Finite Group Databasebeta

← #32019595

Subgroups — #32019595

Order 18176.

1050 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986075C211yesmaximal, characteristic, complemented
2C2×#17986069C211yesmaximal, characteristic, complemented
3C2×#17986068C211yesmaximal, characteristic, complemented
4C4×#14556102C211yesmaximal, characteristic
5#22589137C211yesmaximal, characteristic, complemented
6#22589061C211yesmaximal, characteristic, complemented
7#22588952C211yesmaximal, characteristic, complemented
8#22588945C211yesmaximal, characteristic, complemented
9#22588637C211yesmaximal, characteristic, complemented
10#22588637C211yesmaximal, characteristic, complemented
11#22588521C211yesmaximal, characteristic, complemented
12#22588516C211yesmaximal, characteristic, complemented
13#22588217C211yesmaximal, characteristic, complemented
14#22588102C211yesmaximal, characteristic, complemented
15C2×#423×C71C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C2×#14556102C411yescharacteristic
19C2×C4×D284C2211yescharacteristic
20C2×C4×C22⋊D71C2211yescharacteristic
21C2×C4×C22⋊D71C2211yescharacteristic
22#17986075—24no—
23#17986069—24no—
24#17986068—24no—
25C2×Dic71⋊C8C2211yescharacteristic
26C2×Dic71⋊C8C2211yescharacteristic
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×C22⋊(C71⋊C8)C2211yescharacteristic
29C2×(C2×D71)⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×#14556039C2211yescharacteristic
36C2×#14556039C2211yescharacteristic
37C2×#14556038C2211yescharacteristic
38C2×C8×Dic71C2211yescharacteristic
39#17985901C411yescharacteristic
40#17985897C411yescharacteristic
41#17985890C411yescharacteristic
42#17985890C411yescharacteristic
43#17985878C411yescharacteristic
44#17985878C411yescharacteristic
45#17985859C411yescharacteristic
46C4×C4⋊Dic71C2211yescharacteristic
47C4×(C2×D71)⋊C4C2211yescharacteristic
48C4×(C2×D71)⋊C4C2211yescharacteristic
49#17985754C2211yescharacteristic
50#17985754C2211yescharacteristic
51#17985753C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54#17985753C2211yescharacteristic
55C22×M16×C71C2211yescharacteristic
56C22×M16×C71C2211yescharacteristic
57C22×C42×C71C2211yescharacteristic
58#423×C71—24no—
59C2×C4⋊C8×C71C2211yescharacteristic
60C2×C4⋊C8×C71C2211yescharacteristic
61C2×C4⋊C8×C71C2211yescharacteristic
62C2×C4⋊C8×C71C2211yescharacteristic
63C22×D284C2×C411yescharacteristic
64C22×C22⋊D71C2×C411yescharacteristic
65C22×C22⋊D71C2×C411yescharacteristic
66C22×C4×D71C2311yescharacteristic
67C22×C4×D71C2311yescharacteristic
68C2×#11765848—22no—
69C2×#11765848—22no—
70C2×#11765848—41no—
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74C22×C71⋊C8C2311yescharacteristic
75C2×C8×D71—22no—
76C2×C8×D71—22no—
77C2×C8×D71—41no—
78#14556102—24no—
79C4×D284—22no—
80C4×D284—22no—
81C4×C22⋊D71—22no—
82C4×C22⋊D71—22no—
83C4×C22⋊D71—22no—
84C4×C22⋊D71—22no—
