Finite Group Databasebeta

← #32017108

Subgroups — #32017108

Order 18176.

952 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986054C211yesmaximal, characteristic, complemented
2C2×#17986053C211yesmaximal, characteristic, complemented
3C4×(C22⋊D71)⋊C4C211yesmaximal, characteristic
4#22589132C211yesmaximal, characteristic
5#22589132C211yesmaximal, characteristic
6#22588955C211yesmaximal, characteristic, complemented
7#22588954C211yesmaximal, characteristic, complemented
8#22588952C211yesmaximal, characteristic, complemented
9#22588491C211yesmaximal, characteristic, complemented
10#22588319C211yesmaximal, characteristic, complemented
11#22588318C211yesmaximal, characteristic, complemented
12#22588208C211yesmaximal, characteristic, complemented
13#22588206C211yesmaximal, characteristic, complemented
14#22588188C211yesmaximal, characteristic, complemented
15C71×#1924C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊D71C2211yescharacteristic
17C2×(C22⋊D71)⋊C4C411yescharacteristic
18C2×(C22⋊D71)⋊C4C411yescharacteristic
19C22×C4×Dic71C2211yescharacteristic
20C2×C42×D71C2211yescharacteristic
21#17986054—24no—
22#17986053—24no—
23C2×C4⋊(C71⋊C8)C2211yescharacteristic
24C2×Dic71⋊C8C2211yescharacteristic
25C2×Dic71⋊C8C2211yescharacteristic
26C2×Dic71⋊C8C2211yescharacteristic
27C2×Dic71⋊C8C2211yescharacteristic
28C2×Dic71⋊C8C2211yescharacteristic
29C2×Dic71⋊C8C2211yescharacteristic
30C2×C22⋊(C71⋊C8)C2211yescharacteristic
31C2×C22⋊(C71⋊C8)C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×(C2×D71)⋊C8C2211yescharacteristic
36C2×#14556039C2211yescharacteristic
37C2×#14556038C2211yescharacteristic
38C2×#14556038C2211yescharacteristic
39C2×C8×Dic71C2211yescharacteristic
40C2×C8×Dic71C2211yescharacteristic
41C4×Dic71⋊C4C2211yescharacteristic
42#17985850C411yescharacteristic
43#17985850C411yescharacteristic
44C22⋊C4×Dic71C411yescharacteristic
45C22⋊C4×Dic71C411yescharacteristic
46C4×(C2×D71)⋊C4C2211yescharacteristic
47#17985846C411yescharacteristic
48#17985846C411yescharacteristic
49C42×Dic71C2211yescharacteristic
50#17985754C2211yescharacteristic
51#17985754C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54C2×C4⋊C8×C71C2211yescharacteristic
55C2×C22⋊C8×C71C2211yescharacteristic
56C2×C22⋊C8×C71C2211yescharacteristic
57C2×#97×C71C2211yescharacteristic
58C4×C22⋊C4×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic
60#336×C71C2211yescharacteristic
61C22×C22⋊D71C2×C411yescharacteristic
62C23×Dic71C2×C411yescharacteristic
63C23×Dic71C2×C411yescharacteristic
64C22×C4×D71C2×C411yescharacteristic
65C22×C4×D71C2×C411yescharacteristic
66C22×C4×D71C2311yescharacteristic
67C22×C71⋊C8C2311yescharacteristic
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C4×C22⋊D71—22no—
