Finite Group Databasebeta

← C2×#22590996 #32156166

Subgroups — C2×#22590996 #32156166

Order 18176.

5094 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×#14556096C211yesmaximal, characteristic
2C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
3C22×C22⋊C4×D71C211yesmaximal, characteristic, complemented
4#22590996C2116yesmaximal, direct product factor
5C2×#17985902C211yesmaximal, characteristic, complemented
6C2×#17985899C211yesmaximal, characteristic, complemented
7C2×#17985891C211yesmaximal, characteristic, complemented
8C2×#17985888C211yesmaximal, characteristic, complemented
9C2×#17985887C211yesmaximal, characteristic, complemented
10C2×#17985887C211yesmaximal, characteristic, complemented
11C2×#17985878C211yesmaximal, characteristic, complemented
12C2×#17985875C211yesmaximal, characteristic, complemented
13C2×#17985873C211yesmaximal, characteristic, complemented
14C2×#17985854C211yesmaximal, characteristic, complemented
15C2×#17985846C211yesmaximal, characteristic, complemented
16C2×#386×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C22⋊D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C2×#14556096C4116yescomplemented
23C2×#14556096C2218yes—
24C2×C4×C22⋊D71—28no—
25C2×C4×C22⋊D71C2218yescomplemented
26C22×C4⋊Dic71C2211yescharacteristic, complemented
27C22×Dic71⋊C4C2211yescharacteristic, complemented
28C22×Dic71⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic71C2211yescharacteristic
30C22×C22⋊Dic71C2211yescharacteristic
31C22×C22⋊Dic71C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic, complemented
33C22×C22⋊Dic71C2211yescharacteristic, complemented
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×D71C2218yescomplemented
44C22×C4×Dic71C2211yescharacteristic, complemented
45C22×C4×Dic71C2211yescharacteristic, complemented
46C22×C4×Dic71C2211yescharacteristic, complemented
47#17985902C2218yescomplemented
48#17985899C2218yescomplemented
49#17985891C2218yescomplemented
50#17985888C2218yescomplemented
51#17985887C2218yescomplemented
52#17985887C2218yescomplemented
53#17985878C2218yescomplemented
54#17985875C2218yescomplemented
55#17985873C2218yescomplemented
56#17985854C2218yescomplemented
57#17985846C2218yescomplemented
58C2×C71⋊#95C2211yescharacteristic, complemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C23×D4×C71C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic, complemented
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic, complemented
67#386×C71C2218yescomplemented
68C2×#95×C71C2211yescharacteristic, complemented
69C2×#95×C71C2211yescharacteristic, complemented
70C24×D71—24no—
71C24×D71—24no—
72C24×D71—42no—
73C24×D71—42no—
74C24×D71—42no—
75C24×D71—42no—
76C24×D71C2×C418yescomplemented
77C24×D71C2311yescharacteristic
78C24×D71C2311yescharacteristic
79C24×D71C2314yes—
80C22×C22⋊D71—24no—
81C22×C22⋊D71—24no—
82C22×C22⋊D71—42no—
83C22×C22⋊D71—42no—
84C22×C22⋊D71C2×C418yes—
85C22×C22⋊D71C2×C418yescomplemented
86C22×C22⋊D71C2314yes—
87C22×C22⋊D71C2314yes—
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2311yescharacteristic
