Finite Group Databasebeta

← C2×#22593228 #32167459

Subgroups — C2×#22593228 #32167459

Order 18176.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic, complemented
2C22×#14556096C211yesmaximal, characteristic
3C22×C4×C22⋊D71C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D71C211yesmaximal, characteristic, complemented
5#22593228C2116yesmaximal, direct product factor
6C2×#17985923C211yesmaximal, characteristic, complemented
7C2×#17985922C211yesmaximal, characteristic, complemented
8C2×#17985914C211yesmaximal, characteristic, complemented
9C2×#17985913C211yesmaximal, characteristic, complemented
10C2×#17985891C211yesmaximal, characteristic, complemented
11C2×#17985887C211yesmaximal, characteristic, complemented
12C2×#17985878C211yesmaximal, characteristic, complemented
13C2×#17985861C211yesmaximal, characteristic, complemented
14C2×#17985858C211yesmaximal, characteristic, complemented
15C2×#17985854C211yesmaximal, characteristic, complemented
16C2×#386×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×C4×C22⋊D71—28no—
27C2×C4×C22⋊D71C2218yescomplemented
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#17985923C2218yescomplemented
50#17985922C2218yescomplemented
51#17985914C2218yescomplemented
52#17985913C2218yescomplemented
53#17985891C2218yescomplemented
54#17985887C2218yescomplemented
55#17985878C2218yescomplemented
56#17985861C2218yescomplemented
57#17985858C2218yescomplemented
58#17985854C2218yescomplemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C2×C71⋊#95C2211yescharacteristic, complemented
63C23×D4×C71C2211yescharacteristic
64C24×C4×C71C2211yescharacteristic, complemented
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic, complemented
68#386×C71C2218yescomplemented
69C2×#95×C71C2211yescharacteristic, complemented
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—42no—
86C22×C22⋊D71D418yes—
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—
105C4×C22⋊D71—232no—
106C2×C4⋊Dic71—24no—
107C2×C4⋊Dic71C2314yescomplemented
108C2×Dic71⋊C4—24no—
109C2×Dic71⋊C4—24no—
110C2×Dic71⋊C4—42no—
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—24no—
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—24no—
133C2×(C2×D71)⋊C4—42no—
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×C71—24no—
156C23×C4×C71—42no—
157C23×C4×C71—42no—
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C23×C4×C71C2311yescharacteristic
163C23×C4×C71C2314yescomplemented
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
170#95×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—232no—
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⋊D71C2×D4116yes—
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—28no—
235C2×C4×D71—28no—
236C2×C4×D71—28no—
237C2×C4×D71—416no—
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—44no—
246Dic71⋊C4—44no—
247C22⋊Dic71—28no—
248C22⋊Dic71—28no—
249C22⋊Dic71—28no—
250C22⋊Dic71—28no—
251C22⋊Dic71—28no—
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—28no—
259(C2×D71)⋊C4—44no—
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×C71C2×D414yes—
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×C71—22no—
296C22×C4×C71—28no—
297C22×C4×C71—44no—
298C22×C4×C71—44no—
299C22×C4×C71—416no—
