Finite Group Databasebeta

← #2345×D71 #32156691

Subgroups — #2345×D71 #32156691

Order 18176.

3094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D71C211yesmaximal, characteristic
2#22591219C211yesmaximal, characteristic, complemented
3#22591218C212yesmaximal, complemented
4#22591217C211yesmaximal, characteristic, complemented
5#22591216C212yesmaximal, complemented
6#22591215C211yesmaximal, characteristic, complemented
7#22591214C214yesmaximal, complemented
8#22591213C212yesmaximal, complemented
9#22591212C212yesmaximal, complemented
10#389×D71C212yesmaximal, complemented
11#387×D71C214yesmaximal, complemented
12#380×D71C211yesmaximal, characteristic
13#380×D71C212yesmaximal
14C4×C4⋊C4×D71C212yesmaximal, complemented
15C4×C22⋊C4×D71C211yesmaximal, characteristic
16C4×C22⋊C4×D71C212yesmaximal
17C71×#2345C211yesmaximal, characteristic, complemented
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2212yes—
20C22×C4⋊Dic71C2211yescharacteristic
21C22×Dic71⋊C4C2212yes—
22C2×C4⋊C4×D71C4116yescomplemented
23C2×C4⋊C4×D71C2212yes—
24C2×C4⋊C4×D71C2214yes—
25C2×C4⋊C4×D71C2212yes—
26C2×C4⋊C4×D71C2211yescharacteristic
27C2×C4⋊C4×D71C2211yescharacteristic
28C2×C4⋊C4×D71C2211yescharacteristic
29C2×C4⋊C4×D71C2212yes—
30C2×C4⋊C4×D71C2211yescharacteristic
31C2×C22⋊C4×D71C2211yescharacteristic
32C2×C22⋊C4×D71C2212yes—
33C2×C22⋊C4×D71C2211yescharacteristic
34C2×C42×D71C2212yes—
35C2×C42×D71C2214yes—
36#17985898C2212yescomplemented
37#17985897C2212yescomplemented
38#17985896C2214yescomplemented
39#17985895C2212yescomplemented
40#17985894C2214yescomplemented
41#17985886C2214yescomplemented
42#17985885C2214yescomplemented
43#17985884C2214yescomplemented
44#17985883C2214yescomplemented
45#17985882C2214yescomplemented
46#17985881C2214yescomplemented
47#17985880C2214yescomplemented
48#17985859C2211yescharacteristic
49#17985859C2212yes—
50#17985858C2214yes—
51#17985858C2212yes—
52#17985857C2212yes—
53#17985857C2212yes—
54#17985857C2212yes—
55#17985856C2212yes—
56#17985856C2214yes—
57C4⋊C4×Dic71C2212yescomplemented
58C4⋊C4×Dic71C2212yescomplemented
59C4×Dic71⋊C4C2214yescomplemented
60C4×C4⋊Dic71C2212yescomplemented
61#17985850C2214yescomplemented
62C22⋊C4×Dic71C2211yescharacteristic
63C22⋊C4×Dic71C2212yes—
64C22⋊C4×Dic71C2212yes—
65C22⋊C4×Dic71C2211yescharacteristic
66C4×(C2×D71)⋊C4C2214yes—
67C4×(C2×D71)⋊C4C2212yes—
68C4×C22⋊Dic71C2212yes—
69C4×C22⋊Dic71C2211yescharacteristic
70#17985846C2212yes—
71#17985846C2214yes—
72#95×D71C2212yes—
73#95×D71C2212yes—
74#95×D71C2214yes—
75#95×D71C2214yes—
76C22×C4⋊C4×C71C2211yescharacteristic