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C22×C4×D71—24no—
95C22×C4×D71—42no—
96C22×C4×D71—42no—
97C22×C4×D71—42no—
98C22×C4×D71—42no—
99C22×C4×D71D418yescomplemented
100C22×C4×D71C2314yes—
101C22×C4×D71C2314yes—
102#14556096C2×C4164yescomplemented
103C4×C22⋊D71—232no—
104C2×C4⋊Dic71—42no—
105C2×C4⋊Dic71C2314yescomplemented
106C2×Dic71⋊C4—24no—
107C2×Dic71⋊C4—42no—
108C2×Dic71⋊C4C2314yescomplemented
109C2×Dic71⋊C4C2314yescomplemented
110C2×C22⋊Dic71—24no—
111C2×C22⋊Dic71—24no—
112C2×C22⋊Dic71—42no—
113C2×C22⋊Dic71—42no—
114C2×C22⋊Dic71C2×C418yescomplemented
115C2×C22⋊Dic71C2314yes—
116C2×C22⋊Dic71C2314yes—
117C2×C22⋊Dic71C2314yes—
118C2×C22⋊Dic71C2314yescomplemented
119C2×C22⋊Dic71C2314yescomplemented
120C2×(C2×D71)⋊C4—24no—
121C2×(C2×D71)⋊C4—24no—
122C2×(C2×D71)⋊C4—24no—
123C2×(C2×D71)⋊C4—24no—
124C2×(C2×D71)⋊C4—42no—
125C2×(C2×D71)⋊C4—42no—
126C2×(C2×D71)⋊C4C2×C418yescomplemented
127C2×(C2×D71)⋊C4C2×C418yescomplemented
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—
137C2×C4×Dic71—24no—
138C2×C4×Dic71—42no—
139C2×C4×Dic71—42no—
140C2×C4×Dic71C2314yescomplemented
141C2×C4×Dic71C2314yescomplemented
142C2×C4×Dic71C2314yescomplemented
143C71⋊#95C2314yescomplemented
144C71⋊#95C2314yescomplemented
145C71⋊#95C2314yescomplemented
146C71⋊#95C2314yescomplemented
147C25×C71C2311yescharacteristic
148C25×C71C2311yescharacteristic
149C22×D4×C71—42no—
150C22×D4×C71—42no—
151C22×D4×C71C2×C418yescomplemented
152C22×D4×C71C2314yes—
153C23×C4×C71—24no—
154C23×C4×C71—42no—
155C23×C4×C71—42no—
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2314yescomplemented
162C2×C22⋊C4×C71—24no—
163C2×C22⋊C4×C71—42no—
164C2×C22⋊C4×C71—42no—
165C2×C22⋊C4×C71C2314yes—
166C2×C22⋊C4×C71C2314yes—
167C2×C22⋊C4×C71C2314yescomplemented
168#95×C71C2314yescomplemented
169#95×C71C2314yescomplemented
170C23×D71—22no—
171C23×D71—22no—
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—22no—
177C23×D71—22no—
178C23×D71—22no—
179C23×D71—22no—
180C23×D71—232no—
181C23×D71—28no—
182C23×D71—28no—
183C23×D71—416no—
184C23×D71—416no—
185C23×D71—44no—
186C23×D71—44no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71—416no—
190C23×D71—416no—
191C23×D71—416no—
192C23×D71—416no—
193C23×D71C22×C414yes—
194C23×D71C22×C414yes—
195C23×D71C22×C4116yescomplemented
196C23×D71C2×D414yes—
197C23×D71#4114yes—
198C23×D71C2412yes—
199C23×D71C2412yes—
200C2×C22⋊D71—232no—
201C2×C22⋊D71—28no—
202C2×C22⋊D71—28no—
203C2×C22⋊D71—416no—
204C2×C22⋊D71—44no—
205C2×C22⋊D71—44no—
206C2×C22⋊D71C22×C4116yes—
207C2×C22⋊D71C22×C4116yescomplemented
208C22×Dic71—22no—
209C22×Dic71—22no—
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×Dic71C22×C414yes—
224C22×Dic71C22×C414yes—
225C22×Dic71C2×D414yes—
226C22×Dic71C2412yes—
227C22×Dic71C2412yes—
228C22×Dic71C2412yes—
229C22×Dic71C2412yes—
230C22×Dic71C2412yes—
231C22×Dic71C2412yes—
232C2×C4×D71—28no—
233C2×C4×D71—416no—
234C2×C4×D71—44no—
235C2×C4×D71—44no—
236C2×C4×D71—44no—
237C2×C4×D71—44no—
238C2×C4×D71—416no—