85C2×C4⋊Dic71C2×C411yescharacteristic
86C2×C4⋊Dic71C2×C411yescharacteristic
87C2×C4⋊Dic71C2×C411yescharacteristic
88C2×Dic71⋊C4C2×C411yescharacteristic
89C2×Dic71⋊C4C2×C411yescharacteristic
90C2×C22⋊Dic71C2×C411yescharacteristic
91C2×C22⋊Dic71C2×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×(C2×D71)⋊C4C2×C411yescharacteristic
98C2×(C2×D71)⋊C4C2×C411yescharacteristic
99C2×(C2×D71)⋊C4C2×C411yescharacteristic
100C2×C4×Dic71C2311yescharacteristic
101C2×C4×Dic71C2311yescharacteristic
102Dic71⋊C8—22no—
103Dic71⋊C8—22no—
104C22⋊(C71⋊C8)—22no—
105C22⋊(C71⋊C8)D414yescomplemented
106(C2×D71)⋊C8—22no—
107(C2×D71)⋊C8—22no—
108(C2×D71)⋊C8—22no—
109(C2×D71)⋊C8—22no—
110(C2×D71)⋊C8—41no—
111(C2×D71)⋊C8—41no—
112#14556039—22no—
113#14556039—22no—
114#14556038—22no—
115C8×Dic71—22no—
116C71⋊#95C2×C411yescharacteristic
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C71⋊#95C2×C411yescharacteristic
120C71⋊#95C2×C411yescharacteristic
121C71⋊#95C2×C411yescharacteristic
122C23×C4×C71C2×C411yescharacteristic
123C23×C4×C71C2×C411yescharacteristic
124C23×C4×C71C2311yescharacteristic
125C2×M16×C71—22no—
126C2×M16×C71—22no—
127C2×M16×C71—22no—
128C2×M16×C71—22no—
129C2×M16×C71—41no—
130C2×M16×C71—41no—
131C22×C8×C71C2311yescharacteristic
132C22×C8×C71C2311yescharacteristic
133C22×C8×C71C2311yescharacteristic
134C22×C8×C71C2311yescharacteristic
135C2×C42×C71—22no—
136C2×C42×C71—22no—
137C2×C42×C71C2×C411yescharacteristic
138C2×C42×C71C2×C411yescharacteristic
139C2×C42×C71C2311yescharacteristic
140C2×C42×C71C2311yescharacteristic
141C4⋊C8×C71—22no—
142C4⋊C8×C71—22no—
143C4⋊C8×C71—22no—
144C4⋊C8×C71D414yescomplemented
145C23×D71C22×C411yescharacteristic
146C23×D71C22×C411yescharacteristic
147C2×D284—22no—
148C2×D284—22no—
149C2×D284—41no—
150C2×C22⋊D71—22no—
151C2×C22⋊D71—22no—
152C2×C22⋊D71—22no—
153C2×C22⋊D71—22no—
154C2×C22⋊D71—41no—
155C2×C22⋊D71—41no—
156C22×Dic71C22×C411yescharacteristic
157C22×Dic71C22×C411yescharacteristic
158C22×Dic71C22×C411yescharacteristic
159C22×Dic71C22×C411yescharacteristic
160C22×Dic71C22×C411yescharacteristic
161C22×Dic71C22×C411yescharacteristic
162C2×C4×D71—21no—
163C2×C4×D71—21no—
164C2×C4×D71—21no—
165C2×C4×D71—21no—
166C2×C4×D71—21no—
167C2×C4×D71—21no—
168C2×C4×D71—21no—
169C2×C4×D71—21no—
170C2×C4×D71—21no—
171C2×C4×D71—21no—
172C2×C4×D71—21no—
173C2×C4×D71—21no—
174#11765848—44no—
175C2×C71⋊C8—21no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—21no—
178C2×C71⋊C8—21no—
179C2×C71⋊C8—21no—
180C2×C71⋊C8—21no—
181C2×C71⋊C8—21no—
182C2×C71⋊C8—21no—
183C2×C71⋊C8—21no—
184C2×C71⋊C8—21no—
185C2×C71⋊C8C2×D412yes—
186C2×C71⋊C8C2×D412yes—
187C8×D71—44no—
188C4⋊Dic71—22no—
189C4⋊Dic71—22no—
190C4⋊Dic71—41no—
191Dic71⋊C4—22no—
192Dic71⋊C4—22no—
193C22⋊Dic71—22no—
194C22⋊Dic71—22no—
195(C2×D71)⋊C4—22no—
196(C2×D71)⋊C4—22no—
197(C2×D71)⋊C4—22no—
198(C2×D71)⋊C4—22no—
199(C2×D71)⋊C4—22no—
200(C2×D71)⋊C4—41no—
