Finite Group Databasebeta

← C2×#22593718 #32167679

Subgroups — C2×#22593718 #32167679

Order 18176.

3094 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556106C211yesmaximal, characteristic
2C22×C4⋊C4×D71C211yesmaximal, characteristic
3#22593718C2116yesmaximal, direct product factor
4C2×#17985933C211yesmaximal, characteristic, complemented
5C2×#17985932C211yesmaximal, characteristic, complemented
6C2×#17985920C211yesmaximal, characteristic, complemented
7C2×#17985919C211yesmaximal, characteristic, complemented
8C2×#17985897C211yesmaximal, characteristic, complemented
9C2×#17985894C211yesmaximal, characteristic, complemented
10C2×#17985894C211yesmaximal, characteristic, complemented
11C2×#17985873C211yesmaximal, characteristic
12C2×#17985873C211yesmaximal, characteristic
13C2×#17985870C211yesmaximal, characteristic
14C2×#17985870C211yesmaximal, characteristic
15C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
16C2×#389×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556106—28no—
22C2×#14556106C2218yes—
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C2×C4⋊C4×D71—28no—
35C2×C4⋊C4×D71C2218yes—
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41#17985933C2218yescomplemented
42#17985932C2218yescomplemented
43#17985920C2218yescomplemented
44#17985919C2218yescomplemented
45#17985897C2218yescomplemented
46#17985894C2218yescomplemented
47#17985894C2218yescomplemented
48#17985873C2218yes—
49#17985873C2218yes—
50#17985870C2218yes—
51#17985870C2218yes—
52C4×(C2×D71)⋊C4C2218yes—
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic
66#389×C71C2218yescomplemented
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C22×Dic142—24no—
71C22×Dic142—42no—
72C22×Dic142—42no—
73C22×Dic142C2314yes—
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71—24no—
84C22×C4×D71—24no—
85C22×C4×D71—42no—
86C22×C4×D71—42no—
87C22×C4×D71—42no—
88C22×C4×D71—42no—
89C22×C4×D71D418yes—
90C22×C4×D71C2314yes—
91C22×C4×D71C2314yes—
92C22×C4×D71C2314yes—
93#14556106—232no—
94C2×C4⋊Dic71—24no—
95C2×C4⋊Dic71—24no—
96C2×C4⋊Dic71—42no—
97C2×C4⋊Dic71C2314yes—
98C2×C4⋊Dic71C2314yes—
99C2×C4⋊Dic71C2314yes—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4—24no—
104C2×Dic71⋊C4—24no—
105C2×Dic71⋊C4—24no—
106C2×Dic71⋊C4—42no—
107C2×Dic71⋊C4—42no—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×Dic71⋊C4C2314yes—
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×Dic71⋊C4C2314yes—
116C4⋊C4×D71—232no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4Q818yescomplemented
120C2×(C2×D71)⋊C4Q818yescomplemented
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×C4×Dic71—42no—
126C2×C4×Dic71C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C2×C4⋊C4×C71—24no—
143C2×C4⋊C4×C71—24no—
144C2×C4⋊C4×C71—24no—
145C2×C4⋊C4×C71—42no—
146C2×C4⋊C4×C71C2314yes—
147C2×C4⋊C4×C71C2314yes—
148C2×C4⋊C4×C71C2314yes—
149C2×C4⋊C4×C71C2314yes—
150C2×C42×C71—42no—