72C4×C22⋊D71—22no—
73(C22⋊D71)⋊C4—24no—
74(C22⋊D71)⋊C4—24no—
75C2×Dic71⋊C4C2×C411yescharacteristic
76C2×Dic71⋊C4C2×C411yescharacteristic
77C2×Dic71⋊C4C2×C411yescharacteristic
78C2×C22⋊Dic71C2×C411yescharacteristic
79C2×(C2×D71)⋊C4C2×C411yescharacteristic
80C2×(C2×D71)⋊C4C2×C411yescharacteristic
81C2×(C2×D71)⋊C4C2×C411yescharacteristic
82C2×C4×Dic71—22no—
83C2×C4×Dic71—22no—
84C2×C4×Dic71C2×C411yescharacteristic
85C2×C4×Dic71C2×C411yescharacteristic
86C2×C4×Dic71C2×C411yescharacteristic
87C2×C4×Dic71C2×C411yescharacteristic
88C2×C4×Dic71C2×C411yescharacteristic
89C2×C4×Dic71C2×C411yescharacteristic
90C2×C4×Dic71C2×C411yescharacteristic
91C2×C4×Dic71C2×C411yescharacteristic
92C2×C4×Dic71C2311yescharacteristic
93C2×C4×Dic71C2311yescharacteristic
94C2×C4×Dic71C2311yescharacteristic
95C42×D71—22no—
96C42×D71—22no—
97C4⋊(C71⋊C8)—41no—
98Dic71⋊C8—22no—
99Dic71⋊C8—22no—
100Dic71⋊C8—22no—
101Dic71⋊C8—22no—
102Dic71⋊C8—22no—
103Dic71⋊C8D414yescomplemented
104C22⋊(C71⋊C8)—22no—
105C22⋊(C71⋊C8)—41no—
106(C2×D71)⋊C8—22no—
107(C2×D71)⋊C8—22no—
108(C2×D71)⋊C8—41no—
109(C2×D71)⋊C8—41no—
110#14556039—22no—
111#14556038—22no—
112#14556038—22no—
113C8×Dic71—22no—
114C8×Dic71—22no—
115C71⋊#95C2×C411yescharacteristic
116C71⋊#95C2×C411yescharacteristic
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C23×C4×C71C2311yescharacteristic
120C22×C8×C71C2311yescharacteristic
121C22×C8×C71C2311yescharacteristic
122C22×C8×C71C2311yescharacteristic
123C22×C8×C71C2311yescharacteristic
124C2×C22⋊C4×C71C2×C411yescharacteristic
125C2×C22⋊C4×C71C2×C411yescharacteristic
126C2×C42×C71C2311yescharacteristic
127C2×C42×C71C2311yescharacteristic
128C4⋊C8×C71—41no—
129C22⋊C8×C71—22no—
130C22⋊C8×C71—41no—
131#97×C71—22no—
132#95×C71C2×C411yescharacteristic
133#95×C71C2×C411yescharacteristic
134C23×D71C22×C411yescharacteristic
135C2×C22⋊D71—22no—
136C2×C22⋊D71—22no—
137C2×C22⋊D71M1614yes—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—22no—
141C22×Dic71—22no—
142C22×Dic71—22no—
143C22×Dic71—41no—
144C22×Dic71C22×C411yescharacteristic
145C22×Dic71C22×C411yescharacteristic
146C22×Dic71C22×C411yescharacteristic
147C22×Dic71C22×C411yescharacteristic
148C22×Dic71C22×C411yescharacteristic
149C22×Dic71C22×C411yescharacteristic
150C22×Dic71C22×C411yescharacteristic
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—22no—
159C2×C4×D71—22no—
160C2×C4×D71—22no—
161C2×C4×D71—22no—
162C2×C4×D71—41no—
163C2×C71⋊C8—21no—
164C2×C71⋊C8—21no—
165C2×C71⋊C8—21no—
166C2×C71⋊C8—21no—
167C2×C71⋊C8—21no—
168C2×C71⋊C8—21no—
169C2×C71⋊C8—21no—
170C2×C71⋊C8—21no—
171C2×C71⋊C8—21no—
172C2×C71⋊C8—21no—
173C2×C71⋊C8—21no—
174C2×C71⋊C8C2×D412yes—
175Dic71⋊C4—22no—
176Dic71⋊C4—22no—