201(C2×D71)⋊C4—41no—
202(C2×D71)⋊C4M1614yescomplemented
203C4×Dic71—21no—
204C4×Dic71—21no—
205C4×Dic71—21no—
206C4×Dic71—21no—
207C24×C71C22×C411yescharacteristic
208C22×C4×C71—21no—
209C22×C4×C71—21no—
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—41no—
216C22×C4×C71—41no—
217C22×C4×C71—41no—
218C22×C4×C71C22×C411yescharacteristic
219C22×C4×C71C22×C411yescharacteristic
220C22×C4×C71C22×C411yescharacteristic
221C22×C4×C71C22×C411yescharacteristic
222C22×C4×C71C22×C411yescharacteristic
223C22×C4×C71C2×D412yes—
224C22×C4×C71#4112yes—
225C22×C4×C71C2411yescharacteristic
226M16×C71—44no—
227M16×C71—44no—
228C2×C8×C71—21no—
229C2×C8×C71—21no—
230C2×C8×C71—21no—
231C2×C8×C71—21no—
232C2×C8×C71—21no—
233C2×C8×C71—21no—
234C2×C8×C71—21no—
235C2×C8×C71—21no—
236C2×C8×C71—21no—
237C2×C8×C71—21no—
238C2×C8×C71C2×D412yes—
239C2×C8×C71C2×D412yes—
240C42×C71—22no—
241C42×C71—22no—
242C42×C71—21no—
243C42×C71—21no—
244C42×C71C2×D412yes—
245C42×C71#4112yes—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—21no—
252C23×C71C4×D412yes—
253C23×C71C23×C411yescharacteristic
254C22×D71—21no—
255C22×D71—21no—
256C22×D71—21no—
257C22×D71—21no—
258C22×D71—21no—
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—21no—
262C22×D71—21no—
263C22×D71—21no—
264C22×D71—21no—
265C22×D71—21no—
266C22×D71—21no—
267C22×D71C2×M1612yes—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—21no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—21no—
281C2×C4×C71—21no—
282C2×C4×C71—21no—
283C2×C4×C71—44no—
284C2×C4×C71—44no—
285C2×C4×C71C4×D412yes—
286C2×C4×C71C4×D412yes—
287C2×C4×C71C4×D412yes—
288C2×C4×C71C2×M1612yes—
289C2×C4×C71C22×D411yescharacteristic
290C2×C4×C71C22×D411yescharacteristic
291C2×C4×C71C2×#4111yescharacteristic
292C2×C4×C71C2×#4111yescharacteristic
293C2×C4×C71H(5,𝔽2)11yescharacteristic
294C2×C4×C712−1+411yescharacteristic
295C22⋊D71—44no—
296C22⋊D71—44no—
297C2×Dic71—21no—
298C2×Dic71—21no—
299C2×Dic71—21no—
300C2×Dic71—21no—
301C2×Dic71—21no—
302C2×Dic71—21no—
303C2×Dic71—21no—
304C2×Dic71—21no—
305C2×Dic71—21no—
306C2×Dic71—21no—
307C2×Dic71—21no—
308C2×Dic71—21no—
309C2×Dic71—21no—
310C2×Dic71—21no—
311C2×Dic71—21no—
312C2×Dic71—21no—
313C2×Dic71—21no—
314C2×Dic71C2×M1612yes—
315D284—44no—
316C4×D71—41no—
317C4×D71—41no—
318C4×D71—41no—
319C4×D71—41no—
320C4×D71—41no—
321C4×D71—41no—
322C4×D71—41no—
323C4×D71—41no—
324C8×C71—22no—
325C8×C71—22no—
326C8×C71—41no—
327C8×C71—41no—
328C71⋊C8—22no—
329C71⋊C8—22no—
330C71⋊C8—41no—
331C71⋊C8—41no—
332C22×C71—22no—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—41no—
336C22×C71—41no—
337C22×C71—41no—
338C22×C71—41no—
339C22×C71C2×C4×D411yescharacteristic
340C22×C71C2×C4×D411yescharacteristic
341C22×C71#52011yescharacteristic
342C22×C71C22×M1611yescharacteristic
343C22×C71#56811yescharacteristic
344C22×C71#56811yescharacteristic