239C2×C4×D71C2×D4116yescomplemented
240C4⋊Dic71—44no—
241Dic71⋊C4—28no—
242Dic71⋊C4—44no—
243C22⋊Dic71—28no—
244C22⋊Dic71—28no—
245C22⋊Dic71—44no—
246C22⋊Dic71—44no—
247C22⋊Dic71C22×C4116yescomplemented
248(C2×D71)⋊C4—28no—
249(C2×D71)⋊C4—28no—
250(C2×D71)⋊C4—28no—
251(C2×D71)⋊C4—28no—
252(C2×D71)⋊C4—44no—
253(C2×D71)⋊C4—44no—
254(C2×D71)⋊C4C22×C4116yescomplemented
255(C2×D71)⋊C4C22×C4116yescomplemented
256C4×Dic71—28no—
257C4×Dic71—44no—
258C4×Dic71—44no—
259C24×C71—22no—
260C24×C71—22no—
261C24×C71—22no—
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×C71C22×C414yes—
272C24×C71C22×C414yes—
273C24×C71C2412yes—
274C24×C71C2412yes—
275C24×C71C2411yescharacteristic
276C2×D4×C71—416no—
277C2×D4×C71—44no—
278C2×D4×C71—44no—
279C2×D4×C71C22×C4116yescomplemented
280C22×C4×C71—22no—
281C22×C4×C71—22no—
282C22×C4×C71—22no—
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—28no—
294C22×C4×C71—44no—
295C22×C4×C71—44no—
296C22×C4×C71—416no—
297C22×C4×C71C22×C414yes—
298C22×C4×C71C2×D414yes—
299C22×C4×C71C2412yes—
300C22×C4×C71C2412yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C22⋊C4×C71—28no—
305C22⋊C4×C71—44no—
306C22⋊C4×C71—44no—
307C23×C71—28no—
308C23×C71—28no—
309C23×C71—28no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—28no—
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—22no—
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×C71C23×C414yes—
334C23×C71C23×C414yes—
335C23×C71C23×C412yes—
336C23×C71C22×D412yes—
337C23×C71C2×#4112yes—
338C23×C71H(5,𝔽2)12yes—
339C23×C71H(5,𝔽2)12yes—
340C23×C71H(5,𝔽2)12yes—
341C23×C71H(5,𝔽2)12yes—
342C23×C71C2511yescharacteristic
343C22×D71—28no—
344C22×D71—28no—
345C22×D71—28no—
346C22×D71—28no—
347C22×D71—28no—
348C22×D71—28no—
349C22×D71—22no—
350C22×D71—22no—
351C22×D71—22no—
352C22×D71—22no—
353C22×D71—28no—
354C22×D71—28no—
355C22×D71—28no—
356C22×D71—22no—
357C22×D71—22no—
358C22×D71—22no—
359C22×D71—22no—
360C22×D71—22no—
361C22×D71—22no—
362C22×D71—232no—
363C22×D71—416no—
364C22×D71—416no—
365C22×D71—4128no—
366C22×D71—416no—
367C22×D71—416no—
368C22×D71—416no—
369C22×D71—416no—
370C22×D71—44no—
371C22×D71—44no—
372C22×D71—44no—
373C22×D71—44no—
374C22×D71C4×D4116yes—
375C22×D71C23×C414yes—
376C22×D71C23×C414yes—
377C22×D71C22×D414yes—
378C22×D71C2×#4114yes—
379D4×C71—416no—
380C2×C4×C71—28no—
381C2×C4×C71—28no—
382C2×C4×C71—22no—
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—416no—
396C2×C4×C71—44no—
397C2×C4×C71—44no—
398C2×C4×C71—44no—
399C2×C4×C71C23×C414yes—
400C2×C4×C71C22×D414yes—
401C22⋊D71—232no—
402C22⋊D71—416no—
403C2×Dic71—28no—
404C2×Dic71—28no—
405C2×Dic71—28no—
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×Dic71C23×C414yes—
425C2×Dic71C23×C414yes—
426C2×Dic71C22×D414yes—
427C4×D71—416no—
428C4×D71—416no—
429C22×C71—24no—
430C22×C71—24no—
431C22×C71—24no—
432C22×C71—24no—
433C22×C71—24no—
434C22×C71—24no—
435C22×C71—416no—
436C22×C71—416no—
437C22×C71—42no—
438C22×C71—42no—
439C22×C71—42no—
440C22×C71—42no—
441C22×C71—42no—
442C22×C71—42no—
443C22×C71—42no—