177Dic71⋊C4—22no—
178C22⋊Dic71—22no—
179(C2×D71)⋊C4—22no—
180(C2×D71)⋊C4—22no—
181(C2×D71)⋊C4—22no—
182C4×Dic71—21no—
183C4×Dic71—21no—
184C4×Dic71—22no—
185C4×Dic71—22no—
186C4×Dic71—22no—
187C4×Dic71—22no—
188C4×Dic71—22no—
189C4×Dic71—22no—
190C4×Dic71—41no—
191C4×Dic71M1614yes—
192C4×Dic71C2×D412yes—
193C4×Dic71#4112yes—
194C4×Dic71#4112yes—
195C4×Dic71#4112yes—
196C24×C71C22×C411yescharacteristic
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71C22×C411yescharacteristic
204C22×C4×C71C22×C411yescharacteristic
205C22×C4×C71C22×C411yescharacteristic
206C22×C4×C71C22×C411yescharacteristic
207C22×C4×C71C22×C411yescharacteristic
208C22×C4×C71C2411yescharacteristic
209C2×C8×C71—21no—
210C2×C8×C71—21no—
211C2×C8×C71—21no—
212C2×C8×C71—21no—
213C2×C8×C71—21no—
214C2×C8×C71—21no—
215C2×C8×C71—21no—
216C2×C8×C71—21no—
217C2×C8×C71—21no—
218C2×C8×C71—21no—
219C2×C8×C71—21no—
220C2×C8×C71C2×D412yes—
221C22⋊C4×C71—22no—
222C22⋊C4×C71—22no—
223C42×C71—21no—
224C42×C71—21no—
225C42×C71—21no—
226C42×C71—21no—
227C23×C71—21no—
228C23×C71—21no—
229C23×C71—21no—
230C23×C71—21no—
231C23×C71—21no—
232C23×C71—21no—
233C23×C71C2×M1612yes—
234C23×C71C23×C411yescharacteristic
235C22×D71—21no—
236C22×D71—21no—
237C22×D71—21no—
238C22×D71—21no—
239C22×D71—21no—
240C22×D71—21no—
241C22×D71C2×M1612yes—
242C2×C4×C71—21no—
243C2×C4×C71—21no—
244C2×C4×C71—21no—
245C2×C4×C71—21no—
246C2×C4×C71—21no—
247C2×C4×C71—21no—
248C2×C4×C71—21no—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—21no—
252C2×C4×C71—21no—
253C2×C4×C71—21no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—41no—
257C2×C4×C71—41no—
258C2×C4×C71—41no—
259C2×C4×C71—41no—
260C2×C4×C71C2×M1612yes—
261C2×C4×C71C22×D411yescharacteristic
262C2×C4×C71C2×#4111yescharacteristic
263C2×C4×C71C2×#4111yescharacteristic
264C2×C4×C71C2×#4111yescharacteristic
265C2×C4×C71H(5,𝔽2)11yescharacteristic
266C2×C4×C712−1+411yescharacteristic
267C22⋊D71—28no—
268C2×Dic71—21no—
269C2×Dic71—21no—
270C2×Dic71—21no—
271C2×Dic71—21no—
272C2×Dic71—21no—
273C2×Dic71—21no—
274C2×Dic71—21no—
275C2×Dic71—21no—
276C2×Dic71—21no—
277C2×Dic71—21no—
278C2×Dic71—21no—
279C2×Dic71—21no—
280C2×Dic71—21no—
281C2×Dic71—44no—
282C2×Dic71—44no—
283C2×Dic71#11712yes—
284C2×Dic71#11712yes—
285C2×Dic71C4×D412yes—
286C2×Dic71C4×D412yes—
287C2×Dic71C2×M1612yes—
288C2×Dic71C2×M1612yes—
289C2×Dic71C2×M1612yes—
290C2×Dic71#13112yes—
291C4×D71—44no—
292C4×D71—41no—
293C4×D71—41no—
294C4×D71—41no—
295C4×D71—41no—
296C4×D71—44no—
297C8×C71—22no—
298C8×C71—41no—
299C8×C71—41no—
300C8×C71—41no—
301C71⋊C8—22no—
302C71⋊C8—41no—
303C71⋊C8—41no—
304C71⋊C8—41no—
305C22×C71—22no—
306C22×C71—22no—
307C22×C71—22no—
308C22×C71—41no—
309C22×C71—41no—