345C22×C71#56811yescharacteristic
346C2×D71—22no—
347C2×D71—22no—
348C2×D71—22no—
349C2×D71—41no—
350C2×D71—41no—
351C2×D71—41no—
352C2×D71—41no—
353C2×D71—41no—
354C2×D71—41no—
355C2×D71—41no—
356C2×D71—41no—
357C2×D71—41no—
358C2×D71—41no—
359C2×D71—41no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71—22no—
363C4×C71—22no—
364C4×C71—41no—
365C4×C71D4211yescharacteristic
366C4×C71#54711yescharacteristic
367C4×C71#54811yescharacteristic
368C4×C71#55311yescharacteristic
369Dic71—22no—
370Dic71—41no—
371Dic71—41no—
372Dic71—41no—
373Dic71—41no—
374Dic71—41no—
375#22988—711nomaximal, Sylow
376C2×C71—42no—
377C2×C71#236111yescharacteristic
378C2×C71#293011yescharacteristic
379C2×C71#293211yescharacteristic
380C2×C71D4×M1611yescharacteristic
381C2×C71D4×M1611yescharacteristic
382C2×C71#298911yescharacteristic
383C2×C71#299511yescharacteristic
384D71—42no—
385D71—81no—
386C2×#436—711no—
387C2×#435—711no—
388C2×#435—711no—
389C2×#423D7111yescharacteristic, complemented
390C4×#121—711no—
391#1955—711no—
392#1940—711no—
393#1924—711no—
394#1923—711no—
395#1870—711no—
396#1870—711no—
397#1851—711no—
398#1850—711no—
399#1771—711no—
400#1749—711no—
401C71#2298811yescharacteristic, complemented, Sylow
402C22×M16—711no—
403C22×M16C2×D7111yescharacteristic
404C22×M16C2×D7111yescharacteristic
405C23×C8—711no—
406C2×#121—711no—
407C2×C4×D4—711no—
408C2×C4×D4—711no—
409C2×C4×D4—711no—
410C22×C42C2×D7111yescharacteristic
411#436—1424no—
412#435—1424no—
413#435—1424no—
414#423—24no—
415C2×C4⋊C8—711no—
416C2×C4⋊C8—711no—
417C2×C4⋊C8C2×D7111yescharacteristic
418C2×C4⋊C8C2×D7111yescharacteristic
419C2×C4⋊C8C2×D7111yescharacteristic
420C2×C4⋊C8C2×D7111yescharacteristic
421C2×C22⋊C8—711no—
422C2×C22⋊C8—711no—
423C2×C22⋊C8—711no—
424C2×C22⋊C8—711no—
425C2×C22⋊C8—711no—
426C2×C22⋊C8—711no—
427C2×C22⋊C8—711no—
428C2×C22⋊C8—711no—
429C2×#97—711no—
430C2×#97—711no—
431C2×#97—711no—
432C2×C4×C8—711no—
433#390—711no—
434#389—711no—
435#388—711no—
436#388—711no—
437#386—711no—
438#386—711no—
439#380—711no—
440C4×C4⋊C4—711no—
441C4×C22⋊C4—711no—
442C4×C22⋊C4—711no—
443#336—711no—
444#336—711no—
445#336—711no—
446#336—711no—
447#336—711no—
448#336—711no—
449C22×D4—711no—
450C22×D4—711no—
451C22×D4—711no—
452C23×C4—711no—
453C23×C4—711no—
454C23×C4C4×D7111yescharacteristic
455C23×C4C4×D7111yescharacteristic
456C23×C4C22×D7111yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—41no—
462C2×M16—41no—
463C2×M16—2841no—
464C2×M16—1422no—
465C2×M16—1422no—
466C22×C8—2841no—
467C22×C8—711no—
468C22×C8—711no—
469C22×C8—711no—
470C22×C8—711no—
471C22×C8—1422no—
472C22×C8—1422no—
473C22×C8C22×D7111yescharacteristic
474C22×C8C22×D7111yescharacteristic
475C22×C8C22×D7111yescharacteristic
476C22×C8C22×D7111yescharacteristic
477#121—1424no—
478C4×D4—1422no—
479C4×D4—1422no—
480C4×D4—1422no—
481C4×D4—1422no—
482C4×D4—1422no—