444C22×C71—42no—
445C22×C71C2×C4×D414yes—
446C22×C71#51814yes—
447C22×C71#51814yes—
448C22×C71#53414yes—
449C22×C71#53514yes—
450C22×C71#53814yes—
451C22×C71#53814yes—
452C22×C71C24×C411yescharacteristic
453C22×C71C23×D411yescharacteristic
454C22×C71C22×#4111yescharacteristic
455C22×C71C2×H(5,𝔽2)11yescharacteristic
456C22×C71C2×H(5,𝔽2)11yescharacteristic
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—416no—
471C2×D71—42no—
472C2×D71—42no—
473C2×D71—42no—
474C2×D71—42no—
475C2×D71C2×C4×D418yes—
476C4×C71—24no—
477C4×C71—24no—
478C4×C71—42no—
479C4×C71—42no—
480C4×C71—42no—
481Dic71—24no—
482Dic71—24no—
483Dic71—24no—
484Dic71—42no—
485Dic71—42no—
486Dic71—42no—
487C2×#2321—711nomaximal, Sylow
488C2×C71—44no—
489C2×C71—44no—
490C2×C71#232118yescomplemented
491C2×C71C22×C4×D411yescharacteristic
492C2×C71C2×#51811yescharacteristic
493C2×C71C2×#51811yescharacteristic
494C2×C71C2×#53411yescharacteristic
495C2×C71C2×#53511yescharacteristic
496C2×C71C2×#53811yescharacteristic
497C2×C71C2×#53811yescharacteristic
498D71—28no—
499D71—44no—
500C22×#120—711no—
501C22×C4×D4—711no—
502C23×C22⋊C4—711no—
503#2321—7116no—
504C2×#390—711no—
505C2×#390—711no—
506C2×#388—711no—
507C2×#388—711no—
508C2×#388—711no—
509C2×#388—711no—
510C2×#386—711no—
511C2×#386—711no—
512C2×#386D7111yescharacteristic, complemented
513C2×#385—711no—
514C2×#379—711no—
515C2×C4×C22⋊C4—711no—
516C71C2×#232111yescharacteristic, complemented, Sylow
517C26—711no—
518C23×D4—711no—
519C23×D4—711no—
520C23×D4C2×D7111yescharacteristic
521C24×C4—711no—
522C24×C4—711no—
523C24×C4C2×D7111yescharacteristic, complemented
524C2×#120—7116no—
525C2×#120—718no—
526C2×C4×D4—718no—
527C2×C4×D4—1428no—
528C22×C4⋊C4—711no—
529C22×C4⋊C4—711no—
530C22×C4⋊C4—711no—
531C22×C22⋊C4—711no—
532C22×C22⋊C4—711no—
533C22×C22⋊C4—711no—
534C22×C22⋊C4—711no—
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—718no—
545C22×C22⋊C4—1428no—
546C22×C22⋊C4C2×D7111yescharacteristic
547C22×C22⋊C4C2×D7111yescharacteristic
548C22×C22⋊C4C2×D7111yescharacteristic, complemented
549C22×C42—711no—
550C22×C42—711no—
551C22×C42—711no—
552#390—718no—
553#390—718no—
554#388—718no—
555#388—718no—
556#388—718no—
557#388—718no—
558#386—718no—
559#386—718no—
560#386C2×D7118yescomplemented
561#385—718no—
562#379—718no—
563C4×C22⋊C4—718no—
564C2×#95—711no—
565C2×#95—711no—
566C2×#95—711no—
567C2×#95—711no—
568C2×#95C2×D7111yescharacteristic, complemented
569C2×#95C2×D7111yescharacteristic, complemented
570C25—2842no—
571C25—2842no—
572C25—2842no—
573C25—2842no—
574C25—718no—
575C25—714no—
576C25—711no—
577C25—711no—
578C25—1424no—
579C25—1424no—
580C25C22×D7111yescharacteristic
581C25C22×D7111yescharacteristic
582C22×D4—42no—
583C22×D4—42no—
584C22×D4—2842no—
585C22×D4—2842no—
586C22×D4—718no—
587C22×D4—714no—
588C22×D4—718no—
589C22×D4—714no—
590C22×D4—1424no—
591C22×D4—1424no—
592C22×D4C4×D7118yescomplemented
593C22×D4C22×D7114yes—
594C23×C4—24no—
595C23×C4—42no—
596C23×C4—42no—
597C23×C4—2842no—
598C23×C4—2842no—
599C23×C4—2842no—
600C23×C4—2842no—