151C2×C42×C71C2314yes—
152#95×C71C2314yes—
153#95×C71C2314yes—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71C2×D414yes—
159C23×D71C2×Q814yes—
160C23×D71C2×Q814yes—
161C23×D71C2412yes—
162C2×Dic142—28no—
163C2×Dic142—44no—
164C2×Dic142—44no—
165C2×Dic142—416no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
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×Dic71C2×D414yes—
184C22×Dic71C2×Q814yes—
185C22×Dic71C2×Q814yes—
186C22×Dic71#4114yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C2×C4×D71—232no—
195C2×C4×D71—28no—
196C2×C4×D71—28no—
197C2×C4×D71—28no—
198C2×C4×D71—28no—
199C2×C4×D71—416no—
200C2×C4×D71—44no—
201C2×C4×D71—44no—
202C2×C4×D71—44no—
203C2×C4×D71—44no—
204C2×C4×D71—416no—
205C2×C4×D71C2×D4116yes—
206C4⋊Dic71—28no—
207C4⋊Dic71—28no—
208C4⋊Dic71—44no—
209Dic71⋊C4—28no—
210Dic71⋊C4—28no—
211Dic71⋊C4—28no—
212Dic71⋊C4—28no—
213Dic71⋊C4—28no—
214Dic71⋊C4—28no—
215Dic71⋊C4—44no—
216Dic71⋊C4—44no—
217(C2×D71)⋊C4—28no—
218(C2×D71)⋊C4—28no—
219(C2×D71)⋊C4C2×Q8116yescomplemented
220(C2×D71)⋊C4C2×Q8116yescomplemented
221C4×Dic71—44no—
222C24×C71C2411yescharacteristic
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
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×C71C2×D414yes—
241C22×C4×C71C2×Q814yes—
242C22×C4×C71C2×Q814yes—
243C22×C4×C71#4114yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2412yes—
251C4⋊C4×C71—28no—
252C4⋊C4×C71—28no—
253C4⋊C4×C71—28no—
254C4⋊C4×C71—44no—
255C42×C71—44no—
256C23×C71C22×D412yes—
257C23×C71C22×Q812yes—
258C23×C71C22×Q812yes—
259C23×C71C2×#4112yes—
260C23×C71C2×#4112yes—
261C23×C71H(5,𝔽2)12yes—
262C23×C71H(5,𝔽2)12yes—
263C23×C71C2511yescharacteristic
264C22×D71—28no—
265C22×D71—28no—
266C22×D71—28no—
267C22×D71—28no—
268C22×D71—28no—
269C22×D71—28no—
270C22×D71—22no—
271C22×D71—22no—
272C22×D71—22no—
273C22×D71—22no—
274C22×D71C4⋊Q8116yes—
275C22×D71C22×D414yes—
276C22×D71C22×Q814yes—
277C22×D71C22×Q814yes—
278C2×C4×C71—28no—
279C2×C4×C71—28no—
280C2×C4×C71—28no—
281C2×C4×C71—28no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—44no—
300C2×C4×C71—44no—
301C2×C4×C71—44no—
302C2×C4×C71C22×D414yes—
303C2×C4×C71C22×Q814yes—
304C2×C4×C71C22×Q814yes—
305C2×C4×C71C2×#4114yes—
306C2×Dic71—28no—
307C2×Dic71—28no—
308C2×Dic71—28no—
309C2×Dic71—28no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—44no—
328C2×Dic71—44no—
329C2×Dic71—44no—
330C2×Dic71C22×D414yes—
331C2×Dic71C22×Q814yes—
332C2×Dic71C22×Q814yes—
333C2×Dic71C2×#4114yes—
334C4×D71—232no—
335C4×D71—416no—
336C4×D71—416no—
337Dic142—416no—
338C22×C71#52514yes—
339C22×C71C2×C4⋊Q814yes—
340C22×C71#53414yes—
341C22×C71#55414yes—
342C22×C71#55414yes—
343C22×C71#55414yes—
344C22×C71#55414yes—
345C22×C71C23×D411yescharacteristic
346C22×C71C23×Q811yescharacteristic
347C22×C71C23×Q811yescharacteristic
348C22×C71C22×#4111yescharacteristic
349C22×C71C22×#4111yescharacteristic
350C22×C71C2×H(5,𝔽2)11yescharacteristic