483C4×D4—1422no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C22⋊C4—711no—
490C2×C22⋊C4—711no—
491C2×C22⋊C4—711no—
492C2×C22⋊C4—711no—
493C2×C22⋊C4—711no—
494C2×C22⋊C4—711no—
495C2×C22⋊C4—711no—
496C2×C22⋊C4—711no—
497C2×C22⋊C4—711no—
498C2×C22⋊C4—711no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—711no—
502C2×C42—711no—
503C2×C42C4×D7111yescharacteristic
504C2×C42C4×D7111yescharacteristic
505C2×C42C22×D7111yescharacteristic
506C2×C42C22×D7111yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—22no—
510C4⋊C8—1422no—
511C4⋊C8—1422no—
512C4⋊C8C22⋊D7114yescomplemented
513C22⋊C8—2841no—
514C22⋊C8—2841no—
515C22⋊C8—714no—
516C22⋊C8—1422no—
517C22⋊C8—1422no—
518C22⋊C8—1422no—
519C22⋊C8—1422no—
520C22⋊C8—1422no—
521#97—1422no—
522#97—1422no—
523#97—1422no—
524C4×C8—1422no—
525#95—711no—
526#95—711no—
527#95—711no—
528#95—711no—
529#95—711no—
530#95—711no—
531C24—711no—
532C24—711no—
533C24C2×C4×D7111yescharacteristic
534C2×D4—2841no—
535C2×D4—2841no—
536C2×D4—2841no—
537C2×D4—1422no—
538C2×D4—1422no—
539C2×D4—1422no—
540C2×D4—1422no—
541C2×D4—1422no—
542C2×D4—1422no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—711no—
554C22×C4—711no—
555C22×C4—711no—
556C22×C4—711no—
557C22×C4—711no—
558C22×C4—711no—
559C22×C4—1421no—
560C22×C4—1421no—
561C22×C4—1421no—
562C22×C4—1421no—
563C22×C4—1421no—
564C22×C4—1421no—
565C22×C4—1421no—
566C22×C4—1421no—
567C22×C4—1421no—
568C22×C4—1421no—
569C22×C4—1421no—
570C22×C4—1421no—
571C22×C4C2×C4×D7111yescharacteristic
572C22×C4C2×C4×D7111yescharacteristic
573C22×C4C2×C4×D7111yescharacteristic
574C22×C4C2×C4×D7111yescharacteristic
575C22×C4C2×C4×D7111yescharacteristic
576C22×C4D4×D7112yes—
577C22×C4#1176586612yes—
578C22×C4C23×D7111yescharacteristic
579M16—44no—
580M16—44no—
581M16—2844no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—2844no—
593C2×C8—712no—
594C2×C8—712no—
595C2×C8—1421no—
596C2×C8—1421no—
597C2×C8—1421no—
598C2×C8—1421no—
599C2×C8—1421no—
600C2×C8—1421no—
601C2×C8—1421no—
602C2×C8—1421no—
603C2×C8—1421no—
604C2×C8—1421no—
605C2×C8C2×C22⋊D7112yes—
606C2×C8C2×C22⋊D7112yes—
607C4⋊C4—2841no—
608C4⋊C4—1422no—
609C4⋊C4—1422no—
610C4⋊C4—1422no—
611C4⋊C4—1422no—
612C22⋊C4—2841no—
613C22⋊C4—2841no—
614C22⋊C4—714no—
615C22⋊C4—1422no—
616C22⋊C4—1422no—
617C22⋊C4—1422no—
618C22⋊C4—1422no—
619C22⋊C4—1422no—
620C22⋊C4—1422no—
621C22⋊C4—1422no—
622C42—21no—
623C42—21no—
624C42—22no—
625C42—22no—
626C42—1421no—
627C42—1421no—
628C42—1421no—
629C42—1421no—
630C42C2×C22⋊D7112yes—
631C42#1176586512yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—712no—
639C23—1421no—
640C23—1421no—
641C23—1421no—
642C23—1421no—
643C23—1421no—
644C23—1421no—
645C23—1421no—
646C23—1421no—
647C23—1421no—
648C23—1421no—
649C23—1421no—
650C23—1421no—
651C23—1421no—
652C23#1455609012yes—
653C23C22×C4×D7111yescharacteristic
654D4—2844no—
655D4—2844no—