310C22×C71—41no—
311C22×C71—41no—
312C22×C71C2×#11711yescharacteristic
313C22×C71C2×C4×D411yescharacteristic
314C22×C71#52011yescharacteristic
315C22×C71C22×M1611yescharacteristic
316C22×C71C22×M1611yescharacteristic
317C22×C71C2×#13111yescharacteristic
318C22×C71#56811yescharacteristic
319C2×D71—22no—
320C2×D71—22no—
321C2×D71—22no—
322C2×D71—41no—
323C2×D71—41no—
324C2×D71—41no—
325C2×D71—41no—
326C4×C71—22no—
327C4×C71—41no—
328C4×C71—41no—
329C4×C71—41no—
330C4×C71—41no—
331C4×C71#54711yescharacteristic
332C4×C71#55011yescharacteristic
333C4×C71#55511yescharacteristic
334C4×C71#55611yescharacteristic
335Dic71—22no—
336Dic71—22no—
337Dic71—41no—
338Dic71—41no—
339Dic71—41no—
340Dic71#43214yescomplemented
341Dic71#43614yes—
342#22799—711nomaximal, Sylow
343C2×C71—42no—
344C2×C71#235411yescharacteristic
345C2×C71C2×#43211yescharacteristic
346C2×C71#292511yescharacteristic
347C2×C71C2×#43611yescharacteristic
348C2×C71D4×M1611yescharacteristic
349C2×C71#298911yescharacteristic
350C2×C71#299011yescharacteristic
351D71—42no—
352C2×#432—711no—
353C2×#432—711no—
354C42×D4—711no—
355#1954—711no—
356#1954—711no—
357#1924—711no—
358#1924—711no—
359#1924—711no—
360#1924D7111yescharacteristic, complemented
361#1842—711no—
362#1797—711no—
363#1797—711no—
364#1770—711no—
365#1770—711no—
366C4×C4⋊C8—711no—
367C71#2279911yescharacteristic, complemented, Sylow
368C2×C4×D4—711no—
369C2×C4×D4—711no—
370C2×C4×D4—711no—
371C22×C42—711no—
372C22×C42—711no—
373#432—1424no—
374#432—1424no—
375C2×C4⋊C8—711no—
376C2×C4⋊C8—711no—
377C2×C4⋊C8—711no—
378C2×C4⋊C8—711no—
379C2×C4⋊C8—711no—
380C2×C4⋊C8—711no—
381C2×C4⋊C8—711no—
382C2×C4⋊C8C2×D7111yescharacteristic
383C2×C22⋊C8—711no—
384C2×C22⋊C8—711no—
385C2×C22⋊C8—711no—
386C2×C22⋊C8—711no—
387C2×C22⋊C8—711no—
388C2×C22⋊C8—711no—
389C2×C22⋊C8C2×D7111yescharacteristic
390C2×C22⋊C8C2×D7111yescharacteristic
391C2×#97—711no—
392C2×#97—711no—
393C2×#97—711no—
394C2×#97C2×D7111yescharacteristic
395C2×C4×C8—711no—
396C2×C4×C8—711no—
397C4×C4⋊C4—711no—
398C4×C4⋊C4—711no—
399C4×C4⋊C4—711no—
400C4×C22⋊C4—711no—
401C4×C22⋊C4—711no—
402C4×C22⋊C4—711no—
403C4×C22⋊C4—711no—
404C4×C22⋊C4—711no—
405C4×C22⋊C4C2×D7111yescharacteristic
406C43—711no—
407#336—711no—
408#336—711no—
409#336—711no—
410#336—711no—
411#336C2×D7111yescharacteristic
412#336C2×D7111yescharacteristic
413C22×D4—711no—
414C23×C4—711no—
415C23×C4—711no—
416C23×C4—711no—
417C23×C4—711no—
418C23×C4—711no—
419C23×C4C22×D7111yescharacteristic
420C22×C8—711no—
421C22×C8—711no—
422C22×C8—711no—
423C22×C8—711no—
424C22×C8C22×D7111yescharacteristic
425C22×C8C22×D7111yescharacteristic
426C22×C8C22×D7111yescharacteristic
427C22×C8C22×D7111yescharacteristic
428C4×D4—1424no—
