Finite Group Databasebeta

← C2×#22592008 #32164881

Subgroups — C2×#22592008 #32164881

Order 18176.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556106C211yesmaximal, characteristic, complemented
2C22×#14556105C211yesmaximal, characteristic, complemented
3C23×(C2×D71)⋊C4C211yesmaximal, characteristic
4C22×C22⋊C4×D71C211yesmaximal, characteristic
5#22592008C2116yesmaximal, direct product factor
6C2×#17985934C211yesmaximal, characteristic, complemented
7C2×#17985923C211yesmaximal, characteristic, complemented
8C2×#17985921C211yesmaximal, characteristic, complemented
9C2×#17985912C211yesmaximal, characteristic, complemented
10C2×#17985873C211yesmaximal, characteristic, complemented
11C2×#17985872C211yesmaximal, characteristic, complemented
12C2×#17985871C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×#17985858C211yesmaximal, characteristic, complemented
15C2×#17985854C211yesmaximal, characteristic
16C2×#380×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×Dic142C2211yescharacteristic, complemented
19C24×Dic71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C2×#14556106—28no—
23C2×#14556106C2218yescomplemented
24C2×#14556105—28no—
25C2×#14556105C2218yescomplemented
26C22×C4⋊Dic71C2211yescharacteristic, complemented
27C22×Dic71⋊C4C2211yescharacteristic, complemented
28C22×Dic71⋊C4C2211yescharacteristic, complemented
29C22×Dic71⋊C4C2211yescharacteristic, complemented
30C22×Dic71⋊C4C2211yescharacteristic, complemented
31C22×Dic71⋊C4C2211yescharacteristic, complemented
32C22×Dic71⋊C4C2211yescharacteristic, complemented
33C22×C22⋊Dic71C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×(C2×D71)⋊C4—28no—
36C22×(C2×D71)⋊C4C2218yes—
37C22×(C2×D71)⋊C4C2211yescharacteristic
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
46C22×(C2×D71)⋊C4C2211yescharacteristic
47C2×C22⋊C4×D71—28no—
48C2×C22⋊C4×D71C2218yes—
49#17985934C2218yescomplemented
50#17985923C2218yescomplemented
51#17985921C2218yescomplemented
52#17985912C2218yescomplemented
53#17985873C2218yescomplemented
54#17985872C2218yescomplemented
55#17985871C2218yescomplemented
56#17985870C2218yescomplemented
57#17985858C2218yescomplemented
58#17985854C2218yes—
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C2×C71⋊#95C2211yescharacteristic, complemented
63C24×C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic, complemented
65C22×C4⋊C4×C71C2211yescharacteristic, complemented
66C22×C22⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68#380×C71C2218yescomplemented
69C2×#95×C71C2211yescharacteristic, complemented
70C2×#95×C71C2211yescharacteristic, complemented
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—24no—
75C24×D71—42no—
76C24×D71—42no—
77C24×D71Q818yescomplemented
78C24×D71C2311yescharacteristic