300C22×C4×C71C2×D414yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C22×C4×C71C2412yes—
305C22×C4×C71C2412yes—
306C22⋊C4×C71—28no—
307C22⋊C4×C71—28no—
308C22⋊C4×C71—44no—
309C23×C71—28no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—28no—
313C23×C71—28no—
314C23×C71—28no—
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—22no—
326C23×C71—22no—
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×D414yes—
336C23×C71C22×D412yes—
337C23×C71C22×D412yes—
338C23×C71C2×#4112yes—
339C23×C71C2×#4112yes—
340C23×C71C2×#4114yes—
341C23×C71C2×#4112yes—
342C23×C71H(5,𝔽2)12yes—
343C23×C71H(5,𝔽2)12yes—
344C23×C71C2511yescharacteristic
345C22×D71—28no—
346C22×D71—28no—
347C22×D71—28no—
348C22×D71—28no—
349C22×D71—28no—
350C22×D71—28no—
351C22×D71—22no—
352C22×D71—22no—
353C22×D71—22no—
354C22×D71—22no—
355C22×D71—232no—
356C22×D71—28no—
357C22×D71—28no—
358C22×D71—28no—
359C22×D71—22no—
360C22×D71—22no—
361C22×D71—22no—
362C22×D71—22no—
363C22×D71—22no—
364C22×D71—22no—
365C22×D71—416no—
366C22×D71—416no—
367C22×D71—416no—
368C22×D71—416no—
369C22×D71—416no—
370C22×D71—4128no—
371C22×D71—44no—
372C22×D71—44no—
373C22×D71—44no—
374C22×D71—44no—
375C22×D71—416no—
376C22×D71#121116yes—
377C22×D71C22×D414yes—
378C22×D71C22×D414yes—
379C22×D71C2×#4114yes—
380C22×D71C2×#4114yes—
381D4×C71—416no—
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—22no—
397C2×C4×C71—416no—
398C2×C4×C71—44no—
399C2×C4×C71—44no—
400C2×C4×C71—44no—
401C2×C4×C71—44no—
402C2×C4×C71C22×D414yes—
403C22⋊D71—232no—
404C22⋊D71—416no—
405C2×Dic71—28no—
406C2×Dic71—28no—
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—22no—
422C2×Dic71—22no—
423C2×Dic71—44no—
424C2×Dic71—44no—
425C2×Dic71—44no—
426C2×Dic71—44no—
427C2×Dic71C22×D414yes—
428C2×Dic71C22×D414yes—
429C4×D71—416no—
430C4×D71—416no—
431C22×C71—24no—
432C22×C71—24no—
433C22×C71—24no—
434C22×C71—24no—
435C22×C71—24no—
436C22×C71—24no—
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×C71—416no—
446C22×C71—416no—
447C22×C71C2×#12114yes—
448C22×C71#52514yes—
449C22×C71#53414yes—
450C22×C71#54614yes—
451C22×C71#54614yes—
452C22×C71#55114yes—
453C22×C71#55114yes—
454C22×C71C23×D411yescharacteristic
455C22×C71C23×D411yescharacteristic
456C22×C71C22×#4111yescharacteristic
457C22×C71C22×#4111yescharacteristic
458C22×C71C22×#4111yescharacteristic
459C22×C71C2×H(5,𝔽2)11yescharacteristic
460C22×C71C2×H(5,𝔽2)11yescharacteristic
461C2×D71—24no—
462C2×D71—24no—
463C2×D71—24no—
464C2×D71—24no—
465C2×D71—24no—
466C2×D71—24no—
467C2×D71—232no—
468C2×D71—24no—
469C2×D71—24no—
470C2×D71—24no—
471C2×D71—464no—
472C2×D71—42no—
473C2×D71—42no—
474C2×D71—42no—
475C2×D71—42no—
476C2×D71—416no—
477C2×D71C2×#12118yes—
478C4×C71—24no—
479C4×C71—42no—
480C4×C71—42no—
481C4×C71—42no—
482C4×C71—42no—
483Dic71—24no—
484Dic71—24no—
485Dic71—42no—
486Dic71—42no—
487Dic71—42no—
488Dic71—42no—
489C2×#2534—711nomaximal, Sylow
490C2×C71—44no—
491C2×C71—44no—
492C2×C71#253418yescomplemented
493C2×C71C22×#12111yescharacteristic
494C2×C71C2×#52511yescharacteristic
495C2×C71C2×#53411yescharacteristic
496C2×C71C2×#54611yescharacteristic
497C2×C71C2×#54611yescharacteristic
498C2×C71C2×#55111yescharacteristic
499C2×C71C2×#55111yescharacteristic
500D71—28no—