351C22×C71C2×H(5,𝔽2)11yescharacteristic
352C2×D71—232no—
353C2×D71—24no—
354C2×D71—24no—
355C2×D71—24no—
356C2×D71—24no—
357C2×D71—24no—
358C2×D71—24no—
359C2×D71C2×C4⋊Q818yes—
360C4×C71—24no—
361C4×C71—24no—
362C4×C71—24no—
363C4×C71—24no—
364C4×C71—42no—
365C4×C71—42no—
366C4×C71—42no—
367Dic71—24no—
368Dic71—24no—
369Dic71—24no—
370Dic71—24no—
371Dic71—42no—
372Dic71—42no—
373Dic71—42no—
374C2×#2583—711nomaximal, Sylow
375C2×C71#258318yescomplemented
376C2×C71C2×#52511yescharacteristic
377C2×C71C22×C4⋊Q811yescharacteristic
378C2×C71C2×#53411yescharacteristic
379C2×C71C2×#55411yescharacteristic
380C2×C71C2×#55411yescharacteristic
381C2×C71C2×#55411yescharacteristic
382C2×C71C2×#55411yescharacteristic
383D71—28no—
384C22×C22⋊Q8—711no—
385C23×C4⋊C4—711no—
386#2583—7116no—
387C2×#398—711no—
388C2×#398—711no—
389C2×#395—711no—
390C2×#395—711no—
391C2×#389—711no—
392C2×#389—711no—
393C2×#389—711no—
394C2×#389D7111yescharacteristic, complemented
395C2×#385—711no—
396C2×#385—711no—
397C2×#385—711no—
398C2×#385—711no—
399C2×C4×C22⋊C4—711no—
400C71C2×#258311yescharacteristic, complemented, Sylow
401C23×Q8—711no—
402C24×C4—711no—
403C24×C4—711no—
404C24×C4—711no—
405C2×C22⋊Q8—718no—
406C2×C22⋊Q8—1428no—
407C22×C4⋊C4—711no—
408C22×C4⋊C4—711no—
409C22×C4⋊C4—711no—
410C22×C4⋊C4—711no—
411C22×C4⋊C4—711no—
412C22×C4⋊C4—711no—
413C22×C4⋊C4—711no—
414C22×C4⋊C4—711no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4—711no—
417C22×C4⋊C4—711no—
418C22×C4⋊C4—718no—
419C22×C4⋊C4—1428no—
420C22×C4⋊C4C2×D7111yescharacteristic
421C22×C4⋊C4C2×D7111yescharacteristic
422C22×C4⋊C4C2×D7111yescharacteristic
423C22×C4⋊C4C2×D7111yescharacteristic
424C22×C22⋊C4—711no—
425C22×C22⋊C4—711no—
426C22×C22⋊C4—711no—
427C22×C22⋊C4—711no—
428C22×C42—711no—
429C22×C42C2×D7111yescharacteristic
430#398—718no—
431#398—718no—
432#395—718no—
433#395—718no—
434#389—718no—
435#389—718no—
436#389—718no—
437#389C2×D7118yescomplemented
438#385—718no—
439#385—718no—
440#385—718no—
441#385—718no—
442C4×C22⋊C4—718no—
443C2×#95—711no—
444C2×#95—711no—
445C2×#95—711no—
446C2×#95—711no—
447C2×#95—711no—
448C2×#95—711no—
449C2×#95—711no—
450C2×#95—711no—
451C2×#95C2×D7111yescharacteristic
452C2×#95C2×D7111yescharacteristic
453C25—711no—
454C22×Q8—2842no—
455C22×Q8—2842no—
456C22×Q8—714no—
457C22×Q8—1424no—
458C23×C4—2842no—
459C23×C4—2842no—
460C23×C4—2842no—
461C23×C4—2842no—
462C23×C4—718no—
463C23×C4—714no—
464C23×C4—714no—
465C23×C4—711no—
466C23×C4—711no—
467C23×C4—711no—
468C23×C4—711no—
469C23×C4—711no—
470C23×C4—711no—
471C23×C4—711no—
472C23×C4—714no—
473C23×C4—1424no—
474C23×C4—1424no—
475C23×C4—1424no—
476C23×C4—1424no—
477C23×C4C22×D7111yescharacteristic
478C23×C4C22×D7111yescharacteristic
479C23×C4C22×D7111yescharacteristic
480C23×C4C22×D7111yescharacteristic
481C23×C4C22×D7111yescharacteristic
482C23×C4C22×D7111yescharacteristic
483C23×C4C22×D7111yescharacteristic
