Finite Group Databasebeta

← C2×#22591412 #32157060

Subgroups — C2×#22591412 #32157060

Order 18176.

3678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556114C211yesmaximal, characteristic
2C22×C4×Dic142C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D71C211yesmaximal, characteristic
4#22591412C2116yesmaximal, direct product factor
5C2×#17985903C211yesmaximal, characteristic, complemented
6C2×#17985899C211yesmaximal, characteristic
7C2×#17985893C211yesmaximal, characteristic, complemented
8C2×#17985892C211yesmaximal, characteristic, complemented
9C2×#17985890C211yesmaximal, characteristic, complemented
10C2×#17985890C211yesmaximal, characteristic, complemented
11C2×#17985873C211yesmaximal, characteristic, complemented
12C2×#17985872C211yesmaximal, characteristic, complemented
13C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
14C2×#17985850C211yesmaximal, characteristic, complemented
15C2×#17985846C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556114C4116yescomplemented
21C2×#14556114C2218yes—
22C2×C4×Dic142—28no—
23C2×C4×Dic142C2218yescomplemented
24C2×C4×C22⋊D71—28no—
25C2×C4×C22⋊D71C2218yes—
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic
33C22×C22⋊Dic71C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44C22×C4×Dic71C2211yescharacteristic
45#17985903C2218yescomplemented
46#17985899C2218yes—
47#17985893C2218yescomplemented
48#17985892C2218yescomplemented
49#17985890C2218yescomplemented
50#17985890C2218yescomplemented
51#17985873C2218yescomplemented
52#17985872C2218yescomplemented
53C4×Dic71⋊C4C2218yescomplemented
54#17985850C2218yescomplemented
55#17985846C2218yescomplemented
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C24×C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic
66C22×C42×C71C2211yescharacteristic
67C4×C22⋊C4×C71C2218yescomplemented
68C2×#95×C71C2211yescharacteristic
69C2×#95×C71C2211yescharacteristic
70C24×D71C2311yescharacteristic
71C22×Dic142—24no—
72C22×Dic142—24no—
73C22×Dic142C2×C418yescomplemented
74C22×Dic142C2314yes—
75C22×C22⋊D71—24no—
76C22×C22⋊D71—24no—
77C22×C22⋊D71C2×C418yes—
78C22×C22⋊D71C2314yes—
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C22×C4×D71—24no—
87C22×C4×D71—24no—
88C22×C4×D71—42no—
89C22×C4×D71C2314yes—
90#14556114C2×C4164yescomplemented
91C4×Dic142—232no—
92C4×C22⋊D71—232no—
93C2×C4⋊Dic71—24no—
94C2×C4⋊Dic71C2314yes—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4D418yes—
100C2×Dic71⋊C4C2314yes—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×C22⋊Dic71—24no—
106C2×C22⋊Dic71—42no—
107C2×C22⋊Dic71C2×C418yescomplemented
108C2×C22⋊Dic71C2314yes—
109C2×C22⋊Dic71C2314yes—
110C2×C22⋊Dic71C2314yes—
111C2×(C2×D71)⋊C4—24no—
112C2×(C2×D71)⋊C4—24no—
113C2×(C2×D71)⋊C4—42no—
114C2×(C2×D71)⋊C4C2×C418yescomplemented
