Finite Group Databasebeta

← #32015497

Subgroups — #32015497

Order 18176.

1116 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986072C211yesmaximal, characteristic
2C2×#17986069C211yesmaximal, characteristic
3C2×#17986021C211yesmaximal, characteristic, complemented
4C2×C4⋊C8×D71C211yesmaximal, characteristic, complemented
5C4×#14556090C211yesmaximal, characteristic
6#22589064C211yesmaximal, characteristic, complemented
7#22588524C211yesmaximal, characteristic, complemented
8#22588521C211yesmaximal, characteristic, complemented
9#22588519C211yesmaximal, characteristic, complemented
10#22588516C211yesmaximal, characteristic, complemented
11#22588491C211yesmaximal, characteristic, complemented
12#22588319C211yesmaximal, characteristic, complemented
13#22588319C211yesmaximal, characteristic, complemented
14#22588194C211yesmaximal, characteristic, complemented
15C71×#1940C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20C2×C4×D284C2211yescharacteristic
21C2×#14556090C411yescharacteristic
22C2×#14556090C411yescharacteristic
23C2×C42×D71C2211yescharacteristic
24C2×C42×D71C2211yescharacteristic
25#17986072—24no—
26#17986069—24no—
27#17986021—24no—
28C2×C4⋊(C71⋊C8)C2211yescharacteristic
29C2×C4⋊(C71⋊C8)C2211yescharacteristic
30C2×C4⋊(C71⋊C8)C2211yescharacteristic
31C2×Dic71⋊C8C2211yescharacteristic
32C2×Dic71⋊C8C2211yescharacteristic
33C2×Dic71⋊C8C2211yescharacteristic
34C2×Dic71⋊C8C2211yescharacteristic
35C2×Dic71⋊C8C2211yescharacteristic
36C2×Dic71⋊C8C2211yescharacteristic
37C4⋊C8×D71—24no—
38C2×(C2×D71)⋊C8C2211yescharacteristic
39C2×(C2×D71)⋊C8C2211yescharacteristic
40C2×(C2×D71)⋊C8C2211yescharacteristic
41C2×(C2×D71)⋊C8C2211yescharacteristic
42C2×#14556039C2211yescharacteristic
43C4⋊C4×Dic71C411yescharacteristic
44C4⋊C4×Dic71C411yescharacteristic
45C4×(C2×D71)⋊C4C2211yescharacteristic
46C4×(C2×D71)⋊C4C2211yescharacteristic
47#17985846C411yescharacteristic
48#17985846C411yescharacteristic
49#17985846C411yescharacteristic
50#17985846C411yescharacteristic
51C42×Dic71C2211yescharacteristic
52#17985754C2211yescharacteristic
53#17985754C2211yescharacteristic
54#17985753C2211yescharacteristic
55#17985753C2211yescharacteristic
56C2×C4⋊C8×C71C2211yescharacteristic
57C2×C4⋊C8×C71C2211yescharacteristic
58C2×C4⋊C8×C71C2211yescharacteristic
59C2×#97×C71C2211yescharacteristic
60C4×C4⋊C4×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic
62#336×C71C2211yescharacteristic
63C22×D284C2×C411yescharacteristic
64C22×C4×D71C2×C411yescharacteristic
65C22×C4×D71C2×C411yescharacteristic
66C22×C4×D71C2×C411yescharacteristic
67C22×C4×D71C2×C411yescharacteristic
68C22×C4×D71C2311yescharacteristic
69C22×C4×D71C2311yescharacteristic
70C2×#11765848—22no—
71C2×#11765848—22no—
72C2×#11765848—22no—
73C2×#11765848—22no—
74C2×#11765848—41no—
75C2×#11765848—41no—
