Finite Group Databasebeta

← C2×#22593370 #32169269

Subgroups — C2×#22593370 #32169269

Order 18176.

2446 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556118C211yesmaximal, characteristic
2C22×#14556118C211yesmaximal, characteristic
3#22593370C2116yesmaximal, direct product factor
4C2×#17985933C211yesmaximal, characteristic
5C2×#17985932C211yesmaximal, characteristic
6C2×#17985931C211yesmaximal, characteristic
7C2×#17985896C211yesmaximal, characteristic
8C2×#17985896C211yesmaximal, characteristic
9C2×#17985894C211yesmaximal, characteristic
10C2×#17985894C211yesmaximal, characteristic
11C2×#17985868C211yesmaximal, characteristic
12C2×#17985868C211yesmaximal, characteristic
13C2×#17985868C211yesmaximal, characteristic
14C2×#17985850C211yesmaximal, characteristic
15C2×#17985850C211yesmaximal, characteristic
16C2×#398×C71C211yesmaximal, characteristic
17C2×#14556118—28no—
18C2×#14556118—28no—
19C2×#14556118C2218yes—
20C2×#14556118C2218yes—
21C22×C4⋊Dic71C2211yescharacteristic
22C22×C4⋊Dic71C2211yescharacteristic
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×Dic71⋊C4C2211yescharacteristic
36C22×Dic71⋊C4C2211yescharacteristic
37C22×Dic71⋊C4C2211yescharacteristic
38C22×Dic71⋊C4C2211yescharacteristic
39C22×C4×Dic71C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44#17985933C2218yes—
45#17985932C2218yes—
46#17985931C2218yes—
47#17985896C2218yes—
48#17985896C2218yes—
49#17985894C2218yes—
50#17985894C2218yes—
51#17985868C2218yes—
52#17985868C2218yes—
53#17985868C2218yes—
54#17985850C2218yes—
55#17985850C2218yes—
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
65#398×C71C2218yes—
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C23×Dic71C2311yescharacteristic
70C23×Dic71C2311yescharacteristic
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2311yescharacteristic
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77#14556118—232no—
78#14556118—232no—
79C2×C4⋊Dic71—24no—
80C2×C4⋊Dic71—24no—
81C2×C4⋊Dic71—42no—
82C2×C4⋊Dic71—42no—
83C2×C4⋊Dic71C2314yes—
84C2×C4⋊Dic71C2314yes—
85C2×C4⋊Dic71C2314yes—
86C2×C4⋊Dic71C2314yes—
87C2×Dic71⋊C4—24no—
88C2×Dic71⋊C4—24no—
89C2×Dic71⋊C4—24no—
90C2×Dic71⋊C4—24no—
91C2×Dic71⋊C4—24no—
92C2×Dic71⋊C4—24no—
93C2×Dic71⋊C4—24no—
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—42no—
98C2×Dic71⋊C4—42no—
99C2×Dic71⋊C4D418yes—
100C2×Dic71⋊C4Q818yes—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×Dic71⋊C4C2314yes—
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×C4×Dic71—24no—
116C2×C4×Dic71—24no—
117C2×C4×Dic71—24no—
118C2×C4×Dic71—24no—
119C2×C4×Dic71Q818yes—
120C2×C4×Dic71C2314yes—
121C2×C4×Dic71C2314yes—
122C2×C4×Dic71C2314yes—
123C2×C4×Dic71C2314yes—