115C2×(C2×D71)⋊C4C2×C418yescomplemented
116C2×(C2×D71)⋊C4C2314yes—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×C4×Dic71—24no—
122C2×C4×Dic71—24no—
123C2×C4×Dic71—24no—
124C2×C4×Dic71—42no—
125C2×C4×Dic71C2×C418yescomplemented
126C2×C4×Dic71C2314yes—
127C2×C4×Dic71C2314yes—
128C2×C4×Dic71C2314yes—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C25×C71C2311yescharacteristic
138C23×C4×C71—24no—
139C23×C4×C71—24no—
140C23×C4×C71—42no—
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2314yes—
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C2×C22⋊C4×C71—24no—
149C2×C22⋊C4×C71C2×C418yescomplemented
150C2×C22⋊C4×C71C2314yes—
151C2×C22⋊C4×C71C2314yes—
152C2×C42×C71—24no—
153C2×C42×C71—42no—
154C2×C42×C71C2314yes—
155C2×C42×C71C2314yes—
156#95×C71C2314yes—
157#95×C71C2314yes—
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71—22no—
163C23×D71—22no—
164C23×D71C22×C414yes—
165C23×D71C2412yes—
166C2×Dic142—232no—
167C2×Dic142—28no—
168C2×Dic142—28no—
169C2×Dic142C22×C4116yescomplemented
170C2×C22⋊D71—232no—
171C2×C22⋊D71—28no—
172C2×C22⋊D71—28no—
173C2×C22⋊D71C22×C4116yes—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71C22×C414yes—
190C22×Dic71C22×C414yes—
191C22×Dic71C22×C414yes—
192C22×Dic71C2×D414yes—
193C22×Dic71C2×D414yes—
194C22×Dic71#4114yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C22×Dic71C2412yes—
201C22×Dic71C2412yes—
202C2×C4×D71—28no—
203C2×C4×D71—28no—
204C2×C4×D71—44no—
205C2×C4×D71—416no—
206C4⋊Dic71—28no—
207Dic71⋊C4—28no—
208Dic71⋊C4—28no—
209Dic71⋊C4—28no—
210Dic71⋊C4—28no—
211Dic71⋊C4C2×D4116yes—
212C22⋊Dic71—28no—
213C22⋊Dic71—44no—
214C22⋊Dic71C22×C4116yescomplemented
215(C2×D71)⋊C4—28no—
216(C2×D71)⋊C4—28no—
217(C2×D71)⋊C4—44no—
218(C2×D71)⋊C4C22×C4116yescomplemented
219(C2×D71)⋊C4C22×C4116yescomplemented
220C4×Dic71—28no—
221C4×Dic71—28no—
222C4×Dic71—28no—
223C4×Dic71—44no—
224C4×Dic71C22×C4116yescomplemented
225C24×C71—22no—
226C24×C71—22no—
227C24×C71—22no—
228C24×C71—22no—
229C24×C71—22no—
230C24×C71—22no—
231C24×C71C22×C414yes—
232C24×C71C2412yes—
233C24×C71C2411yescharacteristic
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—28no—
248C22×C4×C71—28no—
249C22×C4×C71—44no—
250C22×C4×C71—416no—
251C22×C4×C71C22×C414yes—
252C22×C4×C71C22×C414yes—
253C22×C4×C71C2×D414yes—
254C22×C4×C71#4114yes—
255C22×C4×C71#4114yes—
256C22×C4×C71C2412yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2412yes—
262C22⋊C4×C71—28no—
263C22⋊C4×C71C22×C4116yescomplemented
264C42×C71—28no—
265C42×C71—44no—
266C23×C71—28no—
267C23×C71—28no—
268C23×C71—28no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—44no—
276C23×C71—44no—
277C23×C71—44no—
278C23×C71—44no—
279C23×C71C23×C414yes—
280C23×C71C23×C412yes—
281C23×C71C22×D412yes—
282C23×C71C2×#4112yes—
283C23×C71C2×#4112yes—
