Finite Group Databasebeta

← #32007032

Subgroups — #32007032

Order 18176.

1434 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11765865C211yesmaximal, characteristic
2C2×#17986051C211yesmaximal, characteristic, complemented
3C2×C4⋊C8×D71C211yesmaximal, characteristic, complemented
4#22589274C212yesmaximal, complemented
5#22589132C212yesmaximal, complemented
6#22588631C212yesmaximal, complemented
7#22588629C212yesmaximal, complemented
8#22588320C211yesmaximal, characteristic, complemented
9#22588317C211yesmaximal, characteristic, complemented
10#22588317C211yesmaximal, characteristic, complemented
11C71×#1797C211yesmaximal, characteristic, complemented
12C22×#11765865C411yescharacteristic
13C22×C8×D71C2212yes—
14C4×#11765865—24no—
15C4×#11765865—24no—
16C2×C4×Dic142C411yescharacteristic
17C2×C4×Dic142C2211yescharacteristic
18C2×C4×D284C411yescharacteristic
19C2×C4×D284C2211yescharacteristic
20C2×C4×C22⋊D71C411yescharacteristic
21C2×C4×C22⋊D71C411yescharacteristic
22C2×C4×C22⋊D71C2211yescharacteristic
23C2×C4×C22⋊D71C2211yescharacteristic
24C2×#14556087C411yescharacteristic
25C2×#14556085C411yescharacteristic
26C2×#14556085C411yescharacteristic
27C2×C42×D71C2211yescharacteristic
28C2×C42×D71C2211yescharacteristic
29#17986051—24no—
30C2×C4⋊(C71⋊C8)C2211yescharacteristic
31C2×C4⋊(C71⋊C8)C2211yescharacteristic
32C2×Dic71⋊C8C2212yes—
33C4⋊C8×D71—24no—
34C2×C22⋊(C71⋊C8)C2212yes—
35C2×(C2×D71)⋊C8C2212yes—
36C2×(C2×D71)⋊C8C2212yes—
37C2×(C2×D71)⋊C8C2212yes—
38C2×C8×Dic71C2212yes—
39#17985754C2212yes—
40#17985753C2212yes—
41#17985753C2212yes—
42C22×C42×C71C2211yescharacteristic
43C2×C4⋊C8×C71C2211yescharacteristic
44C2×C4⋊C8×C71C2211yescharacteristic
45C2×C22⋊C8×C71C2212yes—
46#336×C71C2212yes—
47C2×#11765865—24no—
48C2×#11765865—24no—
49C2×#11765865C818yescomplemented
50C22×Dic142C2×C411yescharacteristic
51C22×D284C2×C411yescharacteristic
52C22×C22⋊D71C2×C411yescharacteristic
53C22×C22⋊D71C2×C411yescharacteristic
54C22×C4×D71C2×C411yescharacteristic
55C22×C4×D71C2×C411yescharacteristic
56C22×C4×D71C2×C411yescharacteristic
57C22×C4×D71C2×C411yescharacteristic
58C22×C4×D71C2311yescharacteristic
59C22×C4×D71C2311yescharacteristic
60C22×C71⋊C8C2312yes—
61C22×C71⋊C8C2312yes—
62C2×C8×D71—24no—
63C2×C8×D71—42no—
64C2×C8×D71—42no—
65C4×Dic142—24no—
66C4×Dic142—22no—
67C4×Dic142—22no—
68C4×D284—24no—
69C4×D284—22no—
70C4×D284—22no—
71C4×C22⋊D71—24no—
72C4×C22⋊D71—22no—
73C4×C22⋊D71—22no—
74C4×C22⋊D71—24no—
75C4×C22⋊D71—22no—
76C4×C22⋊D71—22no—
77#14556087—24no—
78#14556085—24no—
79#14556085—24no—
80C2×C4⋊Dic71C2×C411yescharacteristic
81C2×C4⋊Dic71C2×C411yescharacteristic
82C2×Dic71⋊C4C2×C411yescharacteristic
83C2×Dic71⋊C4C2×C411yescharacteristic
84C2×Dic71⋊C4C2×C411yescharacteristic
85C2×Dic71⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic71C2×C411yescharacteristic