124C2×C4×Dic71C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C23×C4×C71C2311yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C2×C4⋊C4×C71—24no—
138C2×C4⋊C4×C71—24no—
139C2×C4⋊C4×C71—42no—
140C2×C4⋊C4×C71—42no—
141C2×C4⋊C4×C71C2314yes—
142C2×C4⋊C4×C71C2314yes—
143C2×C4⋊C4×C71C2314yes—
144C2×C4⋊C4×C71C2314yes—
145#95×C71C2314yes—
146#95×C71C2314yes—
147#95×C71C2314yes—
148C22×Dic71—22no—
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—22no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71C2×D414yes—
165C22×Dic71C2×D414yes—
166C22×Dic71C2×Q814yes—
167C22×Dic71C2×Q814yes—
168C22×Dic71C2×Q814yes—
169C22×Dic71C2×Q814yes—
170C22×Dic71#4114yes—
171C22×Dic71#4114yes—
172C22×Dic71C2412yes—
173C22×Dic71C2412yes—
174C22×Dic71C2412yes—
175C22×Dic71C2412yes—
176C22×Dic71C2412yes—
177C22×Dic71C2412yes—
178C22×Dic71C2412yes—
179C22×Dic71C2412yes—
180C4⋊Dic71—28no—
181C4⋊Dic71—28no—
182C4⋊Dic71—44no—
183C4⋊Dic71—44no—
184Dic71⋊C4—28no—
185Dic71⋊C4—28no—
186Dic71⋊C4—28no—
187Dic71⋊C4—28no—
188Dic71⋊C4—28no—
189Dic71⋊C4—28no—
190Dic71⋊C4—28no—
191Dic71⋊C4—28no—
192Dic71⋊C4—28no—
193Dic71⋊C4—28no—
194Dic71⋊C4—44no—
195Dic71⋊C4—44no—
196Dic71⋊C4C2×D4116yes—
197Dic71⋊C4C2×Q8116yes—
198C4×Dic71—28no—
199C4×Dic71—28no—
200C4×Dic71—28no—
201C4×Dic71—28no—
202C4×Dic71C2×Q8116yes—
203C24×C71C2411yescharacteristic
204C22×C4×C71—22no—
205C22×C4×C71—22no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71C2×D414yes—
223C22×C4×C71C2×Q814yes—
224C22×C4×C71C2×Q814yes—
225C22×C4×C71C2412yes—
226C22×C4×C71C2412yes—
227C22×C4×C71C2412yes—
228C22×C4×C71C2412yes—
229C22×C4×C71C2412yes—
230C22×C4×C71C2412yes—
231C22×C4×C71C2412yes—
232C4⋊C4×C71—28no—
233C4⋊C4×C71—28no—
234C4⋊C4×C71—44no—
235C4⋊C4×C71—44no—
236C23×C71C22×D412yes—
237C23×C71C22×Q812yes—
238C23×C71C22×Q812yes—
239C23×C71C2×#4112yes—
240C23×C71C2×#4112yes—
241C23×C71H(5,𝔽2)12yes—
242C23×C712−1+412yes—
243C23×C71C2511yescharacteristic
244C2×C4×C71—28no—
245C2×C4×C71—28no—
246C2×C4×C71—28no—
247C2×C4×C71—22no—
248C2×C4×C71—22no—
249C2×C4×C71—22no—
250C2×C4×C71—22no—
251C2×C4×C71—22no—
252C2×C4×C71—22no—
253C2×C4×C71—22no—
254C2×C4×C71—22no—
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—22no—
260C2×C4×C71—22no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—44no—
266C2×C4×C71—44no—
267C2×C4×C71—44no—
268C2×C4×C71—44no—
269C2×C4×C71C22×D414yes—
270C2×C4×C71C22×Q814yes—
271C2×C4×C71C22×Q814yes—
272C2×Dic71—28no—
273C2×Dic71—28no—
274C2×Dic71—22no—
275C2×Dic71—22no—
276C2×Dic71—22no—
277C2×Dic71—22no—
278C2×Dic71—22no—
279C2×Dic71—22no—
280C2×Dic71—22no—
281C2×Dic71—22no—
282C2×Dic71—22no—
283C2×Dic71—22no—
284C2×Dic71—22no—
285C2×Dic71—22no—
286C2×Dic71—22no—