284C23×C71C2×#4112yes—
285C23×C71H(5,𝔽2)12yes—
286C23×C712−1+412yes—
287C23×C71C2511yescharacteristic
288C22×D71—28no—
289C22×D71—28no—
290C22×D71—28no—
291C22×D71—22no—
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—44no—
298C22×D71—44no—
299C22×D71—44no—
300C22×D71—44no—
301C22×D71C23×C414yes—
302C2×C4×C71—28no—
303C2×C4×C71—28no—
304C2×C4×C71—28no—
305C2×C4×C71—28no—
306C2×C4×C71—28no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—416no—
321C2×C4×C71—44no—
322C2×C4×C71C23×C414yes—
323C2×C4×C71C23×C414yes—
324C2×C4×C71C22×D414yes—
325C2×C4×C71C2×#4114yes—
326C2×C4×C71C2×#4114yes—
327C22⋊D71—232no—
328C2×Dic71—28no—
329C2×Dic71—28no—
330C2×Dic71—28no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—44no—
347C2×Dic71—44no—
348C2×Dic71—44no—
349C2×Dic71C4×D4116yes—
350C2×Dic71C23×C414yes—
351C2×Dic71C23×C414yes—
352C2×Dic71C23×C414yes—
353C2×Dic71C22×D414yes—
354C2×Dic71C22×D414yes—
355C2×Dic71C2×#4114yes—
356C4×D71—416no—
357Dic142—232no—
358C22×C71—24no—
359C22×C71—24no—
360C22×C71—24no—
361C22×C71—416no—
362C22×C71—42no—
363C22×C71—42no—
364C22×C71—42no—
365C22×C71—42no—
366C22×C71C2×C4×D414yes—
367C22×C71C4×#4114yes—
368C22×C71#52014yes—
369C22×C71#54614yes—
370C22×C71#54814yes—
371C22×C71#55614yes—
372C22×C71#55914yes—
373C22×C71C24×C411yescharacteristic
374C22×C71C23×D411yescharacteristic
375C22×C71C22×#4111yescharacteristic
376C22×C71C22×#4111yescharacteristic
377C22×C71C22×#4111yescharacteristic
378C22×C71C2×H(5,𝔽2)11yescharacteristic
379C22×C71C2×2−1+411yescharacteristic
380C2×D71—24no—
381C2×D71—24no—
382C2×D71—24no—
383C2×D71—416no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—42no—
388C4×C71—24no—
389C4×C71—24no—
390C4×C71—24no—
391C4×C71—24no—
392C4×C71—24no—
393C4×C71—42no—
394Dic71—24no—
395Dic71—24no—
396Dic71—24no—
397Dic71—42no—
398Dic71—42no—
399Dic71—42no—
400Dic71C2×C4×D418yes—
401C2×#2367—711nomaximal, Sylow
402C2×C71—44no—
403C2×C71#236718yescomplemented
404C2×C71C22×C4×D411yescharacteristic
405C2×C71C2×C4×#4111yescharacteristic
406C2×C71C2×#52011yescharacteristic
407C2×C71C2×#54611yescharacteristic
408C2×C71C2×#54811yescharacteristic
409C2×C71C2×#55611yescharacteristic
410C2×C71C2×#55911yescharacteristic
411D71—44no—
412C22×#124—711no—
413C22×C4×Q8—711no—
414C22×C4×D4—711no—
415#2367—7116no—
416C2×#391—711no—
417C2×#390—711no—
418C2×#388—711no—
419C2×#388—711no—
420C2×#388—711no—
421C2×#388—711no—
422C2×#385—711no—
423C2×#385—711no—
424C2×C4×C4⋊C4—711no—
425C2×C4×C4⋊C4—711no—
426C2×C4×C22⋊C4—711no—
427C2×C4×C22⋊C4D7111yescharacteristic, complemented
428C71C2×#236711yescharacteristic, complemented, Sylow
429C23×Q8—711no—
430C23×D4—711no—
431C24×C4—711no—
432C24×C4C2×D7111yescharacteristic
433C2×#124—7116no—
434C2×#124—718no—
435C2×C4×Q8—718no—
436C2×C4×Q8—1428no—
437C2×C4×D4—718no—