79C24×D71C2314yes—
80C24×D71C2311yescharacteristic
81C22×Dic142—24no—
82C22×Dic142—24no—
83C22×Dic142—42no—
84C22×Dic142C2314yescomplemented
85C23×Dic71—24no—
86C23×Dic71—24no—
87C23×Dic71—42no—
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2314yes—
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2311yescharacteristic
94C23×Dic71C2311yescharacteristic
95C22×C4×D71—24no—
96C22×C4×D71—24no—
97C22×C4×D71—24no—
98C22×C4×D71—24no—
99C22×C4×D71—42no—
100C22×C4×D71—42no—
101C22×C4×D71C2314yes—
102C22×C4×D71C2314yes—
103#14556106—232no—
104#14556105—232no—
105C2×C4⋊Dic71—24no—
106C2×C4⋊Dic71C2314yescomplemented
107C2×Dic71⋊C4—24no—
108C2×Dic71⋊C4—24no—
109C2×Dic71⋊C4—24no—
110C2×Dic71⋊C4—24no—
111C2×Dic71⋊C4—42no—
112C2×Dic71⋊C4—42no—
113C2×Dic71⋊C4C2314yescomplemented
114C2×Dic71⋊C4C2314yescomplemented
115C2×Dic71⋊C4C2314yescomplemented
116C2×Dic71⋊C4C2314yescomplemented
117C2×Dic71⋊C4C2314yescomplemented
118C2×Dic71⋊C4C2314yescomplemented
119C2×C22⋊Dic71—24no—
120C2×C22⋊Dic71D418yes—
121C2×C22⋊Dic71C2314yes—
122C2×C22⋊Dic71C2314yes—
123C2×(C2×D71)⋊C4—24no—
124C2×(C2×D71)⋊C4—24no—
125C2×(C2×D71)⋊C4—24no—
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—24no—
129C2×(C2×D71)⋊C4—232no—
130C2×(C2×D71)⋊C4—24no—
131C2×(C2×D71)⋊C4—42no—
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—
142C2×(C2×D71)⋊C4C2314yes—
143C2×(C2×D71)⋊C4C2314yes—
144C22⋊C4×D71—232no—
145C71⋊#95C2314yescomplemented
146C71⋊#95C2314yescomplemented
147C71⋊#95C2314yescomplemented
148C71⋊#95C2314yescomplemented
149C25×C71C2311yescharacteristic
150C23×C4×C71—24no—
151C23×C4×C71—24no—
152C23×C4×C71—42no—
153C23×C4×C71C2311yescharacteristic
154C23×C4×C71C2311yescharacteristic
155C23×C4×C71C2311yescharacteristic
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2314yes—
159C23×C4×C71C2311yescharacteristic
160C2×C4⋊C4×C71—24no—
161C2×C4⋊C4×C71—42no—
162C2×C4⋊C4×C71C2314yescomplemented
163C2×C4⋊C4×C71C2314yescomplemented
164C2×C22⋊C4×C71—24no—
165C2×C22⋊C4×C71—24no—
166C2×C22⋊C4×C71C2314yes—
167C2×C22⋊C4×C71C2314yes—
168#95×C71C2314yescomplemented
169#95×C71C2314yescomplemented
170C23×D71—22no—
171C23×D71—22no—
172C23×D71—22no—
173C23×D71—22no—
174C23×D71—232no—
175C23×D71—28no—
176C23×D71—22no—
177C23×D71—22no—
178C23×D71—22no—
179C23×D71—28no—
180C23×D71—22no—
181C23×D71—22no—
182C23×D71—22no—
183C23×D71—232no—
184C23×D71—28no—
185C23×D71—28no—
186C23×D71—416no—
187C23×D71—44no—
188C23×D71—44no—
189C23×D71—416no—
190C23×D71—416no—
191C23×D71—416no—
192C23×D71—416no—
193C23×D71C2×D414yes—
194C23×D71C2×Q814yes—
195C23×D71C2×Q814yes—
196C23×D71C2×Q8116yescomplemented
197C23×D71#4114yes—
198C23×D71C2412yes—
199C23×D71C2412yes—
200C2×Dic142—28no—
201C2×Dic142—28no—
202C2×Dic142—44no—
203C2×Dic142—416no—