76C22×C71⋊C8C2311yescharacteristic
77C22×C71⋊C8C2311yescharacteristic
78C22×C71⋊C8C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80C2×C8×D71—22no—
81C2×C8×D71—22no—
82C2×C8×D71—22no—
83C2×C8×D71—22no—
84C2×C8×D71—41no—
85C2×C8×D71—41no—
86C4×D284D414yes—
87C4×D284Q814yes—
88#14556090—24no—
89#14556090—24no—
90C2×C4⋊Dic71C2×C411yescharacteristic
91C2×(C2×D71)⋊C4C2×C411yescharacteristic
92C2×(C2×D71)⋊C4C2×C411yescharacteristic
93C2×(C2×D71)⋊C4C2×C411yescharacteristic
94C2×(C2×D71)⋊C4C2×C411yescharacteristic
95C2×(C2×D71)⋊C4C2×C411yescharacteristic
96C2×(C2×D71)⋊C4C2×C411yescharacteristic
97C2×C4×Dic71C2×C411yescharacteristic
98C2×C4×Dic71C2×C411yescharacteristic
99C2×C4×Dic71C2×C411yescharacteristic
100C2×C4×Dic71C2×C411yescharacteristic
101C2×C4×Dic71C2×C411yescharacteristic
102C2×C4×Dic71C2×C411yescharacteristic
103C2×C4×Dic71C2×C411yescharacteristic
104C2×C4×Dic71C2×C411yescharacteristic
105C2×C4×Dic71C2311yescharacteristic
106C2×C4×Dic71C2311yescharacteristic
107C42×D71—22no—
108C42×D71—22no—
109C42×D71—22no—
110C42×D71—22no—
111C4⋊(C71⋊C8)—22no—
112C4⋊(C71⋊C8)—22no—
113C4⋊(C71⋊C8)—22no—
114Dic71⋊C8—22no—
115Dic71⋊C8—22no—
116Dic71⋊C8—22no—
117Dic71⋊C8—41no—
118Dic71⋊C8—41no—
119Dic71⋊C8D414yescomplemented
120(C2×D71)⋊C8—22no—
121(C2×D71)⋊C8—22no—
122(C2×D71)⋊C8—22no—
123(C2×D71)⋊C8—22no—
124#14556039—22no—
125C71⋊#95C2×C411yescharacteristic
126C71⋊#95C2×C411yescharacteristic
127C71⋊#95C2×C411yescharacteristic
128C71⋊#95C2×C411yescharacteristic
129C22×C8×C71C2311yescharacteristic
130C22×C8×C71C2311yescharacteristic
131C22×C8×C71C2311yescharacteristic
132C22×C8×C71C2311yescharacteristic
133C2×C4⋊C4×C71C2×C411yescharacteristic
134C2×C4⋊C4×C71C2×C411yescharacteristic
135C2×C42×C71C2311yescharacteristic
136C2×C42×C71C2311yescharacteristic
137C2×C42×C71C2311yescharacteristic
138C4⋊C8×C71—22no—
139C4⋊C8×C71—22no—
140C4⋊C8×C71—22no—
141#97×C71—22no—
142#95×C71C2×C411yescharacteristic
143#95×C71C2×C411yescharacteristic
144C23×D71C22×C411yescharacteristic
145C23×D71C22×C411yescharacteristic
146C2×D284—22no—
147C2×D284—22no—
148C2×D284C4⋊C414yes—
149C22×Dic71C22×C411yescharacteristic
150C22×Dic71C22×C411yescharacteristic
151C22×Dic71C22×C411yescharacteristic
152C22×Dic71C22×C411yescharacteristic
153C22×Dic71C22×C411yescharacteristic
154C22×Dic71C22×C411yescharacteristic
155C2×C4×D71—21no—
156C2×C4×D71—21no—
157C2×C4×D71—21no—
158C2×C4×D71—21no—
159C2×C4×D71—21no—
160C2×C4×D71—21no—
161C2×C4×D71—21no—
162C2×C4×D71—21no—
163C2×C4×D71—22no—
164C2×C4×D71—22no—
165C2×C4×D71—22no—
166C2×C4×D71—22no—
167C2×C4×D71—22no—
168C2×C4×D71—22no—
169C2×C4×D71—22no—
170C2×C4×D71—22no—
171C2×C4×D71—22no—
172C2×C4×D71—41no—
173C2×C4×D71—41no—
174C2×C4×D71M1614yescomplemented
175C2×C4×D71C2×D412yes—
176C2×C4×D71C2×D412yes—
177C2×C4×D71C2×Q812yes—
178C2×C4×D71C2×Q812yes—
179#11765848—44no—