438C2×C4×D4—1428no—
439C22×C4⋊C4—711no—
440C22×C4⋊C4—711no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4—711no—
443C22×C4⋊C4—711no—
444C22×C4⋊C4—711no—
445C22×C22⋊C4—711no—
446C22×C22⋊C4—711no—
447C22×C22⋊C4—711no—
448C22×C22⋊C4—711no—
449C22×C22⋊C4—711no—
450C22×C22⋊C4—711no—
451C22×C22⋊C4—711no—
452C22×C22⋊C4—711no—
453C22×C22⋊C4C2×D7111yescharacteristic
454C22×C22⋊C4C2×D7111yescharacteristic
455C22×C42—711no—
456C22×C42—711no—
457C22×C42—711no—
458C22×C42—711no—
459C22×C42—711no—
460C22×C42C2×D7111yescharacteristic
461C22×C42C2×D7111yescharacteristic
462#391—718no—
463#390—718no—
464#388—718no—
465#388—718no—
466#388—718no—
467#388—718no—
468#385—718no—
469#385—718no—
470C4×C4⋊C4—718no—
471C4×C4⋊C4—718no—
472C4×C22⋊C4—718no—
473C4×C22⋊C4C2×D7118yescomplemented
474C2×#95—711no—
475C2×#95—711no—
476C2×#95—711no—
477C2×#95—711no—
478C2×#95—711no—
479C2×#95—711no—
480C2×#95C2×D7111yescharacteristic
481C2×#95C2×D7111yescharacteristic
482C25—711no—
483C25C22×D7111yescharacteristic
484C22×Q8—718no—
485C22×Q8—714no—
486C22×Q8—1424no—
487C22×Q8—1424no—
488C22×D4—718no—
489C22×D4—714no—
490C22×D4—1424no—
491C22×D4—1424no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—42no—
495C23×C4—2842no—
496C23×C4—714no—
497C23×C4—711no—
498C23×C4—711no—
499C23×C4—711no—
500C23×C4—711no—
501C23×C4—711no—
502C23×C4—711no—
503C23×C4—711no—
504C23×C4—1424no—
505C23×C4—1424no—
506C23×C4C22×D7111yescharacteristic
507C23×C4C22×D7114yes—
508C23×C4C22×D7111yescharacteristic
509C23×C4C22×D7111yescharacteristic
510C23×C4C22×D7111yescharacteristic
511C23×C4C22×D7111yescharacteristic
512C23×C4C22×D7111yescharacteristic
513#124—7164no—
514C4×Q8—14232no—
515C4×D4—14232no—
516C2×C4⋊C4—718no—
517C2×C4⋊C4—714no—
518C2×C4⋊C4—714no—
519C2×C4⋊C4—714no—
520C2×C4⋊C4—714no—
521C2×C4⋊C4—714no—
522C2×C4⋊C4—714no—
523C2×C4⋊C4—1424no—
524C2×C4⋊C4—1424no—
525C2×C4⋊C4—1424no—
526C2×C4⋊C4—1424no—
527C2×C4⋊C4—1424no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—2842no—
530C2×C22⋊C4—2842no—
531C2×C22⋊C4—714no—
532C2×C22⋊C4—714no—
533C2×C22⋊C4—718no—
534C2×C22⋊C4—714no—
535C2×C22⋊C4—718no—
536C2×C22⋊C4—718no—
537C2×C22⋊C4—714no—
538C2×C22⋊C4—714no—
539C2×C22⋊C4—714no—
540C2×C22⋊C4—714no—
541C2×C22⋊C4—714no—
542C2×C22⋊C4—1424no—
543C2×C22⋊C4—1424no—
544C2×C22⋊C4—1424no—
545C2×C22⋊C4C4×D7118yescomplemented
546C2×C22⋊C4C22×D7114yes—
547C2×C22⋊C4C22×D7114yes—
548C2×C42—24no—
549C2×C42—42no—
550C2×C42—2842no—
551C2×C42—714no—
552C2×C42—718no—
553C2×C42—714no—
554C2×C42—714no—
555C2×C42—714no—
556C2×C42—714no—
557C2×C42—1424no—
558C2×C42—1424no—
559C2×C42—1424no—
560C2×C42C22×D7114yes—
561C2×C42C22×D7114yes—
562#95—714no—
563#95—714no—
564#95—714no—
565#95—714no—
566#95—714no—
567#95—714no—
568#95C22×D7114yes—
569#95C22×D7114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—714no—