204C22×Dic71—22no—
205C22×Dic71—22no—
206C22×Dic71—22no—
207C22×Dic71—22no—
208C22×Dic71—22no—
209C22×Dic71—22no—
210C22×Dic71—22no—
211C22×Dic71—22no—
212C22×Dic71—28no—
213C22×Dic71—22no—
214C22×Dic71—22no—
215C22×Dic71—22no—
216C22×Dic71—22no—
217C22×Dic71—22no—
218C22×Dic71—22no—
219C22×Dic71—22no—
220C22×Dic71—28no—
221C22×Dic71—44no—
222C22×Dic71—416no—
223C22×Dic71C2×D414yes—
224C22×Dic71C2×D414yes—
225C22×Dic71C2×D414yes—
226C22×Dic71C2412yes—
227C22×Dic71C2412yes—
228C22×Dic71C2412yes—
229C22×Dic71C2412yes—
230C22×Dic71C2412yes—
231C22×Dic71C2412yes—
232C2×C4×D71—28no—
233C2×C4×D71—28no—
234C2×C4×D71—28no—
235C2×C4×D71—28no—
236C2×C4×D71—44no—
237C2×C4×D71—44no—
238C2×C4×D71—416no—
239C2×C4×D71—416no—
240C4⋊Dic71—28no—
241Dic71⋊C4—28no—
242Dic71⋊C4—28no—
243Dic71⋊C4—28no—
244Dic71⋊C4—28no—
245Dic71⋊C4—44no—
246Dic71⋊C4—44no—
247C22⋊Dic71—28no—
248C22⋊Dic71C2×D4116yes—
249(C2×D71)⋊C4—28no—
250(C2×D71)⋊C4—28no—
251(C2×D71)⋊C4—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—44no—
257(C2×D71)⋊C4—44no—
258(C2×D71)⋊C4C2×D4116yes—
259C24×C71—22no—
260C24×C71—22no—
261C24×C71—22no—
262C24×C71—22no—
263C24×C71C2×D414yes—
264C24×C71C2×Q814yes—
265C24×C71#4114yes—
266C24×C71C2412yes—
267C24×C71C2411yescharacteristic
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—22no—
272C22×C4×C71—22no—
273C22×C4×C71—22no—
274C22×C4×C71—22no—
275C22×C4×C71—22no—
276C22×C4×C71—22no—
277C22×C4×C71—22no—
278C22×C4×C71—28no—
279C22×C4×C71—22no—
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—28no—
287C22×C4×C71—44no—
288C22×C4×C71—416no—
289C22×C4×C71C2×D414yes—
290C22×C4×C71C2412yes—
291C22×C4×C71C2412yes—
292C22×C4×C71C2412yes—
293C22×C4×C71C2412yes—
294C22×C4×C71C2412yes—
295C22×C4×C71C2412yes—
296C4⋊C4×C71—28no—
297C4⋊C4×C71—44no—
298C22⋊C4×C71—28no—
299C22⋊C4×C71—28no—
300C23×C71—28no—
301C23×C71—28no—
302C23×C71—28no—
303C23×C71—28no—
304C23×C71—28no—
305C23×C71—28no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71C22⋊Q8116yescomplemented
311C23×C71C22×D414yes—
312C23×C71C22×D412yes—
313C23×C71C22×D412yes—
314C23×C71C22×Q814yes—
315C23×C71C22×Q812yes—
316C23×C71C2×#4112yes—
317C23×C71C2×#4114yes—
318C23×C71C2×#4112yes—
319C23×C71H(5,𝔽2)12yes—
320C23×C71H(5,𝔽2)12yes—
321C23×C71C2511yescharacteristic
322C22×D71—28no—
323C22×D71—28no—
324C22×D71—28no—
325C22×D71—28no—
326C22×D71—28no—
327C22×D71—28no—
328C22×D71—22no—
329C22×D71—22no—
330C22×D71—22no—
331C22×D71—22no—
332C22×D71—28no—
333C22×D71—28no—
334C22×D71—232no—
335C22×D71—28no—
336C22×D71—22no—
337C22×D71—22no—
338C22×D71—22no—
339C22×D71—22no—
340C22×D71—22no—
341C22×D71—22no—
342C22×D71—232no—
343C22×D71—416no—
344C22×D71—4128no—
345C22×D71—416no—
346C22×D71—416no—
347C22×D71—416no—
348C22×D71—416no—
349C22×D71—44no—
350C22×D71—44no—