87C2×C22⋊Dic71C2×C411yescharacteristic
88C2×(C2×D71)⋊C4C2×C411yescharacteristic
89C2×(C2×D71)⋊C4C2×C411yescharacteristic
90C2×(C2×D71)⋊C4C2×C411yescharacteristic
91C2×(C2×D71)⋊C4C2×C411yescharacteristic
92C2×C4×Dic71C2×C411yescharacteristic
93C2×C4×Dic71C2×C411yescharacteristic
94C2×C4×Dic71C2×C411yescharacteristic
95C2×C4×Dic71C2×C411yescharacteristic
96C2×C4×Dic71C2311yescharacteristic
97C2×C4×Dic71C2311yescharacteristic
98C42×D71—22no—
99C42×D71—22no—
100C42×D71D414yes—
101C42×D71D414yes—
102C4⋊(C71⋊C8)—22no—
103C4⋊(C71⋊C8)—22no—
104Dic71⋊C8—24no—
105C22⋊(C71⋊C8)—42no—
106(C2×D71)⋊C8—24no—
107(C2×D71)⋊C8—42no—
108(C2×D71)⋊C8—42no—
109C8×Dic71—24no—
110C23×C4×C71C2×C411yescharacteristic
111C23×C4×C71C2×C411yescharacteristic
112C23×C4×C71C2311yescharacteristic
113C22×C8×C71C2312yes—
114C22×C8×C71C2312yes—
115C2×C42×C71—22no—
116C2×C42×C71—22no—
117C2×C42×C71C2×C411yescharacteristic
118C2×C42×C71C2×C411yescharacteristic
119C2×C42×C71C2311yescharacteristic
120C2×C42×C71C2311yescharacteristic
121C4⋊C8×C71—22no—
122C4⋊C8×C71—22no—
123C22⋊C8×C71—42no—
124C23×D71C22×C411yescharacteristic
125C23×D71C22×C411yescharacteristic
126#11765865—232no—
127C2×Dic142—22no—
128C2×Dic142—22no—
129C2×Dic142C2×C814yescomplemented
130C2×D284—22no—
131C2×D284—22no—
132C2×D284C2×C814yes—
133C2×C22⋊D71—22no—
134C2×C22⋊D71—22no—
135C2×C22⋊D71—22no—
136C2×C22⋊D71—22no—
137C2×C22⋊D71C2×C814yes—
138C2×C22⋊D71C2×C814yescomplemented
139C22×Dic71C22×C411yescharacteristic
140C22×Dic71C22×C411yescharacteristic
141C22×Dic71C22×C411yescharacteristic
142C22×Dic71C22×C411yescharacteristic
143C22×Dic71C22×C411yescharacteristic
144C22×Dic71C22×C411yescharacteristic
145C2×C4×D71—22no—
146C2×C4×D71—22no—
147C2×C4×D71—21no—
148C2×C4×D71—21no—
149C2×C4×D71—21no—
150C2×C4×D71—21no—
151C2×C4×D71—22no—
152C2×C4×D71—21no—
153C2×C4×D71—21no—
154C2×C4×D71—21no—
155C2×C4×D71—21no—
156C2×C4×D71—21no—
157C2×C4×D71—21no—
158C2×C4×D71—41no—
159C2×C4×D71—41no—
160C2×C4×D71—41no—
161C2×C4×D71—41no—
162C2×C4×D71C22⋊C414yes—
163C2×C4×D71C22⋊C414yes—
164C2×C4×D71C2×C814yes—
165C2×C4×D71C2×C814yescomplemented
166C2×C4×D71M1614yes—
167C2×C4×D71C2×D412yes—
168C2×C4×D71C2×D412yes—
169C2×C71⋊C8—22no—
170C2×C71⋊C8—22no—
171C2×C71⋊C8—22no—
172C2×C71⋊C8—22no—
173C2×C71⋊C8—22no—
174C2×C71⋊C8—22no—
175C8×D71—48no—
176C4⋊Dic71—22no—
177C4⋊Dic71—22no—
178Dic71⋊C4—22no—
179Dic71⋊C4—22no—
180Dic71⋊C4—22no—
181Dic71⋊C4—22no—
182C22⋊Dic71—22no—
183C22⋊Dic71—22no—
184(C2×D71)⋊C4—22no—
185(C2×D71)⋊C4—22no—
186(C2×D71)⋊C4—22no—
187(C2×D71)⋊C4—22no—
188C4×Dic71—22no—
189C4×Dic71—22no—
190C4×Dic71—21no—
191C4×Dic71—21no—
192C4×Dic71C22⋊C414yes—
193C4×Dic71C22⋊C414yes—
194C4×Dic71C2×D412yes—
195C4×Dic71C2×D412yes—
196C24×C71C22×C411yescharacteristic
197C22×C4×C71—22no—