77#389×C71C2212yescomplemented
78#387×C71C2214yescomplemented
79#380×C71C2212yes—
80#380×C71C2211yescharacteristic
81C4×C4⋊C4×C71C2212yescomplemented
82C4×C22⋊C4×C71C2211yescharacteristic
83C4×C22⋊C4×C71C2212yes—
84C24×D71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2312yes—
87C22×C4×D71—28no—
88C22×C4×D71—48no—
89C22×C4×D71C2×C418yes—
90C22×C4×D71C2×C4116yes—
91C22×C4×D71C2312yes—
92C22×C4×D71C2314yes—
93C22×C4×D71C2311yescharacteristic
94C22×C4×D71C2312yes—
95C22×C4×D71C2312yes—
96C22×C4×D71C2311yescharacteristic
97C22×C4×D71C2311yescharacteristic
98C22×C4×D71C2312yes—
99C22×C4×D71C2312yes—
100C22×C4×D71C2312yes—
101C22×C4×D71C2311yescharacteristic
102C2×C4⋊Dic71C2×C418yescomplemented
103C2×C4⋊Dic71C2312yes—
104C2×C4⋊Dic71C2314yes—
105C2×C4⋊Dic71C2311yescharacteristic
106C2×C4⋊Dic71C2312yes—
107C2×C4⋊Dic71C2311yescharacteristic
108C2×Dic71⋊C4C2×C4116yescomplemented
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×Dic71⋊C4C2314yes—
112C2×Dic71⋊C4C2312yes—
113C2×Dic71⋊C4C2312yes—
114C2×Dic71⋊C4C2312yes—
115C2×Dic71⋊C4C2312yes—
116C4⋊C4×D71—28no—
117C4⋊C4×D71—48no—
118C4⋊C4×D71C2×C4116yes—
119C4⋊C4×D71C2×C418yes—
120C4⋊C4×D71C2×C418yes—
121C4⋊C4×D71C2×C418yescomplemented
122C4⋊C4×D71C2×C4116yescomplemented
123C4⋊C4×D71C2×C418yescomplemented
124C2×C22⋊Dic71C2312yes—
125C2×C22⋊Dic71C2311yescharacteristic
126C2×C22⋊Dic71C2311yescharacteristic
127C2×(C2×D71)⋊C4C2312yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×(C2×D71)⋊C4C2312yes—
130C22⋊C4×D71—24no—
131C22⋊C4×D71—28no—
132C22⋊C4×D71Q818yes—
133C2×C4×Dic71C2312yes—
134C2×C4×Dic71C2312yes—
135C2×C4×Dic71C2312yes—
136C2×C4×Dic71C2314yes—
137C2×C4×Dic71C2314yes—
138C2×C4×Dic71C2314yes—
139C42×D71—28no—
140C42×D71—48no—
141C71⋊#95C2314yes—
142C71⋊#95C2312yes—
143C71⋊#95C2312yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C71⋊#95C2312yes—
147C71⋊#95C2314yes—
148C71⋊#95C2314yes—
149C71⋊#95C2314yes—
150C71⋊#95C2314yes—
151C71⋊#95C2312yes—
152C23×C4×C71C2311yescharacteristic
153C23×C4×C71C2312yes—
154C2×C4⋊C4×C71C2×C418yescomplemented
155C2×C4⋊C4×C71C2312yes—
156C2×C4⋊C4×C71C2314yes—
157C2×C4⋊C4×C71C2311yescharacteristic
158C2×C4⋊C4×C71C2312yes—
159C2×C4⋊C4×C71C2311yescharacteristic
160C2×C22⋊C4×C71C2311yescharacteristic
161C2×C22⋊C4×C71C2312yes—
162C2×C22⋊C4×C71C2311yescharacteristic
163C2×C42×C71C2312yes—
164C2×C42×C71C2314yes—
165#95×C71C2312yes—
166#95×C71C2314yes—
167#95×C71C2314yes—
168#95×C71C2312yes—
169C23×D71—24no—
170C23×D71—24no—
171C23×D71C22×C414yes—
172C23×D71C2×Q814yes—
173C23×D71#4114yes—
174C23×D71C2411yescharacteristic