351C22×D71—44no—
352C22×D71—44no—
353C22×D71C22⋊Q8116yescomplemented
354C22×D71C22×D414yes—
355C22×D71C22×Q814yes—
356C22×D71C22×Q814yes—
357C22×D71C2×#4114yes—
358C2×C4×C71—28no—
359C2×C4×C71—22no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—22no—
365C2×C4×C71—22no—
366C2×C4×C71—22no—
367C2×C4×C71—22no—
368C2×C4×C71—22no—
369C2×C4×C71—22no—
370C2×C4×C71—22no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—22no—
374C2×C4×C71—22no—
375C2×C4×C71—22no—
376C2×C4×C71—416no—
377C2×C4×C71—44no—
378C2×C4×C71—44no—
379C2×C4×C71—44no—
380C2×C4×C71—44no—
381C2×C4×C71—44no—
382C2×C4×C71C22×D414yes—
383C2×Dic71—28no—
384C2×Dic71—28no—
385C2×Dic71—28no—
386C2×Dic71—22no—
387C2×Dic71—22no—
388C2×Dic71—22no—
389C2×Dic71—22no—
390C2×Dic71—22no—
391C2×Dic71—22no—
392C2×Dic71—22no—
393C2×Dic71—22no—
394C2×Dic71—22no—
395C2×Dic71—22no—
396C2×Dic71—22no—
397C2×Dic71—22no—
398C2×Dic71—22no—
399C2×Dic71—22no—
400C2×Dic71—22no—
401C2×Dic71—416no—
402C2×Dic71—44no—
403C2×Dic71—44no—
404C2×Dic71—44no—
405C2×Dic71C22×D414yes—
406C2×Dic71C22×D414yes—
407C2×Dic71C22×D414yes—
408C4×D71—416no—
409C4×D71—416no—
410Dic142—416no—
411C22×C71—24no—
412C22×C71—24no—
413C22×C71—232no—
414C22×C71—24no—
415C22×C71—24no—
416C22×C71—24no—
417C22×C71—24no—
418C22×C71C2×C22⋊Q814yes—
419C22×C71C2×C22⋊Q814yes—
420C22×C71C2×C22⋊Q818yescomplemented
421C22×C71#54314yes—
422C22×C71D4214yes—
423C22×C71#54614yes—
424C22×C71#54614yes—
425C22×C71#55114yes—
426C22×C71C23×D411yescharacteristic
427C22×C71C23×D411yescharacteristic
428C22×C71C23×Q811yescharacteristic
429C22×C71C22×#4111yescharacteristic
430C22×C71C22×#4111yescharacteristic
431C22×C71C2×H(5,𝔽2)11yescharacteristic
432C22×C71C2×H(5,𝔽2)11yescharacteristic
433C2×D71—24no—
434C2×D71—24no—
435C2×D71—232no—
436C2×D71—24no—
437C2×D71—24no—
438C2×D71—24no—
439C2×D71—24no—
440C2×D71—24no—
441C2×D71—24no—
442C2×D71—24no—
443C2×D71—464no—
444C2×D71—416no—
445C2×D71—42no—
446C2×D71—42no—
447C2×D71—42no—
448C2×D71—42no—
449C2×D71C2×C22⋊Q818yescomplemented
450C4×C71—24no—
451C4×C71—42no—
452C4×C71—42no—
453C4×C71—42no—
454C4×C71—42no—
455C4×C71—42no—
456Dic71—24no—
457Dic71—24no—
458Dic71—24no—
459Dic71—42no—
460Dic71—42no—
461Dic71—42no—
462C2×#2437—711nomaximal, Sylow
463C2×C71—28no—
464C2×C71#243718yescomplemented
465C2×C71C22×C22⋊Q811yescharacteristic
466C2×C71C22×C22⋊Q811yescharacteristic
467C2×C71C2×#54311yescharacteristic
468C2×C71C2×D4211yescharacteristic
469C2×C71C2×#54611yescharacteristic
470C2×C71C2×#54611yescharacteristic
471C2×C71C2×#55111yescharacteristic
472D71—28no—
473D71—44no—
474C22×C22⋊Q8—711no—
475C22×C22⋊Q8—711no—
476C23×C22⋊C4—711no—
477C23×C22⋊C4—711no—
478#2437—7116no—
479C2×#399—711no—
480C2×#396—711no—
481C2×#396—711no—
482C2×#393—711no—
483C2×#385—711no—