601C23×C4—718no—
602C23×C4—714no—
603C23×C4—714no—
604C23×C4—711no—
605C23×C4—711no—
606C23×C4—711no—
607C23×C4—711no—
608C23×C4—711no—
609C23×C4—711no—
610C23×C4—1424no—
611C23×C4C22×D7111yescharacteristic
612C23×C4C22×D7111yescharacteristic
613C23×C4C22×D7111yescharacteristic
614C23×C4C22×D7111yescharacteristic
615C23×C4C22×D7111yescharacteristic
616C23×C4C22×D7114yescomplemented
617#120—7164no—
618C4×D4—14232no—
619C2×C4⋊C4—2842no—
620C2×C4⋊C4—2842no—
621C2×C4⋊C4—714no—
622C2×C4⋊C4—714no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—1424no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—42no—
627C2×C22⋊C4—42no—
628C2×C22⋊C4—2842no—
629C2×C22⋊C4—2842no—
630C2×C22⋊C4—2842no—
631C2×C22⋊C4—2842no—
632C2×C22⋊C4—714no—
633C2×C22⋊C4—714no—
634C2×C22⋊C4—714no—
635C2×C22⋊C4—714no—
636C2×C22⋊C4—718no—
637C2×C22⋊C4—714no—
638C2×C22⋊C4—718no—
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—14232no—
649C2×C22⋊C4—1424no—
650C2×C22⋊C4—1424no—
651C2×C22⋊C4—1424no—
652C2×C22⋊C4—1424no—
653C2×C22⋊C4—1424no—
654C2×C22⋊C4—1424no—
655C2×C22⋊C4C22×D7114yes—
656C2×C22⋊C4C22×D7114yes—
657C2×C22⋊C4C22×D7114yescomplemented
658C2×C42—2842no—
659C2×C42—2842no—
660C2×C42—714no—
661C2×C42—714no—
662C2×C42—714no—
663C2×C42—1424no—
664#95—714no—
665#95—714no—
666#95—714no—
667#95—714no—
668#95C22×D7114yescomplemented
669#95C22×D7114yescomplemented
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—2844no—
683C24—2844no—
684C24—2844no—
685C24—2844no—
686C24—28416no—
687C24—28416no—
688C24—28416no—
689C24—28416no—
690C24—28416no—
691C24—28416no—
692C24—7116no—
693C24—714no—
694C24—714no—
695C24—714no—
696C24—712no—
697C24—714no—
698C24—712no—
699C24—1428no—
700C24—1428no—
701C24—14232no—
702C24—1422no—
703C24—1422no—
704C24—1422no—
705C24—1422no—
706C24—1422no—
707C24—1422no—
708C24—1422no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24C2×C4×D7114yes—
713C24C2×C4×D7114yes—
714C24C23×D7112yes—
715C24C23×D7112yes—
716C24C23×D7111yescharacteristic
717C2×D4—416no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—2844no—
721C2×D4—2844no—
722C2×D4—28416no—
723C2×D4—7116no—
724C2×D4—7116no—
725C2×D4—1428no—
726C2×D4—1428no—
727C2×D4—14232no—
728C2×D4C2×C4×D71116yescomplemented
729C22×C4—22no—
730C22×C4—22no—
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—28no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—416no—
746C22×C4—2844no—
747C22×C4—2844no—
748C22×C4—28416no—
749C22×C4—2844no—
750C22×C4—2844no—
751C22×C4—28416no—
752C22×C4—7116no—
753C22×C4—714no—
754C22×C4—714no—
755C22×C4—714no—
756C22×C4—712no—
757C22×C4—712no—
758C22×C4—712no—
759C22×C4—712no—
760C22×C4—712no—
761C22×C4—712no—
762C22×C4—1428no—
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×C4—1422no—
777C22×C4—1422no—
778C22×C4C2×C4×D7114yes—
779C22×C4D4×D7114yes—
780C22×C4C23×D7112yes—
781C22×C4C23×D7112yes—
782C22×C4C23×D7112yes—
783C22×C4C23×D7112yes—
784C22×C4C23×D7112yes—
785C4⋊C4—2844no—
786C4⋊C4—2844no—
787C4⋊C4—1428no—
788C22⋊C4—28no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—2844no—