175C23×D71C2411yescharacteristic
176C22×Dic71—24no—
177C22×Dic71—44no—
178C22×Dic71C22×C414yes—
179C22×Dic71C22×C418yes—
180C22×Dic71C2412yes—
181C22×Dic71C2414yes—
182C22×Dic71C2411yescharacteristic
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2411yescharacteristic
187C2×C4×D71—24no—
188C2×C4×D71—24no—
189C2×C4×D71—28no—
190C2×C4×D71—28no—
191C2×C4×D71—24no—
192C2×C4×D71—24no—
193C2×C4×D71—24no—
194C2×C4×D71—232no—
195C2×C4×D71—24no—
196C2×C4×D71—24no—
197C2×C4×D71—28no—
198C2×C4×D71—28no—
199C2×C4×D71—28no—
200C2×C4×D71—24no—
201C2×C4×D71—432no—
202C2×C4×D71—44no—
203C2×C4×D71—44no—
204C2×C4×D71C22×C414yes—
205C2×C4×D71C22×C418yes—
206C2×C4×D71C22×C418yes—
207C2×C4×D71C22×C414yes—
208C2×C4×D71C22×C414yes—
209C2×C4×D71C22×C418yes—
210C2×C4×D71C22×C418yes—
211C2×C4×D71C22×C414yes—
212C2×C4×D71C2×Q818yes—
213C2×C4×D71#4118yes—
214C4⋊Dic71—24no—
215C4⋊Dic71—44no—
216C4⋊Dic71C22×C418yes—
217C4⋊Dic71C22×C414yes—
218C4⋊Dic71C22×C414yes—
219Dic71⋊C4—28no—
220Dic71⋊C4—44no—
221Dic71⋊C4—44no—
222Dic71⋊C4C22×C418yes—
223Dic71⋊C4C22×C418yes—
224Dic71⋊C4C22×C418yes—
225Dic71⋊C4C22×C418yes—
226C22⋊Dic71—24no—
227C22⋊Dic71—22no—
228C22⋊Dic71C2×Q814yes—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—28no—
231(C2×D71)⋊C4C2×Q818yes—
232C4×Dic71—24no—
233C4×Dic71—24no—
234C4×Dic71—24no—
235C4×Dic71—44no—
236C4×Dic71—44no—
237C4×Dic71—44no—
238C24×C71C2411yescharacteristic
239C22×C4×C71—24no—
240C22×C4×C71—44no—
241C22×C4×C71C22×C414yes—
242C22×C4×C71C22×C418yes—
243C22×C4×C71C2412yes—
244C22×C4×C71C2414yes—
245C22×C4×C71C2411yescharacteristic
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2411yescharacteristic
250C4⋊C4×C71—24no—
251C4⋊C4×C71—44no—
252C4⋊C4×C71C22×C418yes—
253C4⋊C4×C71C22×C414yes—
254C4⋊C4×C71C22×C414yes—
255C22⋊C4×C71—22no—
256C22⋊C4×C71—24no—
257C22⋊C4×C71C2×Q814yes—
258C42×C71—24no—
259C42×C71—44no—
260C23×C71—22no—
261C23×C71—22no—
262C23×C71C23×C412yes—
263C23×C71C22×Q812yes—
264C23×C71C2×#4112yes—
265C23×C71C2511yescharacteristic
266C22×D71—22no—
267C22×D71—22no—
268C22×D71—28no—
269C22×D71—28no—
270C22×D71—216no—
271C22×D71—216no—
272C22×D71C4×Q8116yes—
273C22×D71C23×C412yes—
274C22×D71C23×C412yes—
275C22×D71C22×Q812yes—
276C22×D71C22×Q812yes—
277C22×D71C2×#4112yes—
278C22×D71C2×#4114yes—
279C22×D71C2×#4112yes—
280C22×D71H(5,𝔽2)14yes—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—24no—
285C2×C4×C71—24no—
286C2×C4×C71—28no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—24no—
290C2×C4×C71—24no—
291C2×C4×C71—24no—
292C2×C4×C71—22no—
293C2×C4×C71—48no—
294C2×C4×C71C23×C414yes—
295C2×C4×C71C23×C414yes—