180#11765848—44no—
181C2×C71⋊C8—21no—
182C2×C71⋊C8—21no—
183C2×C71⋊C8—21no—
184C2×C71⋊C8—21no—
185C2×C71⋊C8—21no—
186C2×C71⋊C8—21no—
187C2×C71⋊C8—21no—
188C2×C71⋊C8—21no—
189C2×C71⋊C8—21no—
190C2×C71⋊C8—21no—
191C2×C71⋊C8—21no—
192C2×C71⋊C8C2×D412yes—
193C8×D71—44no—
194C8×D71—44no—
195C4⋊Dic71C4⋊C414yes—
196(C2×D71)⋊C4—22no—
197(C2×D71)⋊C4—22no—
198(C2×D71)⋊C4—22no—
199(C2×D71)⋊C4C4⋊C414yes—
200(C2×D71)⋊C4C4⋊C414yes—
201(C2×D71)⋊C4M1614yescomplemented
202C4×Dic71—21no—
203C4×Dic71—21no—
204C4×Dic71—22no—
205C4×Dic71—22no—
206C4×Dic71—22no—
207C4×Dic71—22no—
208C4×Dic71—22no—
209C4×Dic71—22no—
210C4×Dic71—22no—
211C4×Dic71—41no—
212C4×Dic71C2×D412yes—
213C4×Dic71#4112yes—
214C22×C4×C71C22×C411yescharacteristic
215C22×C4×C71C22×C411yescharacteristic
216C22×C4×C71C22×C411yescharacteristic
217C22×C4×C71C22×C411yescharacteristic
218C22×C4×C71C22×C411yescharacteristic
219C22×C4×C71C22×C411yescharacteristic
220C22×C4×C71C2411yescharacteristic
221C2×C8×C71—21no—
222C2×C8×C71—21no—
223C2×C8×C71—21no—
224C2×C8×C71—21no—
225C2×C8×C71—21no—
226C2×C8×C71—21no—
227C2×C8×C71—21no—
228C2×C8×C71—21no—
229C2×C8×C71—21no—
230C2×C8×C71—21no—
231C2×C8×C71—21no—
232C2×C8×C71C2×D412yes—
233C4⋊C4×C71—22no—
234C4⋊C4×C71—22no—
235C42×C71—21no—
236C42×C71—21no—
237C42×C71—21no—
238C42×C71—21no—
239C42×C71C2×D412yes—
240C42×C71C2×Q812yes—
241C23×C71C23×C411yescharacteristic
242C22×D71—21no—
243C22×D71—21no—
244C22×D71—21no—
245C22×D71—21no—
246C22×D71—21no—
247C22×D71—21no—
248C22×D71—21no—
249C22×D71—21no—
250C22×D71—21no—
251C22×D71—21no—
252C22×D71C2×C4⋊C412yes—
253C22×D71C2×C4⋊C412yes—
254C22×D71C2×M1612yes—
255C22×D71C2×M1612yes—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—21no—
267C2×C4×C71—21no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71C2×C4⋊C412yes—
271C2×C4×C71C2×C4⋊C412yes—
272C2×C4×C71C2×M1612yes—
273C2×C4×C71C2×M1612yes—
274C2×C4×C71C22×D411yescharacteristic
275C2×C4×C71C22×D411yescharacteristic
276C2×C4×C71C22×Q811yescharacteristic
277C2×C4×C71C2×#4111yescharacteristic
278C2×C4×C71H(5,𝔽2)11yescharacteristic
279C2×C4×C712−1+411yescharacteristic
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×Dic71—21no—
291C2×Dic71C2×C4⋊C412yes—
292C2×Dic71C2×C4⋊C412yes—
293C2×Dic71C4×D412yes—
294C2×Dic71C4×D412yes—
295C2×Dic71C2×M1612yes—
296C2×Dic71C2×M1612yes—
297C2×Dic71#13112yes—
298D284—28no—
299C4×D71—22no—
300C4×D71—22no—
301C4×D71—22no—
302C4×D71—22no—
303C4×D71—22no—
304C4×D71—22no—
305C4×D71—22no—
306C4×D71—22no—
307C4×D71—28no—
308C4×D71—44no—
309C4×D71—44no—
310C4×D71—44no—
311C8×C71—22no—
312C8×C71—41no—
313C8×C71—41no—
314C8×C71—41no—
315C71⋊C8—22no—
316C71⋊C8—41no—
317C71⋊C8—41no—
318C71⋊C8—41no—
319C22×C71C22×C4⋊C411yescharacteristic
320C22×C71C2×C4×D411yescharacteristic
321C22×C71#52011yescharacteristic
322C22×C71C22×M1611yescharacteristic
