—
729C2×D4—1428no—
730C2×D4—1428no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—2844no—
745C22×C4—2844no—
746C22×C4—28416no—
747C22×C4—714no—
748C22×C4—714no—
749C22×C4—712no—
750C22×C4—712no—
751C22×C4—7116no—
752C22×C4—712no—
753C22×C4—712no—
754C22×C4—712no—
755C22×C4—712no—
756C22×C4—1428no—
757C22×C4—1428no—
758C22×C4—1428no—
759C22×C4—14232no—
760C22×C4—1422no—
761C22×C4—1422no—
762C22×C4—1422no—
763C22×C4—1422no—
764C22×C4—1422no—
765C22×C4—1422no—
766C22×C4—1422no—
767C22×C4—1422no—
768C22×C4—1422no—
769C22×C4—1422no—
770C22×C4—1422no—
771C22×C4—1422no—
772C22×C4—1422no—
773C22×C4—1422no—
774C22×C4—1422no—
775C22×C4—1422no—
776C22×C4D4×D7114yes—
777C22×C4D4×D7114yes—
778C22×C4C23×D7112yes—
779C22×C4C23×D7112yes—
780C22×C4C23×D7112yes—
781C22×C4C23×D7112yes—
782C22×C4C23×D7112yes—
783C4⋊C4—28no—
784C4⋊C4—2844no—
785C4⋊C4—2844no—
786C4⋊C4—1428no—
787C4⋊C4—1428no—
788C4⋊C4—1428no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—44no—
793C22⋊C4—2844no—
794C22⋊C4—2844no—
795C22⋊C4—2844no—
796C22⋊C4—7116no—
797C22⋊C4—1428no—
798C22⋊C4—1428no—
799C22⋊C4—1428no—
800C22⋊C4—1428no—
801C22⋊C4—1428no—
802C22⋊C4—1428no—
803C22⋊C4—1428no—
804C22⋊C4—1428no—
805C22⋊C4—1428no—
806C42—1428no—
807C42—1428no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—28416no—
836C23—28416no—
837C23—28416no—
838C23—28416no—
839C23—284128no—
840C23—28416no—
841C23—28416no—
842C23—2844no—
843C23—2844no—
844C23—2844no—
845C23—2844no—
846C23—714no—
847C23—714no—
848C23—714no—
849C23—7116no—
850C23—714no—
851C23—14232no—
852C23—1422no—
853C23—1422no—
854C23—1422no—
855C23—1422no—
856C23—1422no—
857C23—1422no—
858C23—1428no—
859C23—1428no—
860C23—1428no—
861C23—1428no—
862C23—1422no—
863C23—1422no—
864C23—1422no—
865C23—1422no—
866C23—1428no—
867C23—1428no—
868C23—1428no—
869C23—1428no—
870C23—1428no—
871C23C2×D4×D7112yes—
872C23C2×D4×D7112yes—
873C23#41×D7112yes—
874C23#41×D7112yes—
875C23C2×#1176586414yes—
876C23C2×#1176586412yes—
877C23#1455617312yes—
878C23#1455617412yes—
879C23C24×D7111yescharacteristic
880D4—416no—
881D4—28416no—
882D4—28416no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—28416no—
902C2×C4—2844no—
903C2×C4—2844no—
904C2×C4—2844no—
905C2×C4—2844no—
906C2×C4—714no—
907C2×C4—714no—
908C2×C4—14232no—
909C2×C4—1422no—
910C2×C4—1422no—
911C2×C4—1422no—
912C2×C4—1422no—
913C2×C4—1422no—
914C2×C4—1422no—
915C2×C4—1422no—
916C2×C4—1422no—
917C2×C4—1422no—
918C2×C4—1422no—
919C2×C4—1422no—
920C2×C4—1422no—
921C2×C4—1422no—
922C2×C4—1422no—
923C2×C4—1422no—
924C2×C4—1422no—
925C2×C4—1428no—
926C2×C4—1428no—
927C2×C4C2×D4×D7114yes—
928C2×C4C2×D4×D7114yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—416no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—88no—
945C22—28464no—
946C22—2842no—
947C22—2842no—
948C22—2842no—
949C22—2842no—
950C22—28416no—
951C22—718no—
952C22—1424no—
953C22—1424no—
954C22—1424no—
955C22—1424no—
956C22—1424no—
957C22—1424no—
958C22—1424no—
959C22—1424no—
960C22—1424no—
961C22—14232no—
962C22#121×D7114yes—
963C22#1798650914yes—
964C22#1798656514yes—
965C22#1798663614yes—
966C22#1798664214yes—
967C22#1798667214yes—
968C22#1798667714yes—
969C22C22×D4×D7111yescharacteristic
970C22C22×D4×D7111yescharacteristic
971C22C2×#41×D7111yescharacteristic
972C22C2×#41×D7111yescharacteristic