484C22⋊Q8—14232no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—2842no—
490C2×C4⋊C4—2842no—
491C2×C4⋊C4—2842no—
492C2×C4⋊C4—714no—
493C2×C4⋊C4—714no—
494C2×C4⋊C4—714no—
495C2×C4⋊C4—714no—
496C2×C4⋊C4—714no—
497C2×C4⋊C4—714no—
498C2×C4⋊C4—714no—
499C2×C4⋊C4—714no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—714no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—14232no—
504C2×C4⋊C4—1424no—
505C2×C4⋊C4—1424no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4—1424no—
508C2×C4⋊C4—1424no—
509C2×C4⋊C4—1424no—
510C2×C4⋊C4—1424no—
511C2×C4⋊C4—1424no—
512C2×C4⋊C4C22×D7114yes—
513C2×C4⋊C4C22×D7114yes—
514C2×C4⋊C4C22×D7114yes—
515C2×C4⋊C4C22×D7114yes—
516C2×C22⋊C4—718no—
517C2×C22⋊C4—718no—
518C2×C22⋊C4—714no—
519C2×C22⋊C4—714no—
520C2×C22⋊C4—714no—
521C2×C22⋊C4—714no—
522C2×C22⋊C4—1424no—
523C2×C22⋊C4—1424no—
524C2×C42—42no—
525C2×C42—2842no—
526C2×C42—714no—
527C2×C42C22×D7114yes—
528#95—714no—
529#95—714no—
530#95—714no—
531#95—714no—
532#95—714no—
533#95—714no—
534#95—714no—
535#95—714no—
536#95C22×D7114yes—
537#95C22×D7114yes—
538C24—714no—
539C24—714no—
540C24—714no—
541C24—712no—
542C24—1422no—
543C24—1422no—
544C24—1422no—
545C24—1422no—
546C24C23×D7111yescharacteristic
547C2×Q8—2844no—
548C2×Q8—2844no—
549C2×Q8—28416no—
550C2×Q8—1428no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—2844no—
569C22×C4—2844no—
570C22×C4—28416no—
571C22×C4—2844no—
572C22×C4—2844no—
573C22×C4—28416no—
574C22×C4—7116no—
575C22×C4—714no—
576C22×C4—714no—
577C22×C4—714no—
578C22×C4—714no—
579C22×C4—712no—
580C22×C4—712no—
581C22×C4—712no—
582C22×C4—712no—
583C22×C4—712no—
584C22×C4—712no—
585C22×C4—712no—
586C22×C4—1428no—
587C22×C4—1428no—
588C22×C4—1428no—
589C22×C4—14232no—
590C22×C4—1422no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4—1422no—
599C22×C4—1422no—
600C22×C4—1422no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4—1422no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4—1422no—
607C22×C4—1428no—
608C22×C4D4×D7114yes—
609C22×C4Q8×D7114yes—
610C22×C4Q8×D7114yes—
611C22×C4#1176586514yes—
612C22×C4C23×D7112yes—
613C22×C4C23×D7112yes—
614C22×C4C23×D7112yes—
615C22×C4C23×D7112yes—
616C22×C4C23×D7112yes—
617C22×C4C23×D7112yes—
618C22×C4C23×D7112yes—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—44no—
623C4⋊C4—2844no—
624C4⋊C4—2844no—
625C4⋊C4—2844no—
626C4⋊C4—1428no—
627C4⋊C4—1428no—
628C4⋊C4—1428no—
629C4⋊C4—1428no—
630C4⋊C4—1428no—
631C4⋊C4—1428no—
632C4⋊C4—1428no—
633C4⋊C4—1428no—
634C22⋊C4—7116no—
635C22⋊C4—7116no—
636C22⋊C4—1428no—
637C22⋊C4—1428no—
638C42—44no—
639C42—2844no—
640C23—714no—
641C23—714no—
642C23—714no—
643C23—7116no—
644C23—1422no—
645C23—1422no—
646C23—1422no—
647C23—1422no—
648C23—1428no—
649C23—1428no—
650C23—1428no—
651C23—1428no—
652C23—1428no—
653C23—1428no—
654C23C2×D4×D7112yes—
655C23C2×Q8×D7112yes—
656C23C2×Q8×D7112yes—
657C23#41×D7112yes—