501D71—44no—
502C22×#123—711no—
503C22×#120—711no—
504C22×C4×D4—711no—
505C23×C22⋊C4—711no—
506#2534—7116no—
507C2×#396—711no—
508C2×#396—711no—
509C2×#394—711no—
510C2×#394—711no—
511C2×#388—711no—
512C2×#388—711no—
513C2×#386—711no—
514C2×#386D7111yescharacteristic, complemented
515C2×#381—711no—
516C2×#380—711no—
517C2×#379—711no—
518C71C2×#253411yescharacteristic, complemented, Sylow
519C26—711no—
520C23×D4—711no—
521C23×D4—711no—
522C23×D4C2×D7111yescharacteristic
523C24×C4—711no—
524C24×C4—711no—
525C24×C4C2×D7111yescharacteristic, complemented
526C2×#123—718no—
527C2×#123—1428no—
528C2×#120—718no—
529C2×#120—1428no—
530C2×C4×D4—718no—
531C2×C4×D4—1428no—
532C22×C4⋊C4—711no—
533C22×C4⋊C4—711no—
534C22×C4⋊C4—711no—
535C22×C4⋊C4—711no—
536C22×C4⋊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—711no—
549C22×C22⋊C4—711no—
550C22×C22⋊C4—718no—
551C22×C22⋊C4—1428no—
552C22×C22⋊C4C2×D7111yescharacteristic
553C22×C22⋊C4C2×D7111yescharacteristic
554C22×C22⋊C4C2×D7111yescharacteristic, complemented
555C22×C42—711no—
556#396—718no—
557#396—718no—
558#394—718no—
559#394—718no—
560#388—718no—
561#388—718no—
562#386—718no—
563#386C2×D7118yescomplemented
564#381—718no—
565#380—718no—
566#379—718no—
567C2×#95—711no—
568C2×#95—711no—
569C2×#95—711no—
570C2×#95—711no—
571C2×#95C2×D7111yescharacteristic, complemented
572C2×#95C2×D7111yescharacteristic, complemented
573C25—2842no—
574C25—2842no—
575C25—714no—
576C25—711no—
577C25—711no—
578C25—1424no—
579C25—1424no—
580C25—1424no—
581C25—1424no—
582C25—1424no—
583C25C22×D7111yescharacteristic
584C25C22×D7111yescharacteristic
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—2842no—
589C22×D4—714no—
590C22×D4—718no—
591C22×D4—714no—
592C22×D4—1424no—
593C22×D4—1424no—
594C22×D4—1424no—
595C22×D4—1424no—
596C22×D4C22×D7114yes—
597C23×C4—24no—
598C23×C4—42no—
599C23×C4—42no—
600C23×C4—2842no—
601C23×C4—2842no—
602C23×C4—718no—
603C23×C4—714no—
604C23×C4—711no—
605C23×C4—711no—
606C23×C4—711no—
607C23×C4—711no—
608C23×C4—711no—
609C23×C4—711no—
610C23×C4—714no—
611C23×C4—1424no—
612C23×C4—1424no—
613C23×C4—1424no—
614C23×C4C22×D7111yescharacteristic
615C23×C4C22×D7111yescharacteristic
616C23×C4C22×D7111yescharacteristic
617C23×C4C22×D7111yescharacteristic
618C23×C4C22×D7111yescharacteristic
619C23×C4C22×D7114yescomplemented
620#123—14232no—
621#120—14232no—
622C4×D4—14232no—
623C2×C4⋊C4—2842no—
624C2×C4⋊C4—2842no—
625C2×C4⋊C4—714no—
626C2×C4⋊C4—714no—
627C2×C4⋊C4—714no—
628C2×C4⋊C4—714no—
629C2×C4⋊C4—714no—
630C2×C4⋊C4—1424no—
631C2×C4⋊C4—1424no—
632C2×C4⋊C4—1424no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—42no—
636C2×C22⋊C4—2842no—
637C2×C22⋊C4—714no—
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—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⋊C4—1424no—
661C2×C22⋊C4—1424no—
662C2×C22⋊C4—1424no—
663C2×C22⋊C4C22×D7114yes—
664C2×C22⋊C4C22×D7114yes—
665C2×C22⋊C4C22×D7114yescomplemented
666C2×C42—714no—
667C2×C42—1424no—
668#95—714no—
669#95—714no—
670#95—714no—
671#95—714no—
672#95C22×D7114yescomplemented
673#95C22×D7114yescomplemented
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—28416no—
687C24—28416no—
688C24—2844no—
689C24—2844no—
690C24—28416no—
691C24—28416no—
692C24—28416no—