484C2×#385—711no—
485C2×#385—711no—
486C2×#385—711no—
487C2×#380—711no—
488C2×#380D7111yescharacteristic, complemented
489C2×#379—711no—
490C71C2×#243711yescharacteristic, complemented, Sylow
491C26—711no—
492C23×Q8—711no—
493C24×C4—711no—
494C24×C4—711no—
495C24×C4—711no—
496C24×C4C2×D7111yescharacteristic
497C2×C22⋊Q8—718no—
498C2×C22⋊Q8—718no—
499C2×C22⋊Q8—1428no—
500C2×C22⋊Q8—1428no—
501C22×C4⋊C4—711no—
502C22×C4⋊C4—711no—
503C22×C4⋊C4—711no—
504C22×C4⋊C4—711no—
505C22×C4⋊C4—711no—
506C22×C4⋊C4—711no—
507C22×C4⋊C4—711no—
508C22×C4⋊C4C2×D7111yescharacteristic, complemented
509C22×C4⋊C4C2×D7111yescharacteristic, complemented
510C22×C22⋊C4—711no—
511C22×C22⋊C4—711no—
512C22×C22⋊C4—711no—
513C22×C22⋊C4—711no—
514C22×C22⋊C4—711no—
515C22×C22⋊C4—711no—
516C22×C22⋊C4—711no—
517C22×C22⋊C4—711no—
518C22×C22⋊C4—711no—
519C22×C22⋊C4—718no—
520C22×C22⋊C4—711no—
521C22×C22⋊C4—711no—
522C22×C22⋊C4—711no—
523C22×C22⋊C4—718no—
524C22×C22⋊C4—1428no—
525C22×C22⋊C4—1428no—
526C22×C22⋊C4C2×D7111yescharacteristic
527C22×C22⋊C4C2×D7111yescharacteristic
528#399—718no—
529#396—718no—
530#396—718no—
531#393—718no—
532#385—718no—
533#385—718no—
534#385—718no—
535#385—718no—
536#380—718no—
537#380C2×D7118yescomplemented
538#379—718no—
539C2×#95—711no—
540C2×#95—711no—
541C2×#95—711no—
542C2×#95—711no—
543C2×#95C2×D7111yescharacteristic, complemented
544C2×#95C2×D7111yescharacteristic, complemented
545C25—2842no—
546C25—2842no—
547C25—718no—
548C25—714no—
549C25—711no—
550C25—711no—
551C25—1424no—
552C25—1424no—
553C25—1424no—
554C25—1424no—
555C25C22×D7111yescharacteristic
556C22×Q8—2842no—
557C22×Q8—714no—
558C22×Q8—1424no—
559C22×Q8—1424no—
560C23×C4—24no—
561C23×C4—24no—
562C23×C4—42no—
563C23×C4—2842no—
564C23×C4—2842no—
565C23×C4—2842no—
566C23×C4—714no—
567C23×C4—714no—
568C23×C4—714no—
569C23×C4—711no—
570C23×C4—711no—
571C23×C4—711no—
572C23×C4—711no—
573C23×C4—711no—
574C23×C4—711no—
575C23×C4—1424no—
576C23×C4—1424no—
577C23×C4—1424no—
578C23×C4—1424no—
579C23×C4—1424no—
580C23×C4—1424no—
581C23×C4C22×D7111yescharacteristic
582C23×C4C22×D7111yescharacteristic
583C23×C4C22×D7111yescharacteristic
584C23×C4C22×D7111yescharacteristic
585C23×C4C22×D7111yescharacteristic
586C23×C4C22×D7114yes—
587C23×C4C22×D7111yescharacteristic
588C22⋊Q8—14232no—
589C22⋊Q8—14232no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—42no—
592C2×C4⋊C4—2842no—
593C2×C4⋊C4—2842no—
594C2×C4⋊C4—714no—
595C2×C4⋊C4—714no—
596C2×C4⋊C4—714no—
597C2×C4⋊C4—714no—
598C2×C4⋊C4—714no—
599C2×C4⋊C4—714no—
600C2×C4⋊C4—714no—
601C2×C4⋊C4—1424no—
602C2×C4⋊C4—1424no—
603C2×C4⋊C4—1424no—
604C2×C4⋊C4—1424no—
605C2×C4⋊C4—1424no—
606C2×C4⋊C4C22×D7114yescomplemented
607C2×C4⋊C4C22×D7114yescomplemented
608C2×C22⋊C4—24no—
609C2×C22⋊C4—24no—