296C2×C4×C71C23×C412yes—
297C2×C4×C71C23×C412yes—
298C2×C4×C71C22×Q814yes—
299C2×C4×C71C2×#4114yes—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—24no—
304C2×Dic71—24no—
305C2×Dic71—28no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—24no—
309C2×Dic71—24no—
310C2×Dic71—24no—
311C2×Dic71—22no—
312C2×Dic71—48no—
313C2×Dic71C23×C412yes—
314C2×Dic71C23×C414yes—
315C2×Dic71C23×C414yes—
316C2×Dic71C23×C412yes—
317C2×Dic71C22×Q814yes—
318C2×Dic71C2×#4114yes—
319C4×D71—28no—
320C4×D71—216no—
321C4×D71—216no—
322C4×D71—216no—
323C4×D71—28no—
324C4×D71—28no—
325C4×D71—48no—
326C4×D71—48no—
327C4×D71—48no—
328C4×D71—416no—
329C4×D71#117116yes—
330C22×C71—22no—
331C22×C71—22no—
332C22×C71—24no—
333C22×C71—24no—
334C22×C71C2×C4×Q814yes—
335C22×C71C24×C411yescharacteristic
336C22×C71C23×Q811yescharacteristic
337C22×C71C22×#4112yes—
338C22×C71C22×#4111yescharacteristic
339C22×C71C2×H(5,𝔽2)12yes—
340C2×D71—22no—
341C2×D71—22no—
342C2×D71—24no—
343C2×D71—24no—
344C2×D71—232no—
345C2×D71C2×#11714yes—
346C2×D71C2×C4×Q814yes—
347C2×D71C2×C4×Q814yes—
348C2×D71#51814yes—
349C2×D71#55318yes—
350C2×D71#55418yes—
351C4×C71—22no—
352C4×C71—24no—
353C4×C71—24no—
354C4×C71—24no—
355C4×C71—42no—
356C4×C71—44no—
357C4×C71C2×#11714yes—
358Dic71—22no—
359Dic71—24no—
360Dic71—24no—
361Dic71—24no—
362Dic71—42no—
363Dic71—44no—
364Dic71C2×#11714yes—
365C2×#2345—711nomaximal, Sylow
366C2×C71—24no—
367C2×C71C22×#11711yescharacteristic
368C2×C71C22×C4×Q811yescharacteristic
369C2×C71C2×#51811yescharacteristic
370C2×C71C2×#55312yes—
371C2×C71C2×#55412yes—
372D71—24no—
373D71#234518yesdirect product factor
374C23×C4⋊C4—711no—
375#2345—712no—
376#2345—714no—
377#2345—712no—
378#2345—711no—
379#2345—712no—
380#2345—711no—
381#2345—712no—
382#2345—711no—
383#2345D7111yescharacteristic, direct product factor
384C2×#389—712no—
385C2×#387—714no—
386C2×#380—712no—
387C2×#380—711no—
388C2×C4×C4⋊C4—712no—
389C2×C4×C22⋊C4—712no—
390C2×C4×C22⋊C4—711no—
391C71C2×#234511yescharacteristic, complemented, Sylow
392C24×C4—712no—
393C24×C4—711no—
394C22×C4⋊C4—714no—
395C22×C4⋊C4—712no—
396C22×C4⋊C4—711no—
397C22×C4⋊C4—7116no—
398C22×C4⋊C4—712no—
399C22×C4⋊C4—711no—
400C22×C4⋊C4—711no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—712no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—712no—
405C22×C4⋊C4C2×D7111yescharacteristic
406C22×C22⋊C4—711no—
407C22×C22⋊C4—712no—
408C22×C22⋊C4—711no—
409C22×C42—714no—
410C22×C42—712no—
411#389—714no—
412#389—712no—
413#389—712no—
414#389—712no—
415#389—714no—
416#389C2×D7112yescomplemented
417#387—714no—