693C24—28416no—
694C24—714no—
695C24—714no—
696C24—714no—
697C24—712no—
698C24—714no—
699C24—712no—
700C24—1428no—
701C24—1428no—
702C24—1428no—
703C24—1428no—
704C24—14232no—
705C24—1422no—
706C24—1422no—
707C24—1422no—
708C24—1428no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24—1422no—
713C24—1422no—
714C24—1422no—
715C24—1422no—
716C24D4×D7114yes—
717C24#1176586514yes—
718C24C23×D7112yes—
719C24C23×D7112yes—
720C24C23×D7111yescharacteristic
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—44no—
724C2×D4—416no—
725C2×D4—28416no—
726C2×D4—2844no—
727C2×D4—7116no—
728C2×D4—1428no—
729C2×D4—1428no—
730C2×D4—1428no—
731C2×D4—1428no—
732C2×D4—14232no—
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—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—28no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—416no—
751C22×C4—2844no—
752C22×C4—2844no—
753C22×C4—28416no—
754C22×C4—28416no—
755C22×C4—7116no—
756C22×C4—714no—
757C22×C4—714no—
758C22×C4—712no—
759C22×C4—712no—
760C22×C4—712no—
761C22×C4—712no—
762C22×C4—712no—
763C22×C4—712no—
764C22×C4—1428no—
765C22×C4—1428no—
766C22×C4—1428no—
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×C4—1422no—
779C22×C4—1422no—
780C22×C4—1422no—
781C22×C4—1422no—
782C22×C4—1422no—
783C22×C4D4×D7114yes—
784C22×C4C23×D7112yes—
785C22×C4C23×D7112yes—
786C22×C4C23×D7112yes—
787C22×C4C23×D7112yes—
788C22×C4C23×D7112yes—
789C4⋊C4—2844no—
790C4⋊C4—2844no—
791C4⋊C4—1428no—
792C4⋊C4—1428no—
793C4⋊C4—1428no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—44no—
797C22⋊C4—2844no—
798C22⋊C4—1428no—
799C22⋊C4—1428no—
800C22⋊C4—1428no—
801C22⋊C4—1428no—
802C22⋊C4—1428no—
803C22⋊C4—1428no—
804C22⋊C4—1428no—
805C22⋊C4—1428no—
806C22⋊C4—1428no—
807C22⋊C4—1428no—
808C22⋊C4—1428no—
809C22⋊C4—1428no—
810C42—1428no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—28416no—
838C23—28416no—
839C23—28416no—
840C23—28416no—
841C23—284128no—
842C23—28416no—
843C23—28416no—
844C23—2844no—
845C23—2844no—
846C23—2844no—
847C23—2844no—
848C23—714no—
849C23—714no—
850C23—714no—
851C23—7116no—
852C23—714no—
853C23—14232no—
854C23—1422no—
855C23—1422no—
856C23—1422no—
857C23—1422no—
858C23—1422no—
859C23—1422no—
860C23—1428no—
861C23—1428no—
862C23—1428no—
863C23—1422no—
864C23—1422no—
865C23—1422no—
866C23—1422no—
867C23—1428no—
868C23—1428no—
869C23—1428no—
870C23—1428no—
871C23—1428no—
872C23—1428no—
873C23C2×D4×D7114yes—
874C23C2×D4×D7112yes—
875C23C2×D4×D7112yes—
876C23#41×D7112yes—
877C23#41×D7112yes—
878C23C2×#1176586514yes—
879C23C2×#1176586512yes—
880C23#1455617312yes—
881C23#1455617312yes—
882C23C24×D7111yescharacteristic
883D4—416no—
884D4—28416no—
885D4—14232no—
886C2×C4—22no—
887C2×C4—22no—
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—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—416no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—28416no—
907C2×C4—28416no—
908C2×C4—2844no—
909C2×C4—2844no—
910C2×C4—2844no—
911C2×C4—2844no—
912C2×C4—714no—
913C2×C4—714no—
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—1422no—
926C2×C4—1422no—
927C2×C4—1422no—
928C2×C4—1422no—
929C2×C4—1422no—
930C2×C4—1428no—
931C2×C4—1428no—
932C2×C4C2×D4×D7114yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—416no—