198C22×C4×C71—22no—
199C22×C4×C71—22no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—41no—
207C22×C4×C71—41no—
208C22×C4×C71C2×C814yescomplemented
209C22×C4×C71C22×C411yescharacteristic
210C22×C4×C71C22×C411yescharacteristic
211C22×C4×C71C22×C411yescharacteristic
212C22×C4×C71C22×C411yescharacteristic
213C22×C4×C71C22×C411yescharacteristic
214C22×C4×C71C2411yescharacteristic
215C2×C8×C71—22no—
216C2×C8×C71—22no—
217C2×C8×C71—22no—
218C2×C8×C71—22no—
219C2×C8×C71—22no—
220C2×C8×C71—22no—
221C42×C71—22no—
222C42×C71—22no—
223C42×C71—21no—
224C42×C71—21no—
225C42×C71C2×D412yes—
226C42×C71C2×D412yes—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71—21no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71C22×C812yes—
234C23×C71C23×C411yescharacteristic
235C22×D71—21no—
236C22×D71—21no—
237C22×D71—21no—
238C22×D71—21no—
239C22×D71—21no—
240C22×D71—21no—
241C22×D71—21no—
242C22×D71—21no—
243C22×D71—21no—
244C22×D71—21no—
245C22×D71C2×C22⋊C412yes—
246C22×D71C22×C812yes—
247C22×D71C22×C812yes—
248C22×D71C2×M1612yes—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—21no—
252C2×C4×C71—21no—
253C2×C4×C71—28no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—44no—
261C2×C4×C71—41no—
262C2×C4×C71—41no—
263C2×C4×C71—41no—
264C2×C4×C71—41no—
265C2×C4×C71C2×C22⋊C412yes—
266C2×C4×C71C2×C22⋊C412yes—
267C2×C4×C71C22×C812yes—
268C2×C4×C71C22×C812yes—
269C2×C4×C71C2×M1612yes—
270C2×C4×C71C22×D411yescharacteristic
271C2×C4×C71C22×D411yescharacteristic
272C2×C4×C71H(5,𝔽2)11yescharacteristic
273C2×C4×C71H(5,𝔽2)11yescharacteristic
274C2×C4×C712−1+411yescharacteristic
275C2×C4×C712−1+411yescharacteristic
276C22⋊D71—28no—
277C22⋊D71—28no—
278C2×Dic71—21no—
279C2×Dic71—21no—
280C2×Dic71—21no—
281C2×Dic71—21no—
282C2×Dic71—21no—
283C2×Dic71—21no—
284C2×Dic71—21no—
285C2×Dic71—21no—
286C2×Dic71—21no—
287C2×Dic71—21no—
288C2×Dic71—21no—
289C2×Dic71—21no—
290C2×Dic71C2×C22⋊C412yes—
291C2×Dic71C2×C22⋊C412yes—
292C2×Dic71C2×C22⋊C412yes—
293C2×Dic71C22×C812yes—
294C2×Dic71C22×C812yes—
295C2×Dic71C2×M1612yes—
296D284—28no—
297C4×D71—22no—
298C4×D71—22no—
299C4×D71—22no—
300C4×D71—22no—
301C4×D71—28no—
302C4×D71—44no—
303C4×D71—44no—
304C4×D71—41no—
305C4×D71—41no—
306C4×D71—41no—
307C4×D71—41no—
308C4×D71C22⋊C8116yescomplemented
309Dic142—28no—
310C8×C71—42no—
311C8×C71—42no—
312C71⋊C8—42no—
313C71⋊C8—42no—
314C22×C71—22no—
315C22×C71—22no—
316C22×C71—22no—
317C22×C71—41no—
318C22×C71—41no—
319C22×C71—41no—
320C22×C71—41no—
321C22×C71C22×C22⋊C411yescharacteristic
322C22×C71#52011yescharacteristic
323C22×C71#52011yescharacteristic
324C22×C71C23×C811yescharacteristic
325C22×C71C22×M1611yescharacteristic
326C22×C71#56811yescharacteristic
327C22×C71#56811yescharacteristic
328C2×D71—22no—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71—22no—