577C24—712no—
578C24—1422no—
579C24—1422no—
580C24—1422no—
581C24—1422no—
582C24—1422no—
583C24—1422no—
584C24C2×C4×D7114yes—
585C24C23×D7112yes—
586C24C23×D7111yescharacteristic
587C2×Q8—7116no—
588C2×Q8—1428no—
589C2×Q8—1428no—
590C2×Q8—14232no—
591C2×D4—7116no—
592C2×D4—1428no—
593C2×D4—1428no—
594C2×D4—14232no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—28416no—
613C22×C4—2844no—
614C22×C4—714no—
615C22×C4—714no—
616C22×C4—714no—
617C22×C4—712no—
618C22×C4—714no—
619C22×C4—714no—
620C22×C4—714no—
621C22×C4—712no—
622C22×C4—712no—
623C22×C4—712no—
624C22×C4—712no—
625C22×C4—712no—
626C22×C4—712no—
627C22×C4—1428no—
628C22×C4—1422no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4—1422no—
633C22×C4—1422no—
634C22×C4—1422no—
635C22×C4—1422no—
636C22×C4—1422no—
637C22×C4—1428no—
638C22×C4—1422no—
639C22×C4—1422no—
640C22×C4—1422no—
641C22×C4—1422no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4C2×C4×D7114yes—
645C22×C4C2×C4×D7114yes—
646C22×C4D4×D7114yes—
647C22×C4#1176586514yes—
648C22×C4#1176586514yes—
649C22×C4C23×D7112yes—
650C22×C4C23×D7112yes—
651C22×C4C23×D7112yes—
652C22×C4C23×D7112yes—
653C22×C4C23×D7112yes—
654C22×C4C23×D7112yes—
655C4⋊C4—7116no—
656C4⋊C4—1428no—
657C4⋊C4—1428no—
658C4⋊C4—1428no—
659C4⋊C4—1428no—
660C4⋊C4—1428no—
661C22⋊C4—28no—
662C22⋊C4—2844no—
663C22⋊C4—2844no—
664C22⋊C4—7116no—
665C22⋊C4—7116no—
666C22⋊C4—7116no—
667C22⋊C4—1428no—
668C22⋊C4—1428no—
669C22⋊C4—1428no—
670C22⋊C4C2×C4×D71116yescomplemented
671C42—28no—
672C42—44no—
673C42—2844no—
674C42—7116no—
675C42—1428no—
676C42—1428no—
677C42—1428no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—2844no—
692C23—2844no—
693C23—2844no—
694C23—2844no—
695C23—714no—
696C23—1422no—
697C23—1422no—
698C23—1422no—
699C23—1422no—
700C23—1422no—
701C23—1422no—
702C23—1428no—
703C23—1428no—
704C23—1428no—
705C23C22×C4×D7114yes—
706C23C22×C4×D7112yes—
707C23C2×D4×D7112yes—
708C23#41×D7112yes—
709C23C2×#1176586512yes—
710C23C2×#1176586512yes—
711C23#1455617312yes—
712C23#1455617512yes—
713C23C24×D7111yescharacteristic
714Q8—14232no—
715D4—14232no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—28416no—
737C2×C4—2844no—
738C2×C4—2844no—
739C2×C4—2844no—
740C2×C4—714no—
741C2×C4—714no—
742C2×C4—714no—
743C2×C4—7116no—
744C2×C4—714no—
745C2×C4—714no—
746C2×C4—714no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—1422no—
753C2×C4—1422no—
754C2×C4—1422no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1428no—
763C2×C4—1428no—
764C2×C4—1428no—
765C2×C4C22×C4×D7114yes—
766C2×C4C22×C4×D7114yes—
767C2×C4C2×D4×D7114yes—
768C2×C4C2×#1176586514yes—
769C2×C4C2×#1176586514yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—2842no—
779C22—2842no—
780C22—2842no—
781C22—28416no—
782C22—2842no—
783C22—1424no—
