Finite Group Databasebeta

← C2×#22591722 #32166068

Subgroups — C2×#22591722 #32166068

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×#14556085C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D71C211yesmaximal, characteristic, complemented
5#22591722C2116yesmaximal, direct product factor
6C2×#17985922C211yesmaximal, characteristic, complemented
7C2×#17985921C211yesmaximal, characteristic, complemented
8C2×#17985914C211yesmaximal, characteristic, complemented
9C2×#17985913C211yesmaximal, characteristic, complemented
10C2×#17985899C211yesmaximal, characteristic, complemented
11C2×#17985893C211yesmaximal, characteristic, complemented
12C2×#17985890C211yesmaximal, characteristic, complemented
13C2×#17985875C211yesmaximal, characteristic, complemented
14C2×#17985870C211yesmaximal, characteristic, complemented
15C2×#17985854C211yesmaximal, characteristic, complemented
16C2×#390×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×#14556085—28no—
27C2×#14556085C2218yescomplemented
28C22×C4⋊Dic71C2211yescharacteristic, complemented
29C22×Dic71⋊C4C2211yescharacteristic, complemented
30C22×Dic71⋊C4C2211yescharacteristic, 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
49#17985922C2218yescomplemented
50#17985921C2218yescomplemented
51#17985914C2218yescomplemented
52#17985913C2218yescomplemented
53#17985899C2218yescomplemented
54#17985893C2218yescomplemented
55#17985890C2218yescomplemented
56#17985875C2218yescomplemented
57#17985870C2218yescomplemented
58#17985854C2218yescomplemented
59C2×C71⋊#95C2211yescharacteristic, complemented
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
69C22×C42×C71C2211yescharacteristic, complemented
70#390×C71C2218yescomplemented
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#14556085—232no—
106C2×C4⋊Dic71—24no—
107C2×C4⋊Dic71C2314yescomplemented
108C2×Dic71⋊C4—24no—
109C2×Dic71⋊C4—24no—
110C2×Dic71⋊C4—24no—
111C2×Dic71⋊C4—42no—
112C2×Dic71⋊C4C2314yescomplemented
113C2×Dic71⋊C4C2314yescomplemented
114C2×Dic71⋊C4C2314yescomplemented
115C2×Dic71⋊C4C2314yescomplemented
116C2×C22⋊Dic71—24no—
117C2×C22⋊Dic71—24no—
118C2×C22⋊Dic71—24no—
119C2×C22⋊Dic71—24no—
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×Dic71C2314yescomplemented
145C71⋊#95C2314yescomplemented
146C71⋊#95C2314yescomplemented
147C71⋊#95C2314yescomplemented
148C71⋊#95C2314yescomplemented
149C25×C71C2311yescharacteristic
150C25×C71C2311yescharacteristic
151C22×D4×C71—24no—
152C22×D4×C71—24no—
153C22×D4×C71—42no—
154C22×D4×C71C2314yes—
155C23×C4×C71C2311yescharacteristic
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C2×C4⋊C4×C71—42no—
161C2×C4⋊C4×C71C2314yescomplemented
162C2×C22⋊C4×C71—24no—
163C2×C22⋊C4×C71—24no—
164C2×C22⋊C4×C71—42no—
165C2×C22⋊C4×C71—42no—
166C2×C22⋊C4×C71C2314yes—
167C2×C22⋊C4×C71C2314yes—
168C2×C22⋊C4×C71C2314yescomplemented
169C2×C22⋊C4×C71C2314yescomplemented
170C2×C42×C71—24no—
171C2×C42×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—
243Dic71⋊C4—28no—
244Dic71⋊C4—28no—
245Dic71⋊C4—28no—
246Dic71⋊C4—44no—
247C22⋊Dic71—28no—
248C22⋊Dic71—28no—
249C22⋊Dic71—28no—
250C22⋊Dic71—28no—
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—
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×C71—22no—
272C24×C71—22no—
273C24×C71—22no—
274C24×C71#4114yes—
275C24×C71C2412yes—
276C24×C71C2412yes—
277C24×C71C2411yescharacteristic
278C2×D4×C71—28no—
279C2×D4×C71—28no—
280C2×D4×C71—44no—
281C2×D4×C71—416no—
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—22no—
294C22×C4×C71—22no—
295C22×C4×C71C2×D414yes—
296C22×C4×C71C2×D414yes—
297C22×C4×C71C2412yes—
298C22×C4×C71C2412yes—
299C22×C4×C71C2412yes—
300C22×C4×C71C2412yes—
301C22×C4×C71C2412yes—
302C4⋊C4×C71—44no—
303C22⋊C4×C71—28no—
304C22⋊C4×C71—28no—
305C22⋊C4×C71—44no—
306C22⋊C4×C71—44no—
307C42×C71—28no—
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×#394—711no—
509C2×#390—711no—
510C2×#390D7111yescharacteristic, complemented
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×C42C2×D7111yescharacteristic, complemented
556#396—718no—
557#396—718no—
558#394—718no—
559#394—718no—
560#390—718no—
561#390C2×D7118yescomplemented
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×#95—711no—
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—42no—
618C2×C4⋊C4—2842no—
619C2×C4⋊C4—714no—
620C2×C4⋊C4—714no—