287C2×Dic71—22no—
288C2×Dic71—22no—
289C2×Dic71—22no—
290C2×Dic71—44no—
291C2×Dic71—44no—
292C2×Dic71—44no—
293C2×Dic71—44no—
294C2×Dic71#125116yescomplemented
295C2×Dic71C4⋊Q8116yes—
296C2×Dic71C22×D414yes—
297C2×Dic71C22×D414yes—
298C2×Dic71C22×Q814yes—
299C2×Dic71C22×Q814yes—
300C2×Dic71C22×Q814yes—
301C2×Dic71C22×Q814yes—
302C2×Dic71C2×#4114yes—
303C2×Dic71C2×#4114yes—
304C22×C71C2×#12514yes—
305C22×C71C2×C4⋊Q814yes—
306C22×C71#54414yes—
307C22×C71#54714yes—
308C22×C71#55014yes—
309C22×C71#55414yes—
310C22×C71#55714yes—
311C22×C71C23×D411yescharacteristic
312C22×C71C23×Q811yescharacteristic
313C22×C71C23×Q811yescharacteristic
314C22×C71C22×#4111yescharacteristic
315C22×C71C22×#4111yescharacteristic
316C22×C71C2×H(5,𝔽2)11yescharacteristic
317C22×C71C2×2−1+411yescharacteristic
318C4×C71—24no—
319C4×C71—24no—
320C4×C71—24no—
321C4×C71—42no—
322C4×C71—42no—
323C4×C71—42no—
324C4×C71—42no—
325Dic71—24no—
326Dic71—24no—
327Dic71—42no—
328Dic71—42no—
329Dic71—42no—
330Dic71—42no—
331Dic71C2×#12518yescomplemented
332Dic71C2×C4⋊Q818yes—
333C2×#2552—711nomaximal, Sylow
334C2×C71#255218yescomplemented
335C2×C71C22×#12511yescharacteristic
336C2×C71C22×C4⋊Q811yescharacteristic
337C2×C71C2×#54411yescharacteristic
338C2×C71C2×#54711yescharacteristic
339C2×C71C2×#55011yescharacteristic
340C2×C71C2×#55411yescharacteristic
341C2×C71C2×#55711yescharacteristic
342C22×#125—711no—
343C22×#125—711no—
344#2552—7116no—
345C2×#398—711no—
346C2×#398—711no—
347C2×#398—711no—
348C2×#398D7111yescharacteristic
349C2×#389—711no—
350C2×#389—711no—
351C2×#389—711no—
352C2×#389—711no—
353C2×#384—711no—
354C2×#384—711no—
355C2×#384—711no—
356C2×C4×C4⋊C4—711no—
357C2×C4×C4⋊C4—711no—
358C71C2×#255211yescharacteristic, complemented, Sylow
359C2×#125—718no—
360C2×#125—718no—
361C2×#125—1428no—
362C2×#125—1428no—
363C22×C4⋊C4—711no—
364C22×C4⋊C4—711no—
365C22×C4⋊C4—711no—
366C22×C4⋊C4—711no—
367C22×C4⋊C4—711no—
368C22×C4⋊C4—711no—
369C22×C4⋊C4—711no—
370C22×C4⋊C4—711no—
371C22×C4⋊C4—711no—
372C22×C4⋊C4—711no—
373C22×C4⋊C4—711no—
374C22×C4⋊C4—711no—
375C22×C4⋊C4—711no—
376C22×C4⋊C4—711no—
377C22×C4⋊C4—711no—
378C22×C4⋊C4—711no—
379C22×C4⋊C4—711no—
380C22×C4⋊C4—711no—
381C22×C4⋊C4C2×D7111yescharacteristic
382C22×C4⋊C4C2×D7111yescharacteristic
383C22×C4⋊C4C2×D7111yescharacteristic
384C22×C4⋊C4C2×D7111yescharacteristic
385C22×C42—711no—
386C22×C42—711no—
387C22×C42—711no—
388C22×C42—711no—
389C22×C42—711no—
390#398—718no—
391#398—718no—
392#398—718no—
393#398C2×D7118yes—
394#389—718no—
395#389—718no—
396#389—718no—
397#389—718no—
398#384—718no—
399#384—718no—
400#384—718no—
401C4×C4⋊C4—718no—
402C4×C4⋊C4—718no—
403C2×#95—711no—
404C2×#95—711no—
405C2×#95—711no—