784C22—1424no—
785C22—1424no—
786C22C4×D4×D7114yes—
787C22C4×#1176586514yes—
788C22#1798647814yes—
789C22#1798663914yes—
790C22#1798665814yes—
791C22#1798671714yes—
792C22#1798673214yes—
793C22C23×C4×D7111yescharacteristic
794C22C22×D4×D7111yescharacteristic
795C22C2×#41×D7111yescharacteristic
796C22C22×#1176586511yescharacteristic
797C22C22×#1176586511yescharacteristic
798C22C2×#1455617311yescharacteristic
799C22C2×#1455617511yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—24no—
805C4—42no—
806C4—2842no—
807C4—2842no—
808C4—2842no—
809C4—718no—
810C4—1424no—
811C4—1424no—
812C4—1424no—
813C2—44no—
814C2—2844no—
815C2#2259141218yesdirect product factor
816C2C2×C4×D4×D7111yescharacteristic
817C2C2×C4×#1176586511yescharacteristic
818C2C2×#1798647811yescharacteristic
819C2C2×#1798663911yescharacteristic
820C2C2×#1798665811yescharacteristic
821C2C2×#1798671711yescharacteristic
822C2C2×#1798673211yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×C4×C22⋊C4×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
cosocleC23×C71C25
hypercenterC2×C4×C22⋊C4D71
hypocenterC71C2×#2367
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic142C2semidirect
4. #22591412C2direct (N × H)
5. C2×#17985903C2semidirect
7. C2×#17985893C2semidirect
8. C2×#17985892C2semidirect
9. C2×#17985890C2semidirect
10. C2×#17985890C2semidirect
11. C2×#17985873C2semidirect
12. C2×#17985872C2semidirect
13. C2×C4×Dic71⋊C4C2semidirect
14. C2×#17985850C2semidirect
15. C2×#17985846C2semidirect
16. C2×C4×C22⋊C4×C71C2semidirect
20. C2×#14556114C4semidirect
23. C2×C4×Dic142C22semidirect
45. #17985903C22semidirect
47. #17985893C22semidirect
48. #17985892C22semidirect
49. #17985890C22semidirect
50. #17985890C22semidirect
51. #17985873C22semidirect
52. #17985872C22semidirect
53. C4×Dic71⋊C4C22semidirect
54. #17985850C22semidirect
55. #17985846C22semidirect
67. C4×C22⋊C4×C71C22semidirect
73. C22×Dic142C2×C4semidirect
90. #14556114C2×C4semidirect
107. C2×C22⋊Dic71C2×C4semidirect
114. C2×(C2×D71)⋊C4C2×C4semidirect
115. C2×(C2×D71)⋊C4C2×C4semidirect
125. C2×C4×Dic71C2×C4semidirect
149. C2×C22⋊C4×C71C2×C4semidirect
169. C2×Dic142C22×C4semidirect
214. C22⋊Dic71C22×C4semidirect
218. (C2×D71)⋊C4C22×C4semidirect
219. (C2×D71)⋊C4C22×C4semidirect
224. C4×Dic71C22×C4semidirect
263. C22⋊C4×C71C22×C4semidirect
403. C2×C71#2367semidirect
427. C2×C4×C22⋊C4D71semidirect
428. C71C2×#2367semidirect
473. C4×C22⋊C4C2×D71semidirect
545. C2×C22⋊C4C4×D71semidirect
670. C22⋊C4C2×C4×D71semidirect
815. C2#22591412direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561142
C22×C4×Dic1422
C22×C4×C22⋊D712
#225914122
C2×#179859032
C2×#179858992
C2×#179858932
C2×#179858922
C2×#179858902
C2×#179858732
C2×#179858722
C2×C4×Dic71⋊C42
C2×#179858502
C2×#179858462
C2×C4×C22⋊C4×C712
C2×#236771