323C22×C71C22×M1611yescharacteristic
324C22×C71C2×#13111yescharacteristic
325C22×C71#56811yescharacteristic
326C2×D71—22no—
327C2×D71—22no—
328C2×D71—22no—
329C2×D71—22no—
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71—22no—
334C2×D71—22no—
335C2×D71—41no—
336C2×D71—41no—
337C2×D71—41no—
338C2×D71—41no—
339C2×D71#42314yescomplemented
340C4×C71—22no—
341C4×C71—22no—
342C4×C71—22no—
343C4×C71—22no—
344C4×C71—41no—
345C4×C71—41no—
346C4×C71D4211yescharacteristic
347C4×C71#54711yescharacteristic
348C4×C71D4×Q811yescharacteristic
349C4×C71#55411yescharacteristic
350Dic71—22no—
351Dic71—22no—
352Dic71—22no—
353Dic71—22no—
354Dic71—41no—
355Dic71#43514yescomplemented
356#22648—711nomaximal, Sylow
357C2×C71D4×C4⋊C411yescharacteristic
358C2×C71C2×#42311yescharacteristic
359C2×C71#290611yescharacteristic
360C2×C71C2×#43511yescharacteristic
361C2×C71D4×M1611yescharacteristic
362C2×C71#298911yescharacteristic
363C2×C71#299011yescharacteristic
364D71—24no—
365D71—42no—
366C2×#435—711no—
367C2×#435—711no—
368C2×#423—711no—
369C22×C4⋊C8—711no—
370C42×D4—711no—
371#1940—711no—
372#1940D7111yescharacteristic, complemented
373#1851—711no—
374#1851—711no—
375#1850—711no—
376#1850—711no—
377#1842—711no—
378#1797—711no—
379#1797—711no—
380#1767—711no—
381C71#2264811yescharacteristic, complemented, Sylow
382C22×M16—711no—
383C22×M16—711no—
384C23×C8—711no—
385C23×C8—711no—
386C2×C4×D4—711no—
387C2×C4×D4—711no—
388C2×C4×D4—711no—
389C22×C42—711no—
390C22×C42—711no—
391#435—1424no—
392#435—1424no—
393#423—1424no—
394C2×C4⋊C8—711no—
395C2×C4⋊C8—711no—
396C2×C4⋊C8—711no—
397C2×C4⋊C8—711no—
398C2×C4⋊C8—711no—
399C2×C4⋊C8—711no—
400C2×C4⋊C8—711no—
401C2×C4⋊C8—711no—
402C2×C4⋊C8—711no—
403C2×C4⋊C8—1424no—
404C2×C4⋊C8C2×D7111yescharacteristic
405C2×C4⋊C8C2×D7111yescharacteristic
406C2×C4⋊C8C2×D7111yescharacteristic
407C2×C22⋊C8—711no—
408C2×C22⋊C8—711no—
409C2×C22⋊C8—711no—
410C2×C22⋊C8—711no—
411C2×#97—711no—
412C2×#97C2×D7111yescharacteristic
413C4×C4⋊C4—711no—
414C4×C4⋊C4—711no—
415C4×C4⋊C4C2×D7111yescharacteristic
416C4×C22⋊C4—711no—
417C4×C22⋊C4—711no—
418C4×C22⋊C4—711no—
419C4×C22⋊C4—711no—
420C4×C22⋊C4—711no—
421C4×C22⋊C4—711no—
422C43—711no—
423#336—711no—
424#336—711no—
425#336—711no—
426#336—711no—
427#336C2×D7111yescharacteristic
428#336C2×D7111yescharacteristic
429C22×D4—711no—
430C23×C4—711no—
431C23×C4—711no—
432C23×C4—711no—
433C23×C4—711no—
434C23×C4—711no—
435C23×C4—711no—
436C2×M16—2841no—
437C2×M16—2841no—
438C2×M16—1422no—
439C2×M16—1422no—
440C2×M16—1422no—
441C2×M16—1422no—
442C22×C8—2841no—
443C22×C8—2841no—
444C22×C8—711no—
445C22×C8—711no—
446C22×C8—711no—
447C22×C8—711no—
448C22×C8—1422no—
449C22×C8—1422no—
450C22×C8—1422no—
451C22×C8—1422no—
452C22×C8C22×D7111yescharacteristic
453C22×C8C22×D7111yescharacteristic
454C22×C8C22×D7111yescharacteristic