418#387—714no—
419#387—714no—
420#387—714no—
421#387—714no—
422#387—714no—
423#387—714no—
424#387C2×D7114yescomplemented
425#380—712no—
426#380—711no—
427#380—714no—
428#380—712no—
429#380—712no—
430#380—712no—
431#380—712no—
432#380—714no—
433#380—712no—
434#380C2×D7112yes—
435#380C2×D7111yescharacteristic
436C4×C4⋊C4—712no—
437C4×C4⋊C4—712no—
438C4×C4⋊C4—712no—
439C4×C4⋊C4—714no—
440C4×C4⋊C4—714no—
441C4×C4⋊C4C2×D7112yescomplemented
442C4×C22⋊C4—711no—
443C4×C22⋊C4—712no—
444C4×C22⋊C4—711no—
445C4×C22⋊C4—711no—
446C4×C22⋊C4—712no—
447C4×C22⋊C4—712no—
448C4×C22⋊C4—712no—
449C4×C22⋊C4—714no—
450C4×C22⋊C4—712no—
451C4×C22⋊C4—714no—
452C4×C22⋊C4C2×D7111yescharacteristic
453C4×C22⋊C4C2×D7112yes—
454C2×#95—712no—
455C2×#95—714no—
456C2×#95—714no—
457C2×#95—712no—
458C25—711no—
459C23×C4—2848no—
460C23×C4—712no—
461C23×C4—7116no—
462C23×C4—712no—
463C23×C4—712no—
464C23×C4—711no—
465C23×C4—711no—
466C23×C4—718no—
467C23×C4—712no—
468C23×C4—712no—
469C23×C4—711no—
470C23×C4—712no—
471C23×C4—711no—
472C23×C4—711no—
473C23×C4—714no—
474C23×C4—712no—
475C23×C4—1428no—
476C23×C4C22×D7111yescharacteristic
477C23×C4C22×D7112yes—
478C2×C4⋊C4—2848no—
479C2×C4⋊C4—714no—
480C2×C4⋊C4—714no—
481C2×C4⋊C4—714no—
482C2×C4⋊C4—7116no—
483C2×C4⋊C4—718no—
484C2×C4⋊C4—712no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—712no—
487C2×C4⋊C4—712no—
488C2×C4⋊C4—712no—
489C2×C4⋊C4—712no—
490C2×C4⋊C4—711no—
491C2×C4⋊C4—718no—
492C2×C4⋊C4—718no—
493C2×C4⋊C4—7116no—
494C2×C4⋊C4—7116no—
495C2×C4⋊C4—718no—
496C2×C4⋊C4—718no—
497C2×C4⋊C4—714no—
498C2×C4⋊C4—712no—
499C2×C4⋊C4—1428no—
500C2×C4⋊C4C4×D7118yescomplemented
501C2×C4⋊C4C22×D7112yes—
502C2×C4⋊C4C22×D7114yes—
503C2×C4⋊C4C22×D7111yescharacteristic
504C2×C4⋊C4C22×D7112yes—
505C2×C4⋊C4C22×D7111yescharacteristic
506C2×C22⋊C4—711no—
507C2×C22⋊C4—712no—
508C2×C22⋊C4—718no—
509C2×C22⋊C4—711no—
510C2×C22⋊C4—712no—
511C2×C22⋊C4—712no—
512C2×C22⋊C4—714no—
513C2×C22⋊C4—1428no—
514C2×C22⋊C4—1424no—
515C2×C22⋊C4C22×D7111yescharacteristic
516C2×C22⋊C4C22×D7112yes—
517C2×C22⋊C4C22×D7111yescharacteristic
518C2×C42—2848no—
519C2×C42—714no—
520C2×C42—714no—
521C2×C42—714no—
522C2×C42—712no—
523C2×C42—712no—
524C2×C42—712no—
525C2×C42—1428no—
526C2×C42C22×D7112yes—
527C2×C42C22×D7114yes—
528#95—712no—
529#95—712no—
530#95—712no—
531#95—714no—
532#95—714no—
533#95—714no—
534#95—714no—
535#95—714no—
536#95—714no—
537#95—714no—
538#95—712no—
539#95C22×D7112yes—
540#95C22×D7114yes—
541#95C22×D7114yes—
542#95C22×D7112yes—
543C24—711no—
544C24—714no—
545C24—714no—
546C24—714no—
547C24—711no—
548C24—1424no—