429C4×D4—1422no—
430C4×D4—1422no—
431C4×D4—1424no—
432C2×C4⋊C4—711no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C22⋊C4—711no—
436C2×C22⋊C4—711no—
437C2×C22⋊C4—711no—
438C2×C22⋊C4—711no—
439C2×C22⋊C4C4×D7111yescharacteristic
440C2×C22⋊C4C4×D7111yescharacteristic
441C2×C42—711no—
442C2×C42—711no—
443C2×C42—711no—
444C2×C42—711no—
445C2×C42—711no—
446C2×C42—711no—
447C2×C42—711no—
448C2×C42—711no—
449C2×C42—711no—
450C2×C42—711no—
451C2×C42—711no—
452C2×C42—1422no—
453C2×C42—1422no—
454C2×C42—1422no—
455C2×C42—1422no—
456C2×C42C22×D7111yescharacteristic
457C2×C42C22×D7111yescharacteristic
458C4⋊C8—41no—
459C4⋊C8—2841no—
460C4⋊C8—714no—
461C4⋊C8—1422no—
462C4⋊C8—1422no—
463C4⋊C8—1422no—
464C4⋊C8—1422no—
465C4⋊C8—1422no—
466C22⋊C8—22no—
467C22⋊C8—41no—
468C22⋊C8—2841no—
469C22⋊C8—2841no—
470C22⋊C8—2841no—
471C22⋊C8—1422no—
472C22⋊C8—1422no—
473C22⋊C8—1422no—
474#97—22no—
475#97—1422no—
476#97—1422no—
477#97—1422no—
478C4×C8—1422no—
479C4×C8—1422no—
480#95—711no—
481#95—711no—
482#95—711no—
483#95—711no—
484#95C4×D7111yescharacteristic
485#95C4×D7111yescharacteristic
486C24—711no—
487C24C2×C4×D7111yescharacteristic
488C2×D4—714no—
489C2×D4—1422no—
490C2×D4—1422no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—2841no—
498C22×C4—2841no—
499C22×C4—711no—
500C22×C4—711no—
501C22×C4—711no—
502C22×C4—711no—
503C22×C4—711no—
504C22×C4—711no—
505C22×C4—711no—
506C22×C4—1422no—
507C22×C4—1422no—
508C22×C4—1422no—
509C22×C4—1422no—
510C22×C4—1422no—
511C22×C4—1422no—
512C22×C4—1422no—
513C22×C4—1422no—
514C22×C4—1422no—
515C22×C4—1422no—
516C22×C4—1421no—
517C22×C4—1421no—
518C22×C4—1421no—
519C22×C4—1421no—
520C22×C4—1421no—
521C22×C4—1421no—
522C22×C4C2×C4×D7111yescharacteristic
523C22×C4C2×C4×D7111yescharacteristic
524C22×C4C2×C4×D7111yescharacteristic
525C22×C4C2×C4×D7111yescharacteristic
526C22×C4C2×C4×D7111yescharacteristic
527C22×C4C23×D7111yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—712no—
540C2×C8—1421no—
541C2×C8—1421no—
542C2×C8—1421no—
543C2×C8—1421no—
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C2×C8D4×D7112yes—
552C4⋊C4—1422no—
553C4⋊C4—1422no—
554C4⋊C4—1422no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—1422no—
558C22⋊C4—1422no—
559C22⋊C4—1422no—
560C22⋊C4—1422no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—2841no—
566C42—712no—
567C42—712no—
568C42—712no—
569C42—712no—
570C42—714no—
571C42—1422no—
572C42—1422no—
573C42—1422no—
574C42—1422no—
575C42—1422no—
576C42—1422no—
577C42—1421no—
578C42—1421no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—712no—
586C23—1421no—
587C23—1421no—
588C23—1421no—
589C23—1421no—
590C23—1421no—
591C23—1421no—
592C23M16×D7112yes—
593C23C22×C4×D7111yescharacteristic