406C2×#95—711no—
407C2×#95—711no—
408C2×#95C2×D7111yescharacteristic
409C2×#95C2×D7111yescharacteristic
410C2×#95C2×D7111yescharacteristic
411C23×C4—711no—
412C23×C4—711no—
413C23×C4—711no—
414C23×C4—711no—
415C23×C4—711no—
416C23×C4—711no—
417C23×C4—711no—
418C23×C4—711no—
419C23×C4C22×D7111yescharacteristic
420C23×C4C22×D7111yescharacteristic
421C23×C4C22×D7111yescharacteristic
422C23×C4C22×D7111yescharacteristic
423C23×C4C22×D7111yescharacteristic
424C23×C4C22×D7111yescharacteristic
425C23×C4C22×D7111yescharacteristic
426#125—14232no—
427#125—14232no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—2842no—
433C2×C4⋊C4—2842no—
434C2×C4⋊C4—2842no—
435C2×C4⋊C4—2842no—
436C2×C4⋊C4—714no—
437C2×C4⋊C4—714no—
438C2×C4⋊C4—714no—
439C2×C4⋊C4—714no—
440C2×C4⋊C4—718no—
441C2×C4⋊C4—718no—
442C2×C4⋊C4—714no—
443C2×C4⋊C4—714no—
444C2×C4⋊C4—714no—
445C2×C4⋊C4—714no—
446C2×C4⋊C4—714no—
447C2×C4⋊C4—714no—
448C2×C4⋊C4—714no—
449C2×C4⋊C4—714no—
450C2×C4⋊C4—714no—
451C2×C4⋊C4—714no—
452C2×C4⋊C4—714no—
453C2×C4⋊C4—714no—
454C2×C4⋊C4—714no—
455C2×C4⋊C4—714no—
456C2×C4⋊C4—1424no—
457C2×C4⋊C4—1424no—
458C2×C4⋊C4—1424no—
459C2×C4⋊C4—1424no—
460C2×C4⋊C4—1424no—
461C2×C4⋊C4—1424no—
462C2×C4⋊C4—1424no—
463C2×C4⋊C4—1424no—
464C2×C4⋊C4—1424no—
465C2×C4⋊C4—1424no—
466C2×C4⋊C4—1424no—
467C2×C4⋊C4—1424no—
468C2×C4⋊C4C22×D7114yes—
469C2×C4⋊C4C22×D7114yes—
470C2×C4⋊C4C22×D7114yes—
471C2×C4⋊C4C22×D7114yes—
472C2×C42—718no—
473C2×C42—714no—
474C2×C42—714no—
475C2×C42—714no—
476C2×C42—714no—
477C2×C42—714no—
478C2×C42—1424no—
479C2×C42—1424no—
480C2×C42—1424no—
481C2×C42—1424no—
482#95—714no—
483#95—714no—
484#95—714no—
485#95—714no—
486#95—714no—
487#95C22×D7114yes—
488#95C22×D7114yes—
489#95C22×D7114yes—
490C24C23×D7111yescharacteristic
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—714no—
510C22×C4—714no—
511C22×C4—714no—
512C22×C4—714no—
513C22×C4—714no—
514C22×C4—714no—
515C22×C4—712no—
516C22×C4—712no—
517C22×C4—714no—
518C22×C4—714no—
519C22×C4—712no—
520C22×C4—712no—
521C22×C4—712no—
522C22×C4—712no—
523C22×C4—712no—
524C22×C4—712no—
525C22×C4—1422no—
526C22×C4—1422no—
527C22×C4—1422no—
528C22×C4—1422no—
529C22×C4—1422no—
530C22×C4—1422no—
531C22×C4—1422no—
532C22×C4—1422no—
533C22×C4—1422no—
534C22×C4—1422no—
535C22×C4—1422no—
536C22×C4—1422no—
537C22×C4—1422no—
538C22×C4—1422no—
539C22×C4—1422no—
540C22×C4—1422no—
541C22×C4D4×D7114yes—
542C22×C4Q8×D7114yes—
543C22×C4Q8×D7114yes—
544C22×C4C23×D7112yes—
545C22×C4C23×D7112yes—
546C22×C4C23×D7112yes—
547C22×C4C23×D7112yes—
548C22×C4C23×D7112yes—
549C22×C4C23×D7112yes—
550C22×C4C23×D7112yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—2844no—
556C4⋊C4—2844no—
557C4⋊C4—2844no—