948C22—416no—
949C22—28464no—
950C22—2842no—
951C22—2842no—
952C22—2842no—
953C22—2842no—
954C22—28416no—
955C22—718no—
956C22—1424no—
957C22—1424no—
958C22—1424no—
959C22—1424no—
960C22—1424no—
961C22—1424no—
962C22—1424no—
963C22—1424no—
964C22—1424no—
965C22—14232no—
966C22#121×D7114yes—
967C22#1798650814yes—
968C22#1798655914yes—
969C22#1798663814yes—
970C22#1798663914yes—
971C22#1798667714yes—
972C22#1798667814yes—
973C22C22×D4×D7111yescharacteristic
974C22C22×D4×D7111yescharacteristic
975C22C2×#41×D7111yescharacteristic
976C22C2×#41×D7111yescharacteristic
977C22C22×#1176586511yescharacteristic
978C22C2×#1455617311yescharacteristic
979C22C2×#1455617311yescharacteristic
980C4—24no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—2842no—
986C4—2842no—
987C4—2842no—
988C4—2842no—
989C4—1424no—
990C4—1424no—
991C2—44no—
992C2—44no—
993C2—2844no—
994C2—1428no—
995C2#2259322818yesdirect product factor
996C2C2×#121×D7111yescharacteristic
997C2C2×#1798650811yescharacteristic
998C2C2×#1798655911yescharacteristic
999C2C2×#1798663811yescharacteristic
1000C2C2×#1798663911yescharacteristic
1001C2C2×#1798667711yescharacteristic
1002C2C2×#1798667811yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#386×C71C2
socleC24×C71C24
prime radicalC22×#14556096C2
hypercenterC2×#386D71
hypocenterC71C2×#2534
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#14556110C2semidirect
3. C22×C4×C22⋊D71C2semidirect
4. C22×C22⋊C4×D71C2semidirect
5. #22593228C2direct (N × H)
6. C2×#17985923C2semidirect
7. C2×#17985922C2semidirect
8. C2×#17985914C2semidirect
9. C2×#17985913C2semidirect
10. C2×#17985891C2semidirect
11. C2×#17985887C2semidirect
12. C2×#17985878C2semidirect
13. C2×#17985861C2semidirect
14. C2×#17985858C2semidirect
15. C2×#17985854C2semidirect
16. C2×#386×C71C2semidirect
23. C2×#14556110C22semidirect
27. C2×C4×C22⋊D71C22semidirect
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. #17985923C22semidirect
50. #17985922C22semidirect
51. #17985914C22semidirect
52. #17985913C22semidirect
53. #17985891C22semidirect
54. #17985887C22semidirect
55. #17985878C22semidirect
56. #17985861C22semidirect
57. #17985858C22semidirect
58. #17985854C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
62. C2×C71⋊#95C22semidirect
64. C24×C4×C71C22semidirect
67. C22×C22⋊C4×C71C22semidirect
68. #386×C71C22semidirect
69. C2×#95×C71C22semidirect
70. C2×#95×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
163. C23×C4×C71C23semidirect
169. C2×C22⋊C4×C71C23semidirect
170. #95×C71C23semidirect
171. #95×C71C23semidirect
241. C2×C4×D71C2×D4semidirect
492. C2×C71#2534semidirect
514. C2×#386D71semidirect
518. C71C2×#2534semidirect
525. C24×C4C2×D71semidirect
554. C22×C22⋊C4C2×D71semidirect
563. #386C2×D71semidirect
571. C2×#95C2×D71semidirect
572. C2×#95C2×D71semidirect
619. C23×C4C22×D71semidirect
665. C2×C22⋊C4C22×D71semidirect
672. #95C22×D71semidirect
673. #95C22×D71semidirect
995. C2#22593228direct (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×C4×C22⋊D712
C22×C22⋊C4×D712
#225932282
C2×#179859232
C2×#179859222
C2×#179859142
C2×#179859132
C2×#179858912
C2×#179858872
C2×#179858782
C2×#179858612
C2×#179858582
C2×#179858542
C2×#386×C712
C2×#253471