656D4—2844no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—2841no—
675C2×C4—2841no—
676C2×C4—2841no—
677C2×C4—2841no—
678C2×C4—2841no—
679C2×C4—2841no—
680C2×C4—2841no—
681C2×C4—2841no—
682C2×C4—712no—
683C2×C4—1421no—
684C2×C4—1421no—
685C2×C4—1421no—
686C2×C4—1421no—
687C2×C4—1421no—
688C2×C4—1421no—
689C2×C4—1421no—
690C2×C4—1421no—
691C2×C4—1421no—
692C2×C4—1421no—
693C2×C4—1421no—
694C2×C4—1421no—
695C2×C4—1421no—
696C2×C4—1421no—
697C2×C4—1421no—
698C2×C4—1421no—
699C2×C4—1421no—
700C2×C4C4×C22⋊D7112yes—
701C2×C4C4×C22⋊D7112yes—
702C2×C4#1455609012yes—
703C2×C4M16×D7112yes—
704C2×C4C2×D4×D7111yescharacteristic
705C2×C4C22×C22⋊D7111yescharacteristic
706C2×C4C2×#1176586511yescharacteristic
707C2×C4C2×#1176586611yescharacteristic
708C2×C4#1455617311yescharacteristic
709C2×C4#1455617611yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—2841no—
715C8—2841no—
716C8—1422no—
717C8—1422no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—2841no—
726C22—2841no—
727C22—2841no—
728C22—2841no—
729C22—2841no—
730C22—2841no—
731C22—2841no—
732C22—2841no—
733C22—2841no—
734C22—2841no—
735C22—2841no—
736C22—1422no—
737C22—1422no—
738C22—1422no—
739C22C2×C4×C22⋊D7111yescharacteristic
740C22C2×#1455609011yescharacteristic
741C22#1798648011yescharacteristic
742C22C2×M16×D7111yescharacteristic
743C22#1798676511yescharacteristic
744C22#1798676511yescharacteristic
745C22#1798676511yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—2841no—
752C4—2841no—
753C4—2841no—
754C4—2841no—
755C4—2841no—
756C4—1422no—
757C4D4×C22⋊D7111yescharacteristic
758C4#1798665011yescharacteristic
759C4#1798666011yescharacteristic
760C4#1798669711yescharacteristic
761C2—42no—
762C2—2842no—
763C2—5681no—
764C2#2259135611yescharacteristic
765C2#2259704311yescharacteristic
766C2#2259705711yescharacteristic
767C2M16×C22⋊D7111yescharacteristic
768C2#2259707511yescharacteristic
769C2#2259745411yescharacteristic
770C2#2259750711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC2×#423×C71C2
prime radicalC2×#14556102C4
cosocleC22×C4×C71C24
hypercenterC2×#423D71
hypocenterC71#22988
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. C2×#17986075C2semidirect
2. C2×#17986069C2semidirect
3. C2×#17986068C2semidirect
5. #22589137C2semidirect
6. #22589061C2semidirect
7. #22588952C2semidirect
8. #22588945C2semidirect
9. #22588637C2semidirect
10. #22588637C2semidirect
11. #22588521C2semidirect
12. #22588516C2semidirect
13. #22588217C2semidirect
14. #22588102C2semidirect
15. C2×#423×C71C2semidirect
105. C22⋊(C71⋊C8)D4semidirect
144. C4⋊C8×C71D4semidirect
202. (C2×D71)⋊C4M16semidirect
389. C2×#423D71semidirect
401. C71#22988semidirect
512. C4⋊C8C22⋊D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860752
C2×#179860692
C2×#179860682
C4×#145561022
#225891372
#225890612
#225889522
#225889452
#225886372
#225885212
#225885162
#225882172
#225881022
C2×#423×C712
#2298871