549C24—1424no—
550C24C23×D7111yescharacteristic
551C22×C4—24no—
552C22×C4—44no—
553C22×C4—2844no—
554C22×C4—2844no—
555C22×C4—28432no—
556C22×C4—2844no—
557C22×C4—718no—
558C22×C4—718no—
559C22×C4—718no—
560C22×C4—711no—
561C22×C4—714no—
562C22×C4—718no—
563C22×C4—714no—
564C22×C4—711no—
565C22×C4—712no—
566C22×C4—712no—
567C22×C4—712no—
568C22×C4—714no—
569C22×C4—718no—
570C22×C4—718no—
571C22×C4—714no—
572C22×C4—714no—
573C22×C4—718no—
574C22×C4—712no—
575C22×C4—714no—
576C22×C4—1428no—
577C22×C4—1424no—
578C22×C4—1428no—
579C22×C4—1424no—
580C22×C4—1424no—
581C22×C4—1428no—
582C22×C4—1424no—
583C22×C4—14232no—
584C22×C4—1424no—
585C22×C4—1428no—
586C22×C4—1424no—
587C22×C4—1428no—
588C22×C4—1424no—
589C22×C4—1424no—
590C22×C4—1424no—
591C22×C4C2×C4×D7114yes—
592C22×C4C2×C4×D7118yes—
593C22×C4C23×D7112yes—
594C22×C4C23×D7114yes—
595C22×C4C23×D7111yescharacteristic
596C22×C4C23×D7112yes—
597C22×C4C23×D7112yes—
598C22×C4C23×D7112yes—
599C22×C4C23×D7111yescharacteristic
600C4⋊C4—24no—
601C4⋊C4—44no—
602C4⋊C4—2844no—
603C4⋊C4—2844no—
604C4⋊C4—2844no—
605C4⋊C4—718no—
606C4⋊C4—718no—
607C4⋊C4—718no—
608C4⋊C4—718no—
609C4⋊C4—718no—
610C4⋊C4—714no—
611C4⋊C4—714no—
612C4⋊C4—1428no—
613C4⋊C4—1424no—
614C4⋊C4C2×C4×D7118yes—
615C4⋊C4C2×C4×D7114yes—
616C4⋊C4C2×C4×D7114yes—
617C22⋊C4—22no—
618C22⋊C4—24no—
619C22⋊C4—714no—
620C22⋊C4—718no—
621C22⋊C4—1424no—
622C22⋊C4—1428no—
623C22⋊C4—1422no—
624C22⋊C4—1424no—
625C22⋊C4Q8×D7114yes—
626C42—24no—
627C42—44no—
628C42—2844no—
629C42—2844no—
630C42—2844no—
631C42—1424no—
632C42—1424no—
633C42—1424no—
634C23—22no—
635C23—22no—
636C23—712no—
637C23—712no—
638C23—714no—
639C23—712no—
640C23—714no—
641C23—712no—
642C23—712no—
643C23—712no—
644C23—7116no—
645C23—1428no—
646C23—1428no—
647C23—14216no—
648C23—14216no—
649C23—1422no—
650C23—1422no—
651C23C22×C4×D7112yes—
652C23C2×Q8×D7112yes—
653C23#41×D7112yes—
654C23C24×D7111yescharacteristic
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—28no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—48no—
668C2×C4—2848no—
669C2×C4—2848no—
670C2×C4—28416no—
671C2×C4—2848no—
672C2×C4—2848no—
673C2×C4—712no—
674C2×C4—714no—
675C2×C4—7116no—
676C2×C4—712no—
677C2×C4—714no—
678C2×C4—714no—
679C2×C4—714no—
680C2×C4—1428no—
681C2×C4—14216no—
682C2×C4—14216no—
683C2×C4—1428no—
684C2×C4—14216no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4—1424no—
688C2×C4—1424no—
689C2×C4—1424no—
690C2×C4—1422no—
691C2×C4—1428no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1424no—
696C2×C4—1424no—
697C2×C4—1428no—
698C2×C4C22×C4×D7112yes—
699C2×C4C22×C4×D7114yes—