610C2×C22⋊C4—2842no—
611C2×C22⋊C4—2842no—
612C2×C22⋊C4—714no—
613C2×C22⋊C4—714no—
614C2×C22⋊C4—718no—
615C2×C22⋊C4—714no—
616C2×C22⋊C4—718no—
617C2×C22⋊C4—714no—
618C2×C22⋊C4—714no—
619C2×C22⋊C4—714no—
620C2×C22⋊C4—714no—
621C2×C22⋊C4—714no—
622C2×C22⋊C4—714no—
623C2×C22⋊C4—714no—
624C2×C22⋊C4—714no—
625C2×C22⋊C4—714no—
626C2×C22⋊C4—14232no—
627C2×C22⋊C4—14232no—
628C2×C22⋊C4—1424no—
629C2×C22⋊C4—1424no—
630C2×C22⋊C4—1424no—
631C2×C22⋊C4—1424no—
632C2×C22⋊C4—1424no—
633C2×C22⋊C4—1424no—
634C2×C22⋊C4—1424no—
635C2×C22⋊C4—1424no—
636C2×C22⋊C4C22×D7114yes—
637C2×C22⋊C4C22×D7114yes—
638#95—714no—
639#95—714no—
640#95—714no—
641#95—714no—
642#95C22×D7114yescomplemented
643#95C22×D7114yescomplemented
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—28416no—
649C24—28416no—
650C24—28416no—
651C24—28416no—
652C24—2844no—
653C24—2844no—
654C24—28416no—
655C24—7116no—
656C24—714no—
657C24—714no—
658C24—714no—
659C24—712no—
660C24—714no—
661C24—712no—
662C24—1428no—
663C24—1428no—
664C24—14232no—
665C24—1428no—
666C24—1422no—
667C24—1422no—
668C24—1422no—
669C24—1428no—
670C24—1422no—
671C24—1422no—
672C24—1422no—
673C24—14232no—
674C24—1422no—
675C24—1422no—
676C24—1422no—
677C24—1422no—
678C24D4×D7114yes—
679C24Q8×D7114yes—
680C24#1176586514yes—
681C24C23×D7112yes—
682C24C23×D7111yescharacteristic
683C2×Q8—2844no—
684C2×Q8—28416no—
685C2×Q8—1428no—
686C2×Q8—1428no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—28no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—28no—
706C22×C4—44no—
707C22×C4—416no—
708C22×C4—2844no—
709C22×C4—2844no—
710C22×C4—28416no—
711C22×C4—28416no—
712C22×C4—28416no—
713C22×C4—2844no—
714C22×C4—714no—
715C22×C4—714no—
716C22×C4—714no—
717C22×C4—712no—
718C22×C4—712no—
719C22×C4—712no—
720C22×C4—712no—
721C22×C4—712no—
722C22×C4—712no—
723C22×C4—1428no—
724C22×C4—1428no—
725C22×C4—1428no—
726C22×C4—1428no—
727C22×C4—1428no—
728C22×C4—1422no—
729C22×C4—1422no—
730C22×C4—1422no—
731C22×C4—1428no—
732C22×C4—1422no—
733C22×C4—1422no—
734C22×C4—1422no—
735C22×C4—1422no—
736C22×C4—1422no—
737C22×C4—1422no—
738C22×C4—1422no—
739C22×C4—1422no—
740C22×C4—1422no—
741C22×C4—1422no—
742C22×C4—1422no—
743C22×C4—1422no—
744C22×C4D4×D7114yes—
745C22×C4C23×D7112yes—
746C22×C4C23×D7112yes—
747C22×C4C23×D7112yes—
748C22×C4C23×D7112yes—
749C22×C4C23×D7112yes—
750C22×C4C23×D7112yes—
751C4⋊C4—28no—
752C4⋊C4—44no—
753C4⋊C4—2844no—
754C4⋊C4—2844no—
755C4⋊C4—1428no—
756C4⋊C4—1428no—
757C4⋊C4—1428no—
758C4⋊C4—1428no—
759C4⋊C4—1428no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—2844no—
763C22⋊C4—2844no—
764C22⋊C4—7116no—
765C22⋊C4—7116no—
766C22⋊C4—1428no—
767C22⋊C4—1428no—
768C22⋊C4—1428no—
769C22⋊C4—1428no—
770C22⋊C4—1428no—
771C22⋊C4—1428no—
772C22⋊C4—1428no—