334C2×D71—22no—
335C2×D71—22no—
336C2×D71—22no—
337C2×D71—41no—
338C2×D71—41no—
339C2×D71—41no—
340C2×D71—41no—
341C2×D71C2×C22⋊C814yes—
342C4×C71—22no—
343C4×C71—22no—
344C4×C71—41no—
345C4×C71—41no—
346C4×C71C2×C22⋊C814yes—
347C4×C71#53511yescharacteristic
348C4×C71#53611yescharacteristic
349C4×C71#53711yescharacteristic
350C4×C71#53711yescharacteristic
351Dic71—22no—
352Dic71—22no—
353Dic71—22no—
354Dic71—41no—
355Dic71—41no—
356Dic71C2×C22⋊C814yes—
357#21847—711nomaximal, Sylow
358C2×C71—42no—
359C2×C71#231111yescharacteristic
360C2×C71C22×C22⋊C811yescharacteristic
361C2×C71#287911yescharacteristic
362C2×C71#298811yescharacteristic
363C2×C71#298811yescharacteristic
364C2×C71#298911yescharacteristic
365C2×C71#298911yescharacteristic
366D71—24no—
367D71—42no—
368C2×C4×#41—711no—
369C2×#431—711no—
370C22×C4⋊C8—711no—
371#1984—712no—
372#1954—712no—
373#1869—712no—
374#1869—712no—
375#1797—711no—
376#1797—711no—
377#1797—711no—
378#1797D7111yescharacteristic, complemented
379C71#2184711yescharacteristic, complemented, Sylow
380C22×#41—711no—
381C23×C8—712no—
382C4×#41—1424no—
383C4×#41—1424no—
384C2×C4×Q8—711no—
385C2×C4×Q8—711no—
386C2×C4×D4—711no—
387C2×C4×D4—711no—
388C2×C4×D4—711no—
389C2×C4×D4—711no—
390C2×C4×D4—711no—
391C2×C4×D4—711no—
392C2×#117—711no—
393C2×#117—711no—
394C2×#117—711no—
395C22×C42—711no—
396C22×C42—711no—
397C22×C42C2×D7111yescharacteristic
398#431—1424no—
399C2×C4⋊C8—712no—
400C2×C4⋊C8—711no—
401C2×C4⋊C8—711no—
402C2×C4⋊C8—1424no—
403C2×C4⋊C8C2×D7111yescharacteristic
404C2×C4⋊C8C2×D7111yescharacteristic
405C2×C22⋊C8—712no—
406C2×C22⋊C8—712no—
407C2×C22⋊C8—712no—
408C2×C22⋊C8—712no—
409C2×C22⋊C8C2×D7112yes—
410C2×C4×C8—712no—
411#336—712no—
412#336—712no—
413#336—712no—
414#336C2×D7112yes—
415C2×#41—718no—
416C2×#41—1424no—
417C2×#41—1424no—
418C22×Q8—711no—
419C22×D4—711no—
420C22×D4—711no—
421C22×D4—711no—
422C23×C4—711no—
423C23×C4—711no—
424C23×C4—711no—
425C23×C4—711no—
426C23×C4—711no—
427C23×C4—711no—
428C23×C4C4×D7111yescharacteristic
429C23×C4C4×D7111yescharacteristic
430C23×C4C22×D7111yescharacteristic
431C22×C8—2842no—
432C22×C8—2842no—
433C22×C8—712no—
434C22×C8—712no—
435C22×C8—1424no—
436C22×C8C22×D7112yes—
437C22×C8C22×D7112yes—
438C4×Q8—1422no—
439C4×Q8—1422no—
440C4×Q8—1424no—
441C4×D4—1422no—
442C4×D4—1422no—
443C4×D4—1424no—
444C4×D4—1422no—
445C4×D4—1422no—
446C4×D4—1424no—
447C4×D4—1422no—
448C4×D4—1422no—
449C4×D4—1424no—
450#117—1424no—
451#117—1424no—
452#117—1424no—
453C2×C4⋊C4—711no—
454C2×C4⋊C4—711no—
455C2×C4⋊C4—711no—
456C2×C4⋊C4—711no—
457C2×C4⋊C4—711no—
458C2×C4⋊C4—711no—
459C2×C22⋊C4—711no—
460C2×C22⋊C4—711no—
461C2×C22⋊C4—711no—
462C2×C22⋊C4—711no—
463C2×C22⋊C4—711no—
464C2×C22⋊C4—711no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—711no—