700C2×C4C22×C4×D7114yes—
701C2×C4C22×C4×D7112yes—
702C2×C4C2×Q8×D7114yes—
703C2×C4#41×D7114yes—
704C22—22no—
705C22—22no—
706C22—24no—
707C22—24no—
708C22—714no—
709C22—714no—
710C22—714no—
711C22—718no—
712C22—718no—
713C22—714no—
714C22—14232no—
715C22—1422no—
716C22—1422no—
717C22—1424no—
718C22—1424no—
719C22C4×Q8×D7114yes—
720C22C23×C4×D7111yescharacteristic
721C22C22×Q8×D7111yescharacteristic
722C22C2×#41×D7112yes—
723C22C2×#41×D7111yescharacteristic
724C22H(5,𝔽2)×D7112yes—
725C4—22no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—42no—
730C4—44no—
731C4—2842no—
732C4—2844no—
733C4—714no—
734C4—1422no—
735C4—1424no—
736C4—1424no—
737C4—1424no—
738C4#117×D7114yes—
739C2—24no—
740C2—718no—
741C2—1424no—
742C2C2×#117×D7111yescharacteristic
743C2C2×C4×Q8×D7111yescharacteristic
744C2#518×D7111yescharacteristic
745C2#553×D7112yes—
746C2#554×D7112yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2345C2
socle, cosocleC23×C71C25
prime radicalC24×D71C23
hypercenter#2345D71
hypocenterC71C2×#2345
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #22591219C2semidirect
3. #22591218C2semidirect
4. #22591217C2semidirect
5. #22591216C2semidirect
6. #22591215C2semidirect
7. #22591214C2semidirect
8. #22591213C2semidirect
9. #22591212C2semidirect
10. #389×D71C2semidirect
11. #387×D71C2semidirect
14. C4×C4⋊C4×D71C2semidirect
17. C71×#2345C2semidirect
22. C2×C4⋊C4×D71C4semidirect
36. #17985898C22semidirect
37. #17985897C22semidirect
38. #17985896C22semidirect
39. #17985895C22semidirect
40. #17985894C22semidirect
41. #17985886C22semidirect
42. #17985885C22semidirect
43. #17985884C22semidirect
44. #17985883C22semidirect
45. #17985882C22semidirect
46. #17985881C22semidirect
47. #17985880C22semidirect
57. C4⋊C4×Dic71C22semidirect
58. C4⋊C4×Dic71C22semidirect
59. C4×Dic71⋊C4C22semidirect
60. C4×C4⋊Dic71C22semidirect
61. #17985850C22semidirect
77. #389×C71C22semidirect
78. #387×C71C22semidirect
81. C4×C4⋊C4×C71C22semidirect
102. C2×C4⋊Dic71C2×C4semidirect
108. C2×Dic71⋊C4C2×C4semidirect
121. C4⋊C4×D71C2×C4semidirect
122. C4⋊C4×D71C2×C4semidirect
123. C4⋊C4×D71C2×C4semidirect
154. C2×C4⋊C4×C71C2×C4semidirect
373. D71#2345direct (N × H)
383. #2345D71direct (N × H)
391. C71C2×#2345semidirect
416. #389C2×D71semidirect
424. #387C2×D71semidirect
441. C4×C4⋊C4C2×D71semidirect
500. C2×C4⋊C4C4×D71semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D712
#225912192
#225912182
#225912172
#225912162
#225912152
#225912142
#225912132
#225912122
#389×D712
#387×D712
#380×D712
C4×C4⋊C4×D712
C4×C22⋊C4×D712
C71×#23452
C2×#234571