973C22C22×#1176586411yescharacteristic
974C22C2×#1455617311yescharacteristic
975C22C2×#1455617411yescharacteristic
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—2842no—
982C4—2842no—
983C4—2842no—
984C4—2842no—
985C4—1424no—
986C4—1424no—
987C2—44no—
988C2—82no—
989C2—2844no—
990C2—1428no—
991C2#2259171818yesdirect product factor
992C2C2×#121×D7111yescharacteristic
993C2C2×#1798650911yescharacteristic
994C2C2×#1798656511yescharacteristic
995C2C2×#1798663611yescharacteristic
996C2C2×#1798664211yescharacteristic
997C2C2×#1798667211yescharacteristic
998C2C2×#1798667711yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#394×C71C2
socleC24×C71C24
prime radicalC22×#14556096C2
hypercenterC2×#394D71
hypocenterC71C2×#2411
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#14556110C2semidirect
3. C22×#14556086C2semidirect
4. C22×C22⋊C4×D71C2semidirect
5. #22591718C2direct (N × H)
6. C2×#17985922C2semidirect
7. C2×#17985921C2semidirect
8. C2×#17985915C2semidirect
9. C2×#17985902C2semidirect
10. C2×#17985899C2semidirect
11. C2×#17985892C2semidirect
12. C2×#17985891C2semidirect
13. C2×#17985875C2semidirect
14. C2×#17985873C2semidirect
15. C2×#17985854C2semidirect
16. C2×#394×C71C2semidirect
23. C2×#14556110C22semidirect
27. C2×#14556086C22semidirect
28. C22×C4⋊Dic71C22semidirect
29. C22×C4⋊Dic71C22semidirect
30. C22×C4⋊Dic71C22semidirect
31. C22×Dic71⋊C4C22semidirect
32. C22×Dic71⋊C4C22semidirect
36. C22×C22⋊Dic71C22semidirect
37. C22×C22⋊Dic71C22semidirect
47. C2×C22⋊C4×D71C22semidirect
48. C22×C4×Dic71C22semidirect
49. C22×C4×Dic71C22semidirect
50. #17985922C22semidirect
51. #17985921C22semidirect
52. #17985915C22semidirect
53. #17985902C22semidirect
54. #17985899C22semidirect
55. #17985892C22semidirect
56. #17985891C22semidirect
57. #17985875C22semidirect
58. #17985873C22semidirect
59. #17985854C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
62. C2×C71⋊#95C22semidirect
64. C22×C4⋊C4×C71C22semidirect
67. C22×C22⋊C4×C71C22semidirect
68. C22×C22⋊C4×C71C22semidirect
69. #394×C71C22semidirect
70. C2×#95×C71C22semidirect
100. C22×C4×D71D4semidirect
109. C2×C4⋊Dic71C23semidirect
110. C2×C4⋊Dic71C23semidirect
111. C2×C4⋊Dic71C23semidirect
114. C2×Dic71⋊C4C23semidirect
115. C2×Dic71⋊C4C23semidirect
124. C2×C22⋊Dic71C23semidirect
125. C2×C22⋊Dic71C23semidirect
145. C2×C4×Dic71C23semidirect
146. C2×C4×Dic71C23semidirect
147. C71⋊#95C23semidirect
148. C71⋊#95C23semidirect
149. C71⋊#95C23semidirect
162. C2×C4⋊C4×C71C23semidirect
169. C2×C22⋊C4×C71C23semidirect
170. C2×C22⋊C4×C71C23semidirect
171. #95×C71C23semidirect
241. C2×C4×D71C2×D4semidirect
490. C2×C71#2411semidirect
508. C2×#394D71semidirect
516. C71C2×#2411semidirect
534. C22×C4⋊C4C2×D71semidirect
552. C22×C22⋊C4C2×D71semidirect
553. C22×C22⋊C4C2×D71semidirect
559. #394C2×D71semidirect
570. C2×#95C2×D71semidirect
628. C2×C4⋊C4C22×D71semidirect
662. C2×C22⋊C4C22×D71semidirect
663. C2×C22⋊C4C22×D71semidirect
671. #95C22×D71semidirect
991. C2#22591718direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561102
C22×#145560962
C22×#145560862
C22×C22⋊C4×D712
#225917182
C2×#179859222
C2×#179859212
C2×#179859152
C2×#179859022
C2×#179858992
C2×#179858922
C2×#179858912
C2×#179858752
C2×#179858732
C2×#179858542
C2×#394×C712
C2×#241171