558C4⋊C4—2844no—
559C4⋊C4—7116no—
560C4⋊C4—7116no—
561C4⋊C4—1428no—
562C4⋊C4—1428no—
563C4⋊C4—1428no—
564C4⋊C4—1428no—
565C4⋊C4—1428no—
566C4⋊C4—1428no—
567C4⋊C4—1428no—
568C4⋊C4—1428no—
569C4⋊C4—1428no—
570C4⋊C4—1428no—
571C4⋊C4—1428no—
572C4⋊C4—1428no—
573C42—7116no—
574C42—1428no—
575C42—1428no—
576C42—1428no—
577C42—1428no—
578C23C2×D4×D7112yes—
579C23C2×Q8×D7112yes—
580C23C2×Q8×D7112yes—
581C23#41×D7112yes—
582C23#41×D7112yes—
583C23#1455617312yes—
584C23#1455617512yes—
585C23C24×D7111yescharacteristic
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—28no—
593C2×C4—28no—
594C2×C4—28no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—2844no—
612C2×C4—2844no—
613C2×C4—2844no—
614C2×C4—2844no—
615C2×C4—714no—
616C2×C4—714no—
617C2×C4—714no—
618C2×C4—714no—
619C2×C4—714no—
620C2×C4—714no—
621C2×C4—7116no—
622C2×C4—7116no—
623C2×C4—714no—
624C2×C4—714no—
625C2×C4—1422no—
626C2×C4—1422no—
627C2×C4—1422no—
628C2×C4—1422no—
629C2×C4—1422no—
630C2×C4—1422no—
631C2×C4—1422no—
632C2×C4—1422no—
633C2×C4—1422no—
634C2×C4—1422no—
635C2×C4—1422no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1422no—
640C2×C4—1422no—
641C2×C4—1428no—
642C2×C4—1428no—
643C2×C4C2×D4×D7114yes—
644C2×C4C2×Q8×D7114yes—
645C2×C4C2×Q8×D7114yes—
646C22#125×D7114yes—
647C22C4⋊Q8×D7114yes—
648C22#1798662814yes—
649C22#1798664714yes—
650C22#1798666714yes—
651C22#1798670314yes—
652C22#1798672614yes—
653C22C22×D4×D7111yescharacteristic
654C22C22×Q8×D7111yescharacteristic
655C22C22×Q8×D7111yescharacteristic
656C22C2×#41×D7111yescharacteristic
657C22C2×#41×D7111yescharacteristic
658C22C2×#1455617311yescharacteristic
659C22C2×#1455617511yescharacteristic
660C4—24no—
661C4—24no—
662C4—24no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—2842no—
668C4—2842no—
669C4—2842no—
670C4—2842no—
671C4—718no—
672C4—718no—
673C4—1424no—
674C4—1424no—
675C2#2259337018yesdirect product factor
676C2C2×#125×D7111yescharacteristic
677C2C2×C4⋊Q8×D7111yescharacteristic
678C2C2×#1798662811yescharacteristic
679C2C2×#1798664711yescharacteristic
680C2C2×#1798666711yescharacteristic
681C2C2×#1798670311yescharacteristic
682C2C2×#1798672611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#398×C71C2
socle, prime radicalC24×C71C24
hypercenterC2×#398D71
hypocenterC71C2×#2552
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #22593370C2direct (N × H)
294. C2×Dic71#125semidirect
331. Dic71C2×#125semidirect
334. C2×C71#2552semidirect
358. C71C2×#2552semidirect
675. C2#22593370direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561182
#225933702
C2×#179859332
C2×#179859322
C2×#179859312
C2×#179858962
C2×#179858942
C2×#179858682
C2×#179858502
C2×#398×C712
C2×#255271