658C23C2×#1176586512yes—
659C23#1455617312yes—
660C23#1455617412yes—
661C23C24×D7111yescharacteristic
662Q8—28416no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—28416no—
688C2×C4—28416no—
689C2×C4—2844no—
690C2×C4—2844no—
691C2×C4—2844no—
692C2×C4—714no—
693C2×C4—714no—
694C2×C4—714no—
695C2×C4—714no—
696C2×C4—14232no—
697C2×C4—1422no—
698C2×C4—1422no—
699C2×C4—1422no—
700C2×C4—1422no—
701C2×C4—1422no—
702C2×C4—1422no—
703C2×C4—1422no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4—1422no—
708C2×C4—1422no—
709C2×C4—1422no—
710C2×C4—1422no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4—1428no—
715C2×C4—1428no—
716C2×C4—1428no—
717C2×C4—1428no—
718C2×C4C2×D4×D7114yes—
719C2×C4C2×Q8×D7114yes—
720C2×C4C2×Q8×D7114yes—
721C2×C4C2×#1176586514yes—
722C22—718no—
723C22—1424no—
724C22—1424no—
725C22—1424no—
726C22—1424no—
727C22—1424no—
728C22—1424no—
729C22—14232no—
730C22#1798650814yes—
731C22C4⋊Q8×D7114yes—
732C22#1798655714yes—
733C22#1798670314yes—
734C22#1798670414yes—
735C22#1798670514yes—
736C22#1798670914yes—
737C22C22×D4×D7111yescharacteristic
738C22C22×Q8×D7111yescharacteristic
739C22C22×Q8×D7111yescharacteristic
740C22C2×#41×D7111yescharacteristic
741C22C22×#1176586511yescharacteristic
742C22C2×#1455617311yescharacteristic
743C22C2×#1455617411yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—2842no—
752C4—2842no—
753C4—2842no—
754C4—1424no—
755C4—1424no—
756C4—1424no—
757C4—1424no—
758C2—1428no—
759C2#2259371818yesdirect product factor
760C2C2×#1798650811yescharacteristic
761C2C2×C4⋊Q8×D7111yescharacteristic
762C2C2×#1798655711yescharacteristic
763C2C2×#1798670311yescharacteristic
764C2C2×#1798670411yescharacteristic
765C2C2×#1798670511yescharacteristic
766C2C2×#1798670911yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#389×C71C2
socleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×#389D71
hypocenterC71C2×#2583
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #22593718C2direct (N × H)
4. C2×#17985933C2semidirect
5. C2×#17985932C2semidirect
6. C2×#17985920C2semidirect
7. C2×#17985919C2semidirect
8. C2×#17985897C2semidirect
9. C2×#17985894C2semidirect
10. C2×#17985894C2semidirect
16. C2×#389×C71C2semidirect
41. #17985933C22semidirect
42. #17985932C22semidirect
43. #17985920C22semidirect
44. #17985919C22semidirect
45. #17985897C22semidirect
46. #17985894C22semidirect
47. #17985894C22semidirect
66. #389×C71C22semidirect
119. C2×(C2×D71)⋊C4Q8semidirect
120. C2×(C2×D71)⋊C4Q8semidirect
219. (C2×D71)⋊C4C2×Q8semidirect
220. (C2×D71)⋊C4C2×Q8semidirect
375. C2×C71#2583semidirect
394. C2×#389D71semidirect
400. C71C2×#2583semidirect
437. #389C2×D71semidirect
759. C2#22593718direct (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×C4⋊C4×D712
#225937182
C2×#179859332
C2×#179859322
C2×#179859202
C2×#179859192
C2×#179858972
C2×#179858942
C2×#179858732
C2×#179858702
C2×C4×(C2×D71)⋊C42
C2×#389×C712
C2×#258371