773C22⋊C4—1428no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—28no—
779C23—28no—
780C23—28no—
781C23—28no—
782C23—28no—
783C23—28no—
784C23—284128no—
785C23—28416no—
786C23—28416no—
787C23—28416no—
788C23—28416no—
789C23—28416no—
790C23—2844no—
791C23—2844no—
792C23—2844no—
793C23—2844no—
794C23—714no—
795C23—714no—
796C23—714no—
797C23—7116no—
798C23—714no—
799C23—14232no—
800C23—1422no—
801C23—1422no—
802C23—1422no—
803C23—1422no—
804C23—1422no—
805C23—1422no—
806C23—1428no—
807C23—1428no—
808C23—1428no—
809C23—14232no—
810C23—1422no—
811C23—1422no—
812C23—1422no—
813C23—1422no—
814C23—1428no—
815C23—1428no—
816C23—1428no—
817C23—1428no—
818C23—1428no—
819C23—1428no—
820C23#14556106116yescomplemented
821C23C2×D4×D7114yes—
822C23C2×D4×D7112yes—
823C23C2×D4×D7112yes—
824C23C2×Q8×D7114yes—
825C23C2×Q8×D7112yes—
826C23#41×D7112yes—
827C23C2×#1176586514yes—
828C23C2×#1176586512yes—
829C23#1455617312yes—
830C23#1455617412yes—
831C23C24×D7111yescharacteristic
832Q8—28416no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—28no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—28416no—
858C2×C4—28416no—
859C2×C4—2844no—
860C2×C4—2844no—
861C2×C4—2844no—
862C2×C4—28416no—
863C2×C4—714no—
864C2×C4—714no—
865C2×C4—714no—
866C2×C4—1422no—
867C2×C4—1422no—
868C2×C4—1422no—
869C2×C4—1422no—
870C2×C4—1422no—
871C2×C4—1422no—
872C2×C4—1422no—
873C2×C4—1422no—
874C2×C4—1422no—
875C2×C4—1422no—
876C2×C4—1422no—
877C2×C4—1422no—
878C2×C4—1422no—
879C2×C4—1422no—
880C2×C4—1422no—
881C2×C4—1428no—
882C2×C4—1428no—
883C2×C4—1428no—
884C2×C4C2×D4×D7114yes—
885C22—24no—
886C22—232no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—28464no—
893C22—28416no—
894C22—2842no—
895C22—2842no—
896C22—2842no—
897C22—2842no—
898C22—718no—
899C22—1424no—
900C22—1424no—
901C22—1424no—
902C22—1424no—
903C22—14232no—
904C22—1424no—
905C22—1424no—
906C22—1424no—
907C22—1424no—
908C22—1424no—
909C22C22⋊Q8×D7114yes—
910C22C2×#1455610614yes—
911C22C2×#1455610618yescomplemented
912C22#1798662414yes—
913C22#1798663314yes—
914C22#1798663814yes—
915C22#1798663914yes—
916C22#1798667314yes—
917C22C22×D4×D7111yescharacteristic
918C22C22×D4×D7111yescharacteristic
919C22C22×Q8×D7111yescharacteristic
920C22C2×#41×D7111yescharacteristic
921C22C22×#1176586511yescharacteristic
922C22C2×#1455617311yescharacteristic
923C22C2×#1455617411yescharacteristic
924C4—24no—
925C4—42no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—2842no—
931C4—2842no—
932C4—2842no—
933C4—1424no—
934C4—1424no—
935C4—1424no—
936C2—28no—
937C2—2844no—
938C2—1428no—
939C2#2259200818yesdirect product factor
940C2C2×C22⋊Q8×D7111yescharacteristic
941C2C22×#1455610611yescharacteristic
942C2C2×#1798662411yescharacteristic
943C2C2×#1798663311yescharacteristic