455C22×C8C22×D7111yescharacteristic
456C4×D4—714no—
457C4×D4—714no—
458C4×D4—1424no—
459C4×D4—1424no—
460C2×C4⋊C4—711no—
461C2×C4⋊C4C4×D7111yescharacteristic
462C2×C4⋊C4C4×D7111yescharacteristic
463C2×C22⋊C4—711no—
464C2×C22⋊C4—711no—
465C2×C22⋊C4—711no—
466C2×C22⋊C4—711no—
467C2×C22⋊C4—711no—
468C2×C22⋊C4—711no—
469C2×C42—711no—
470C2×C42—711no—
471C2×C42—711no—
472C2×C42—711no—
473C2×C42—711no—
474C2×C42—711no—
475C2×C42—711no—
476C2×C42—711no—
477C2×C42—711no—
478C2×C42—711no—
479C2×C42—1422no—
480C2×C42—1422no—
481C2×C42—1422no—
482C2×C42—1422no—
483C2×C42C22×D7111yescharacteristic
484C2×C42C22×D7111yescharacteristic
485C2×C42C22×D7111yescharacteristic
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8—2841no—
490C4⋊C8—2841no—
491C4⋊C8—714no—
492C4⋊C8—1422no—
493C4⋊C8—1422no—
494C4⋊C8—1422no—
495C4⋊C8—1422no—
496C4⋊C8—1422no—
497C4⋊C8—1422no—
498C22⋊C8—1422no—
499C22⋊C8—1422no—
500C22⋊C8—1422no—
501C22⋊C8—1422no—
502#97—22no—
503#97—1422no—
504#95—711no—
505#95—711no—
506#95—711no—
507#95—711no—
508#95C4×D7111yescharacteristic
509#95C4×D7111yescharacteristic
510C24—711no—
511C24—711no—
512C2×D4—714no—
513C2×D4—1422no—
514C2×D4—1422no—
515C22×C4—2841no—
516C22×C4—2841no—
517C22×C4—711no—
518C22×C4—711no—
519C22×C4—711no—
520C22×C4—711no—
521C22×C4—711no—
522C22×C4—712no—
523C22×C4—712no—
524C22×C4—712no—
525C22×C4—712no—
526C22×C4—714no—
527C22×C4—711no—
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—1421no—
538C22×C4—1421no—
539C22×C4—1421no—
540C22×C4—1421no—
541C22×C4—1421no—
542C22×C4—1421no—
543C22×C4—1421no—
544C22×C4—1421no—
545C22×C4C2×C4×D7111yescharacteristic
546C22×C4C2×C4×D7111yescharacteristic
547C22×C4C2×C4×D7111yescharacteristic
548C22×C4C2×C4×D7111yescharacteristic
549C22×C4C2×C4×D7111yescharacteristic
550C22×C4C2×C4×D7111yescharacteristic
551C22×C4C23×D7111yescharacteristic
552M16—2844no—
553M16—2844no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—2844no—
566C2×C8—2844no—
567C2×C8—712no—
568C2×C8—1421no—
569C2×C8—1421no—
570C2×C8—1421no—
571C2×C8—1421no—
572C2×C8—1421no—
573C2×C8—1421no—
574C2×C8—1421no—
575C2×C8—1421no—
576C2×C8—1421no—
577C2×C8—1421no—
578C2×C8—1421no—
579C2×C8D4×D7112yes—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—714no—
583C22⋊C4—714no—
584C22⋊C4—714no—
585C22⋊C4—714no—
586C22⋊C4—1422no—
587C22⋊C4—1422no—
588C22⋊C4—1422no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—2841no—
594C42—712no—
595C42—712no—
596C42—1422no—
597C42—1422no—
598C42—1422no—
599C42—1422no—
600C42—1422no—
601C42—1422no—
602C42—1422no—
603C42—1421no—
604C42—1421no—
605C42D4×D7112yes—
606C42Q8×D7112yes—
607C23—712no—
608C23—712no—
609C23—712no—
610C23—712no—
611C23—1421no—
612C23—1421no—
613C23—1421no—
614C23—1421no—
615C23—1421no—
616C23—1421no—
617C23—1421no—
618C23—1421no—
619C23—1421no—
620C23—1421no—