621C2×C4⋊C4—714no—
622C2×C4⋊C4—714no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—1424no—
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—42no—
632C2×C22⋊C4—42no—
633C2×C22⋊C4—2842no—
634C2×C22⋊C4—2842no—
635C2×C22⋊C4—714no—
636C2×C22⋊C4—714no—
637C2×C22⋊C4—718no—
638C2×C22⋊C4—714no—
639C2×C22⋊C4—714no—
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—14232no—
650C2×C22⋊C4—1424no—
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—24no—
665C2×C42—714no—
666C2×C42—1424no—
667C2×C42C22×D7114yescomplemented
668#95—714no—
669#95—714no—
670#95—714no—
671#95—714no—
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#1176586514yes—
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—44no—
784C4⋊C4—2844no—
785C4⋊C4—1428no—
786C4⋊C4—1428no—
787C4⋊C4—1428no—
788C4⋊C4—1428no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—2844no—
794C22⋊C4—2844no—
795C22⋊C4—7116no—
796C22⋊C4—1428no—
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—28no—
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×#1176586514yes—
876C23C2×#1176586512yes—
877C23#1455617312yes—
878C23#1455617312yes—
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#1798650814yes—
964C22#1798656214yes—
965C22#1798663914yes—
966C22#1798664614yes—
967C22#1798667814yes—
968C22#1798667914yes—
969C22C22×D4×D7111yescharacteristic
970C22C22×D4×D7111yescharacteristic
971C22C2×#41×D7111yescharacteristic
972C22C2×#41×D7111yescharacteristic
973C22C22×#1176586511yescharacteristic
974C22C2×#1455617311yescharacteristic
975C22C2×#1455617311yescharacteristic
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#2259172218yesdirect product factor
992C2C2×#121×D7111yescharacteristic
993C2C2×#1798650811yescharacteristic
994C2C2×#1798656211yescharacteristic
995C2C2×#1798663911yescharacteristic
996C2C2×#1798664611yescharacteristic
997C2C2×#1798667811yescharacteristic
998C2C2×#1798667911yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#390×C71C2
socleC24×C71C24
prime radicalC22×#14556096C2
hypercenterC2×#390D71
hypocenterC71C2×#2411
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#14556110C2semidirect
3. C22×#14556085C2semidirect
4. C22×C22⋊C4×D71C2semidirect
5. #22591722C2direct (N × H)
6. C2×#17985922C2semidirect
7. C2×#17985921C2semidirect
8. C2×#17985914C2semidirect
9. C2×#17985913C2semidirect
10. C2×#17985899C2semidirect
11. C2×#17985893C2semidirect
12. C2×#17985890C2semidirect
13. C2×#17985875C2semidirect
14. C2×#17985870C2semidirect
15. C2×#17985854C2semidirect
16. C2×#390×C71C2semidirect
23. C2×#14556110C22semidirect
27. C2×#14556085C22semidirect
28. C22×C4⋊Dic71C22semidirect
29. C22×Dic71⋊C4C22semidirect
30. C22×Dic71⋊C4C22semidirect
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. #17985922C22semidirect
50. #17985921C22semidirect
51. #17985914C22semidirect
52. #17985913C22semidirect
53. #17985899C22semidirect
54. #17985893C22semidirect
55. #17985890C22semidirect
56. #17985875C22semidirect
57. #17985870C22semidirect
58. #17985854C22semidirect
59. C2×C71⋊#95C22semidirect
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. C22×C42×C71C22semidirect
70. #390×C71C22semidirect
100. C22×C4×D71D4semidirect
107. C2×C4⋊Dic71C23semidirect
112. C2×Dic71⋊C4C23semidirect
113. C2×Dic71⋊C4C23semidirect
114. C2×Dic71⋊C4C23semidirect
115. C2×Dic71⋊C4C23semidirect
124. C2×C22⋊Dic71C23semidirect
125. C2×C22⋊Dic71C23semidirect
144. C2×C4×Dic71C23semidirect
145. C71⋊#95C23semidirect
146. C71⋊#95C23semidirect
147. C71⋊#95C23semidirect
148. C71⋊#95C23semidirect
161. C2×C4⋊C4×C71C23semidirect
168. C2×C22⋊C4×C71C23semidirect
169. C2×C22⋊C4×C71C23semidirect
171. C2×C42×C71C23semidirect
241. C2×C4×D71C2×D4semidirect
490. C2×C71#2411semidirect
510. C2×#390D71semidirect
516. C71C2×#2411semidirect
534. C22×C4⋊C4C2×D71semidirect
552. C22×C22⋊C4C2×D71semidirect
553. C22×C22⋊C4C2×D71semidirect
555. C22×C42C2×D71semidirect
561. #390C2×D71semidirect
628. C2×C4⋊C4C22×D71semidirect
662. C2×C22⋊C4C22×D71semidirect
663. C2×C22⋊C4C22×D71semidirect
667. C2×C42C22×D71semidirect
991. C2#22591722direct (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×#145560852
C22×C22⋊C4×D712
#225917222
C2×#179859222
C2×#179859212
C2×#179859142
C2×#179859132
C2×#179858992
C2×#179858932
C2×#179858902
C2×#179858752
C2×#179858702
C2×#179858542
C2×#390×C712
C2×#241171