792C22⋊C4—2844no—
793C22⋊C4—2844no—
794C22⋊C4—2844no—
795C22⋊C4—7116no—
796C22⋊C4—7116no—
797C22⋊C4—7116no—
798C22⋊C4—1428no—
799C22⋊C4—1428no—
800C22⋊C4—1428no—
801C22⋊C4—1428no—
802C22⋊C4—1428no—
803C22⋊C4—1428no—
804C42—2844no—
805C42—2844no—
806C42—1428no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—28no—
820C23—28no—
821C23—28no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—28416no—
834C23—28416no—
835C23—284128no—
836C23—28416no—
837C23—28416no—
838C23—28416no—
839C23—28416no—
840C23—2844no—
841C23—2844no—
842C23—2844no—
843C23—2844no—
844C23—714no—
845C23—714no—
846C23—714no—
847C23—7116no—
848C23—714no—
849C23—14232no—
850C23—1422no—
851C23—1422no—
852C23—1422no—
853C23—1422no—
854C23—1422no—
855C23—1422no—
856C23—1428no—
857C23—1428no—
858C23—1428no—
859C23—1428no—
860C23—1422no—
861C23—1422no—
862C23—1422no—
863C23—1422no—
864C23—1428no—
865C23—1428no—
866C23—1428no—
867C23—1428no—
868C23—1428no—
869C23C22×C4×D7114yes—
870C23C22×C4×D7114yes—
871C23C22×C4×D7112yes—
872C23C2×D4×D7112yes—
873C23#41×D7112yes—
874C23#1455617312yes—
875C23#1455617312yes—
876C23#1455617312yes—
877C23#1455617412yes—
878C23C24×D7111yescharacteristic
879D4—416no—
880D4—28416no—
881D4—14232no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—22no—
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—416no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—28416no—
902C2×C4—28416no—
903C2×C4—2844no—
904C2×C4—2844no—
905C2×C4—2844no—
906C2×C4—714no—
907C2×C4—714no—
908C2×C4—714no—
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—1428no—
925C2×C4—1428no—
926C2×C4—1428no—
927C2×C4C22×C4×D7114yes—
928C2×C4C2×D4×D7114yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—24no—
935C22—416no—
936C22—416no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—28464no—
946C22—28416no—
947C22—2842no—
948C22—2842no—
949C22—2842no—
950C22—2842no—
951C22—718no—
952C22—1424no—
953C22—1424no—
954C22—1424no—
955C22—14232no—
956C22—1424no—
957C22—1424no—
958C22—1424no—
959C22—1424no—
960C22—1424no—
961C22—1424no—
962C22C4×D4×D7114yes—
963C22#1798647114yes—
964C22#1798647214yes—
965C22#1798655914yes—
966C22#1798656514yes—
967C22#1798658114yes—
968C22#1798658514yes—
969C22C23×C4×D7111yescharacteristic
970C22C22×D4×D7111yescharacteristic
971C22C2×#41×D7111yescharacteristic
972C22C2×#1455617311yescharacteristic
973C22C2×#1455617311yescharacteristic
974C22C2×#1455617311yescharacteristic
975C22C2×#1455617411yescharacteristic
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—2842no—
982C4—2842no—
983C4—2842no—
984C4—1424no—
985C4—1424no—
986C4—1424no—
987C2—44no—
988C2—44no—
989C2—2844no—
990C2—1428no—
991C2#2259099618yesdirect product factor
992C2C2×C4×D4×D7111yescharacteristic
993C2C2×#1798647111yescharacteristic
994C2C2×#1798647211yescharacteristic
995C2C2×#1798655911yescharacteristic
996C2C2×#1798656511yescharacteristic
997C2C2×#1798658111yescharacteristic
998C2C2×#1798658511yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#386×C71C2
socleC24×C71C24