621C23C22×C4×D7111yescharacteristic
622D4—1428no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—2844no—
638C2×C4—2844no—
639C2×C4—2844no—
640C2×C4—712no—
641C2×C4—712no—
642C2×C4—712no—
643C2×C4—712no—
644C2×C4—712no—
645C2×C4—712no—
646C2×C4—712no—
647C2×C4—1428no—
648C2×C4—1421no—
649C2×C4—1421no—
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—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1422no—
667C2×C4C4⋊C4×D7112yes—
668C2×C4C4⋊C4×D7112yes—
669C2×C4M16×D7112yes—
670C2×C4M16×D7112yes—
671C2×C4C2×D4×D7111yescharacteristic
672C2×C4C2×D4×D7111yescharacteristic
673C2×C4C2×Q8×D7111yescharacteristic
674C2×C4#41×D7111yescharacteristic
675C2×C4#1455617411yescharacteristic
676C2×C4#1455617611yescharacteristic
677C8—22no—
678C8—41no—
679C8—41no—
680C8—41no—
681C8—2841no—
682C8—2841no—
683C8—2841no—
684C8—1422no—
685C22—2841no—
686C22—2841no—
687C22—2841no—
688C22—2841no—
689C22—714no—
690C22—1422no—
691C22—1422no—
692C22—1422no—
693C22—1422no—
694C22—1422no—
695C22—1422no—
696C22—1422no—
697C22—1422no—
698C22—1422no—
699C22C2×C4⋊C4×D7111yescharacteristic
700C22C4×D4×D7111yescharacteristic
701C22#1798648111yescharacteristic
702C22C2×M16×D7111yescharacteristic
703C22C2×M16×D7111yescharacteristic
704C22#131×D7111yescharacteristic
705C22#1798676411yescharacteristic
706C4—22no—
707C4—22no—
708C4—22no—
709C4—22no—
710C4—41no—
711C4—41no—
712C4—2841no—
713C4—714no—
714C4—1422no—
715C4—1422no—
716C4—1422no—
717C4—1422no—
718C4#1798663311yescharacteristic
719C4#1798665111yescharacteristic
720C4#1798666411yescharacteristic
721C4#1798670511yescharacteristic
722C2—2842no—
723C2—1424no—
724C2#2259124111yescharacteristic
725C2#423×D7111yescharacteristic
726C2#2259690711yescharacteristic
727C2#435×D7111yescharacteristic
728C2#2259707311yescharacteristic
729C2#2259745611yescharacteristic
730C2#2259746411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1940C2
prime radicalC22×D284C2×C4
cosocleC22×C4×C71C24
hypercenter#1940D71
hypocenterC71#22648
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
3. C2×#17986021C2semidirect
4. C2×C4⋊C8×D71C2semidirect
6. #22589064C2semidirect
7. #22588524C2semidirect
8. #22588521C2semidirect
9. #22588519C2semidirect
10. #22588516C2semidirect
11. #22588491C2semidirect
12. #22588319C2semidirect
13. #22588319C2semidirect
14. #22588194C2semidirect
15. C71×#1940C2semidirect
119. Dic71⋊C8D4semidirect
174. C2×C4×D71M16semidirect
201. (C2×D71)⋊C4M16semidirect
339. C2×D71#423semidirect
355. Dic71#435semidirect
372. #1940D71semidirect
381. C71#22648semidirect

Maximal subgroups

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

subgroupindex
C2×#179860722
C2×#179860692
C2×#179860212
C2×C4⋊C8×D712
C4×#145560902
#225890642
#225885242
#225885212
#225885192
#225885162
#225884912
#225883192
#225881942
C71×#19402
#2264871