468C2×C42—711no—
469C2×C42—711no—
470C2×C42—714no—
471C2×C42—714no—
472C2×C42—711no—
473C2×C42—711no—
474C2×C42—711no—
475C2×C42—1422no—
476C2×C42—1422no—
477C2×C42C4×D7111yescharacteristic
478C2×C42C4×D7111yescharacteristic
479C2×C42C22×D7111yescharacteristic
480C2×C42C22×D7111yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—22no—
483C4⋊C8—1424no—
484C4⋊C8—1422no—
485C4⋊C8—1422no—
486C22⋊C8—42no—
487C22⋊C8—2842no—
488C22⋊C8—2842no—
489C22⋊C8—2842no—
490C22⋊C8—1424no—
491C4×C8—1424no—
492C24—711no—
493C24—711no—
494C24C2×C4×D7111yescharacteristic
495#41—14232no—
496C2×Q8—714no—
497C2×Q8—1422no—
498C2×Q8—1422no—
499C2×D4—714no—
500C2×D4—714no—
501C2×D4—714no—
502C2×D4—1422no—
503C2×D4—1422no—
504C2×D4—1422no—
505C2×D4—1422no—
506C2×D4—1422no—
507C2×D4—1422no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—2841no—
520C22×C4—2841no—
521C22×C4—2841no—
522C22×C4—2841no—
523C22×C4—714no—
524C22×C4—711no—
525C22×C4—714no—
526C22×C4—714no—
527C22×C4—714no—
528C22×C4—711no—
529C22×C4—711no—
530C22×C4—711no—
531C22×C4—712no—
532C22×C4—712no—
533C22×C4—714no—
534C22×C4—711no—
535C22×C4—711no—
536C22×C4—1421no—
537C22×C4—1421no—
538C22×C4—1421no—
539C22×C4—1421no—
540C22×C4—1421no—
541C22×C4—1421no—
542C22×C4—1422no—
543C22×C4—1421no—
544C22×C4—1421no—
545C22×C4—1421no—
546C22×C4—1421no—
547C22×C4—1422no—
548C22×C4—1422no—
549C22×C4C8×D7114yescomplemented
550C22×C4C2×C4×D7111yescharacteristic
551C22×C4C2×C4×D7111yescharacteristic
552C22×C4C2×C4×D7111yescharacteristic
553C22×C4C2×C4×D7111yescharacteristic
554C22×C4C2×C4×D7111yescharacteristic
555C22×C4C23×D7111yescharacteristic
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—2848no—
563C2×C8—1422no—
564C2×C8—1422no—
565C2×C8—1422no—
566C2×C8—1422no—
567C2×C8—1422no—
568C2×C8—1422no—
569C4⋊C4—1422no—
570C4⋊C4—1422no—
571C4⋊C4—1422no—
572C4⋊C4—1422no—
573C4⋊C4—1422no—
574C4⋊C4—1422no—
575C22⋊C4—1422no—
576C22⋊C4—1422no—
577C22⋊C4—1422no—
578C22⋊C4—1422no—
579C22⋊C4—1422no—
580C22⋊C4—1422no—
581C42—21no—
582C42—21no—
583C42—22no—
584C42—22no—
585C42—712no—
586C42—712no—
587C42—714no—
588C42—714no—
589C42—1421no—
590C42—1421no—
591C42—1422no—
592C42—1422no—
593C42D4×D7112yes—
594C42D4×D7112yes—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—712no—
602C23—712no—
603C23—712no—
604C23—712no—
605C23—1421no—
606C23—1421no—
607C23—1421no—
608C23—1421no—
609C23—1421no—
610C23—1421no—
611C23—1421no—
612C23—1421no—
613C23—1421no—
614C23—1421no—
615C23C2×C8×D7112yes—
616C23C22×C4×D7111yescharacteristic
617Q8—1428no—
618D4—1428no—
619D4—1428no—
620D4—1428no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—28no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—44no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—2844no—
638C2×C4—2844no—
639C2×C4—2841no—