944C2C2×#1798663811yescharacteristic
945C2C2×#1798663911yescharacteristic
946C2C2×#1798667311yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#380×C71C2
socleC24×C71C24
prime radicalC25×D71C22
hypercenterC2×#380D71
hypocenterC71C2×#2437
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#14556106C2semidirect
2. C22×#14556105C2semidirect
5. #22592008C2direct (N × H)
6. C2×#17985934C2semidirect
7. C2×#17985923C2semidirect
8. C2×#17985921C2semidirect
9. C2×#17985912C2semidirect
10. C2×#17985873C2semidirect
11. C2×#17985872C2semidirect
12. C2×#17985871C2semidirect
13. C2×#17985870C2semidirect
14. C2×#17985858C2semidirect
16. C2×#380×C71C2semidirect
18. C23×Dic142C22semidirect
23. C2×#14556106C22semidirect
25. C2×#14556105C22semidirect
26. C22×C4⋊Dic71C22semidirect
27. C22×Dic71⋊C4C22semidirect
28. C22×Dic71⋊C4C22semidirect
29. C22×Dic71⋊C4C22semidirect
30. C22×Dic71⋊C4C22semidirect
31. C22×Dic71⋊C4C22semidirect
32. C22×Dic71⋊C4C22semidirect
49. #17985934C22semidirect
50. #17985923C22semidirect
51. #17985921C22semidirect
52. #17985912C22semidirect
53. #17985873C22semidirect
54. #17985872C22semidirect
55. #17985871C22semidirect
56. #17985870C22semidirect
57. #17985858C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
62. C2×C71⋊#95C22semidirect
64. C22×C4⋊C4×C71C22semidirect
65. C22×C4⋊C4×C71C22semidirect
68. #380×C71C22semidirect
69. C2×#95×C71C22semidirect
70. C2×#95×C71C22semidirect
77. C24×D71Q8semidirect
84. C22×Dic142C23semidirect
106. C2×C4⋊Dic71C23semidirect
113. C2×Dic71⋊C4C23semidirect
114. C2×Dic71⋊C4C23semidirect
115. C2×Dic71⋊C4C23semidirect
116. C2×Dic71⋊C4C23semidirect
117. C2×Dic71⋊C4C23semidirect
118. C2×Dic71⋊C4C23semidirect
145. C71⋊#95C23semidirect
146. C71⋊#95C23semidirect
147. C71⋊#95C23semidirect
148. C71⋊#95C23semidirect
162. C2×C4⋊C4×C71C23semidirect
163. C2×C4⋊C4×C71C23semidirect
168. #95×C71C23semidirect
169. #95×C71C23semidirect
196. C23×D71C2×Q8semidirect
310. C23×C71C22⋊Q8semidirect
353. C22×D71C22⋊Q8semidirect
420. C22×C71C2×C22⋊Q8semidirect
449. C2×D71C2×C22⋊Q8semidirect
464. C2×C71#2437semidirect
488. C2×#380D71semidirect
490. C71C2×#2437semidirect
508. C22×C4⋊C4C2×D71semidirect
509. C22×C4⋊C4C2×D71semidirect
537. #380C2×D71semidirect
543. C2×#95C2×D71semidirect
544. C2×#95C2×D71semidirect
606. C2×C4⋊C4C22×D71semidirect
607. C2×C4⋊C4C22×D71semidirect
642. #95C22×D71semidirect
643. #95C22×D71semidirect
820. C23#14556106semidirect
911. C22C2×#14556106semidirect
939. C2#22592008direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561062
C22×#145561052
C23×(C2×D71)⋊C42
C22×C22⋊C4×D712
#225920082
C2×#179859342
C2×#179859232
C2×#179859212
C2×#179859122
C2×#179858732
C2×#179858722
C2×#179858712
C2×#179858702
C2×#179858582
C2×#179858542
C2×#380×C712
C2×#243771