prime radicalC22×#14556096C2
cosocleC23×C71C25
hypercenterC2×#386D71
hypocenterC71C2×#2321
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D71C2semidirect
3. C22×C22⋊C4×D71C2semidirect
4. #22590996C2direct (N × H)
5. C2×#17985902C2semidirect
6. C2×#17985899C2semidirect
7. C2×#17985891C2semidirect
8. C2×#17985888C2semidirect
9. C2×#17985887C2semidirect
10. C2×#17985887C2semidirect
11. C2×#17985878C2semidirect
12. C2×#17985875C2semidirect
13. C2×#17985873C2semidirect
14. C2×#17985854C2semidirect
15. C2×#17985846C2semidirect
16. C2×#386×C71C2semidirect
22. C2×#14556096C4semidirect
25. C2×C4×C22⋊D71C22semidirect
26. C22×C4⋊Dic71C22semidirect
27. C22×Dic71⋊C4C22semidirect
28. C22×Dic71⋊C4C22semidirect
32. C22×C22⋊Dic71C22semidirect
33. C22×C22⋊Dic71C22semidirect
43. C2×C22⋊C4×D71C22semidirect
44. C22×C4×Dic71C22semidirect
45. C22×C4×Dic71C22semidirect
46. C22×C4×Dic71C22semidirect
47. #17985902C22semidirect
48. #17985899C22semidirect
49. #17985891C22semidirect
50. #17985888C22semidirect
51. #17985887C22semidirect
52. #17985887C22semidirect
53. #17985878C22semidirect
54. #17985875C22semidirect
55. #17985873C22semidirect
56. #17985854C22semidirect
57. #17985846C22semidirect
58. C2×C71⋊#95C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
63. C24×C4×C71C22semidirect
66. C22×C22⋊C4×C71C22semidirect
67. #386×C71C22semidirect
68. C2×#95×C71C22semidirect
69. C2×#95×C71C22semidirect
76. C24×D71C2×C4semidirect
85. C22×C22⋊D71C2×C4semidirect
99. C22×C4×D71D4semidirect
102. #14556096C2×C4semidirect
105. C2×C4⋊Dic71C23semidirect
108. C2×Dic71⋊C4C23semidirect
109. C2×Dic71⋊C4C23semidirect
114. C2×C22⋊Dic71C2×C4semidirect
118. C2×C22⋊Dic71C23semidirect
119. C2×C22⋊Dic71C23semidirect
126. C2×(C2×D71)⋊C4C2×C4semidirect
127. C2×(C2×D71)⋊C4C2×C4semidirect
140. C2×C4×Dic71C23semidirect
141. C2×C4×Dic71C23semidirect
142. C2×C4×Dic71C23semidirect
143. C71⋊#95C23semidirect
144. C71⋊#95C23semidirect
145. C71⋊#95C23semidirect
146. C71⋊#95C23semidirect
151. C22×D4×C71C2×C4semidirect
161. C23×C4×C71C23semidirect
167. C2×C22⋊C4×C71C23semidirect
168. #95×C71C23semidirect
169. #95×C71C23semidirect
195. C23×D71C22×C4semidirect
207. C2×C22⋊D71C22×C4semidirect
239. C2×C4×D71C2×D4semidirect
247. C22⋊Dic71C22×C4semidirect
254. (C2×D71)⋊C4C22×C4semidirect
255. (C2×D71)⋊C4C22×C4semidirect
279. C2×D4×C71C22×C4semidirect
490. C2×C71#2321semidirect
512. C2×#386D71semidirect
516. C71C2×#2321semidirect
523. C24×C4C2×D71semidirect
548. C22×C22⋊C4C2×D71semidirect
560. #386C2×D71semidirect
568. C2×#95C2×D71semidirect
569. C2×#95C2×D71semidirect
592. C22×D4C4×D71semidirect
616. C23×C4C22×D71semidirect
657. C2×C22⋊C4C22×D71semidirect
668. #95C22×D71semidirect
669. #95C22×D71semidirect
728. C2×D4C2×C4×D71semidirect
991. C2#22590996direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145560962
C22×C4×C22⋊D712
C22×C22⋊C4×D712
#225909962
C2×#179859022
C2×#179858992
C2×#179858912
C2×#179858882
C2×#179858872
C2×#179858782
C2×#179858752
C2×#179858732
C2×#179858542
C2×#179858462
C2×#386×C712
C2×#232171