640C2×C4—2841no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—712no—
644C2×C4—712no—
645C2×C4—712no—
646C2×C4—7116no—
647C2×C4—712no—
648C2×C4—712no—
649C2×C4—712no—
650C2×C4—1421no—
651C2×C4—1421no—
652C2×C4—1421no—
653C2×C4—1421no—
654C2×C4—1421no—
655C2×C4—1421no—
656C2×C4—1421no—
657C2×C4—1421no—
658C2×C4—1421no—
659C2×C4—1421no—
660C2×C4—1421no—
661C2×C4—1421no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1428no—
667C2×C4C22⋊C4×D7112yes—
668C2×C4C22⋊C4×D7112yes—
669C2×C4C2×C8×D7112yes—
670C2×C4C2×C8×D7112yes—
671C2×C4M16×D7112yes—
672C2×C4C2×D4×D7111yescharacteristic
673C2×C4C2×D4×D7111yescharacteristic
674C2×C4#1455617311yescharacteristic
675C2×C4#1455617411yescharacteristic
676C2×C4#1455617511yescharacteristic
677C2×C4#1455617611yescharacteristic
678C8—42no—
679C8—42no—
680C8—2842no—
681C8—2842no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—2841no—
690C22—2841no—
691C22—2841no—
692C22—2841no—
693C22—714no—
694C22—1422no—
695C22—1422no—
696C22—1422no—
697C22—1422no—
698C22—1422no—
699C22—1422no—
700C22—1422no—
701C22—1422no—
702C22—1422no—
703C22C2×C22⋊C4×D7111yescharacteristic
704C22#1798647911yescharacteristic
705C22#1798648011yescharacteristic
706C22C22×C8×D7111yescharacteristic
707C22C2×M16×D7111yescharacteristic
708C22#1798676511yescharacteristic
709C22#1798676511yescharacteristic
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—2841no—
715C4—2841no—
716C4—714no—
717C4—1422no—
718C4—1422no—
719C4—1422no—
720C4C22⋊C8×D7114yes—
721C4#1798656511yescharacteristic
722C4#1798657211yescharacteristic
723C4#1798657811yescharacteristic
724C4#1798657911yescharacteristic
725C2—42no—
726C2—2842no—
727C2—1424no—
728C2#2259092911yescharacteristic
729C2C2×C22⋊C8×D7111yescharacteristic
730C2#2259678311yescharacteristic
731C2#2259744811yescharacteristic
732C2#2259744911yescharacteristic
733C2#2259745411yescharacteristic
734C2#2259745911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC71×#1797C2
socleC23×C71C23×C4
prime radicalC22×#11765865C4
cosocleC22×C4×C71C24
hypercenter#1797D71
hypocenterC71#21847
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#17986051C2semidirect
3. C2×C4⋊C8×D71C2semidirect
4. #22589274C2semidirect
5. #22589132C2semidirect
6. #22588631C2semidirect
7. #22588629C2semidirect
8. #22588320C2semidirect
9. #22588317C2semidirect
10. #22588317C2semidirect
11. C71×#1797C2semidirect
49. C2×#11765865C8semidirect
129. C2×Dic142C2×C8semidirect
138. C2×C22⋊D71C2×C8semidirect
165. C2×C4×D71C2×C8semidirect
208. C22×C4×C71C2×C8semidirect
308. C4×D71C22⋊C8semidirect
378. #1797D71semidirect
379. C71#21847semidirect
549. C22×C4C8×D71semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117658652
C2×#179860512
C2×C4⋊C8×D712
#225892742
#225891322
#225886312
#225886292
#225883202
#225883172
C71×#17972
#2184771