594D4—1428no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—2844no—
614C2×C4—2844no—
615C2×C4—2844no—
616C2×C4—2844no—
617C2×C4—2841no—
618C2×C4—2841no—
619C2×C4—2841no—
620C2×C4—2841no—
621C2×C4—712no—
622C2×C4—712no—
623C2×C4—712no—
624C2×C4—712no—
625C2×C4—712no—
626C2×C4—712no—
627C2×C4—712no—
628C2×C4—712no—
629C2×C4—1421no—
630C2×C4—1421no—
631C2×C4—1421no—
632C2×C4—1421no—
633C2×C4—1421no—
634C2×C4—1421no—
635C2×C4—1421no—
636C2×C4—1421no—
637C2×C4—1421no—
638C2×C4—1421no—
639C2×C4—1421no—
640C2×C4—1421no—
641C2×C4—1421no—
642C2×C4M16×D7112yes—
643C2×C4C2×D4×D7111yescharacteristic
644C2×C4#41×D7111yescharacteristic
645C2×C4#41×D7111yescharacteristic
646C2×C4#41×D7111yescharacteristic
647C2×C4#1455617311yescharacteristic
648C2×C4#1455617511yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C8—2841no—
654C8—2841no—
655C8—2841no—
656C8—1422no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—2841no—
665C22—2841no—
666C22—2841no—
667C22—2841no—
668C22—1422no—
669C22—1422no—
670C22—1422no—
671C22#117×D7111yescharacteristic
672C22C4×D4×D7111yescharacteristic
673C22#1798647811yescharacteristic
674C22C2×M16×D7111yescharacteristic
675C22C2×M16×D7111yescharacteristic
676C22#131×D7111yescharacteristic
677C22#1798676411yescharacteristic
678C4—22no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—2841no—
684C4—2841no—
685C4—2841no—
686C4—714no—
687C4—714no—
688C4—1422no—
689C4—1422no—
690C4#1798664711yescharacteristic
691C4#1798666711yescharacteristic
692C4#1798671111yescharacteristic
693C4#1798671611yescharacteristic
694C2—42no—
695C2—2842no—
696C2#2259128611yescharacteristic
697C2#432×D7111yescharacteristic
698C2#2259700311yescharacteristic
699C2#436×D7111yescharacteristic
700C2#2259707311yescharacteristic
701C2#2259745211yescharacteristic
702C2#2259746011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1924C2
prime radicalC22×C22⋊D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1924D71
hypocenterC71#22799
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#17986054C2semidirect
2. C2×#17986053C2semidirect
6. #22588955C2semidirect
7. #22588954C2semidirect
8. #22588952C2semidirect
9. #22588491C2semidirect
10. #22588319C2semidirect
11. #22588318C2semidirect
12. #22588208C2semidirect
13. #22588206C2semidirect
14. #22588188C2semidirect
15. C71×#1924C2semidirect
103. Dic71⋊C8D4semidirect
340. Dic71#432semidirect
360. #1924D71semidirect
367. C71#22799semidirect

Maximal subgroups

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

subgroupindex
C2×#179860542
C2×#179860532
C4×(C22⋊D71)⋊C42
#225891322
#225889552
#225889542
#225889522
#225884912
#225883192
#225883182
#225882082
#225882062
#225881882
C71×#19242
#2279971