Finite Group Databasebeta

← C2×#22600948 #32876183

Subgroups — C2×#22600948 #32876183

Order 18176.

1866 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986720C211yesmaximal, characteristic
2C2×#17986704C211yesmaximal, characteristic
3#22600948C2116yesmaximal, direct product factor
4C2×#17986396C211yesmaximal, characteristic, complemented
5C2×#17986343C211yesmaximal, characteristic, complemented
6C2×#17986341C211yesmaximal, characteristic, complemented
7C2×#17986328C211yesmaximal, characteristic, complemented
8C2×#17986292C211yesmaximal, characteristic, complemented
9C2×#17986283C211yesmaximal, characteristic, complemented
10C2×#17986256C211yesmaximal, characteristic, complemented
11C2×#17986255C211yesmaximal, characteristic, complemented
12C2×#17986091C211yesmaximal, characteristic, complemented
13C2×#17986074C211yesmaximal, characteristic
14C2×#17986039C211yesmaximal, characteristic, complemented
15C2×#17986038C211yesmaximal, characteristic, complemented
16C2×#483×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20#17986720—24no—
21#17986720C2218yes—
22#17986704—24no—
23#17986704C2218yes—
24C2×#14556127C2211yescharacteristic
25C2×#14556127C2211yescharacteristic
26C2×#14556123—21no—
27C2×#14556121—21no—
28C2×#14556118—21no—
29C2×#14556114—21no—
30C2×#14556108C2211yescharacteristic
31C2×#14556107—21no—
32C2×#14556107C2211yescharacteristic
33C2×#14556106—21no—
34C2×#14556104C2211yescharacteristic
35C2×Q8×Dic71C2211yescharacteristic
36C2×#14556093—21no—
37C2×#14556093C2211yescharacteristic
38C2×C4×C22⋊D71—21no—
39C2×C4×C22⋊D71C2211yescharacteristic
40C2×#14556087C2211yescharacteristic
41C2×#14556086C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43#17986396C2218yescomplemented
44#17986343C2218yescomplemented
45#17986341C2218yescomplemented
46#17986328C2218yescomplemented
47#17986292C2218yescomplemented
48#17986283C2218yescomplemented
49#17986256C2218yescomplemented
50#17986255C2218yescomplemented
51#17986091C2218yescomplemented
52#17986074C2218yes—
53#17986039C2218yescomplemented
54#17986038C2218yescomplemented
55C2×#14556062C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556059C2211yescharacteristic
60C2×#14556059C2211yescharacteristic
61C2×#14556059C2211yescharacteristic
62C2×Dic71⋊C8C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556052C2211yescharacteristic
66C2×#14556051C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C2×C22⋊Q8×C71C2211yescharacteristic
70C22×C4⋊C4×C71C2211yescharacteristic
71#483×C71C2218yescomplemented
72C2×#106×C71C2211yescharacteristic
73C2×#106×C71C2211yescharacteristic
74C2×#103×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C22×C22⋊D71D411yescharacteristic
81C22×C4×D71—21no—
82C22×C4×D71C2311yescharacteristic
83C2×#11765855—24no—
84C2×#11765855C2314yes—
85C2×#11765849—24no—
86C2×#11765849C2314yes—
87C2×#11765848—24no—
88C2×#11765848C2314yes—
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91#14556127—22no—
92#14556127—22no—
93#14556127C2314yes—
94#14556127C2314yes—
95#14556123—28no—
96#14556121—28no—
97#14556118—28no—
98#14556114—28no—
99#14556108—22no—
100#14556108C2314yes—
101#14556107—28no—
102#14556107—22no—
103#14556107C2314yes—
104#14556106—28no—
105#14556104—22no—
106#14556104C2314yes—
107Q8×Dic71—22no—
108Q8×Dic71C2314yes—
109#14556093—28no—
110#14556093—22no—
111#14556093C2314yes—
112C4×C22⋊D71—28no—
113C4×C22⋊D71D414yes—
114C4×C22⋊D71C2314yes—
115#14556087—22no—
116#14556087C2314yes—
117#14556086—22no—
118#14556086C2314yes—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4D411yescharacteristic
131C4⋊C4×D71—22no—
132C4⋊C4×D71C2314yes—
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71—21no—
135C2×C22⋊Dic71D411yescharacteristic
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4D411yescharacteristic
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71C2311yescharacteristic
145#14556062C2314yes—
146#14556061C2314yes—
147#14556061C2314yes—
148#14556060C2314yes—
149#14556059C2314yes—
150#14556059C2314yes—
151#14556059C2314yes—
152Dic71⋊C8C2314yes—
153#14556053C2314yes—
154#14556053C2314yes—
155#14556052C2314yes—
156#14556051C2314yes—
157(C2×D71)⋊C8C2314yes—
158C8×Dic71C2314yes—
159C22×Q8×C71C2311yescharacteristic
160C23×C4×C71—21no—
161C23×C4×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2311yescharacteristic
164C22⋊Q8×C71—22no—
165C22⋊Q8×C71C2314yes—
166C2×C4⋊C4×C71—22no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2314yes—
173C2×C22⋊C4×C71—21no—
174#106×C71C2314yes—
175#106×C71C2314yes—
176#103×C71C2314yes—
177#103×C71C2314yes—
178C22⋊C8×C71C2314yes—
179C23×D71C2×D411yescharacteristic
180C2×Dic142—22no—
181C2×Dic142—22no—
182C2×Dic142—21no—
183C2×Dic142—24no—
184C2×Dic142—24no—
185C2×Dic142—44no—
186C2×Dic142—82no—
187C2×Dic142C2412yes—
188C2×C22⋊D71—24no—
189C2×C22⋊D71C2×D414yes—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71C2×D411yescharacteristic
195C22×Dic71C2×D411yescharacteristic
196C22×Dic71C2×D411yescharacteristic
197C2×C4×D71—22no—
198C2×C4×D71—22no—
199C2×C4×D71—24no—
200C2×C4×D71—82no—
201C2×C4×D71C2×D412yes—
202C2×C4×D71C2412yes—
203#11765855—28no—
204#11765849—28no—
205#11765848—28no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8#4114yes—
208C2×C71⋊C8C2412yes—
209C2×C71⋊C8C2412yes—
210C4⋊Dic71—21no—
211C4⋊Dic71—21no—
212C4⋊Dic71—21no—
213C4⋊Dic71—24no—
214C4⋊Dic71—24no—
215C4⋊Dic71C2412yes—
216C4⋊Dic71C2412yes—
217C4⋊Dic71C2412yes—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4C2×D414yes—
225C22⋊Dic71—24no—
226C22⋊Dic71—24no—
227C22⋊Dic71C2×D414yes—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4C2×D414yes—
232C4×Dic71—24no—
233C4×Dic71—24no—
234C4×Dic71—24no—
235C4×Dic71—24no—
236C4×Dic71C2×D412yes—
237C4×Dic71C2412yes—
238C24×C71C2×D411yescharacteristic
239C2×Q8×C71—21no—
240C2×Q8×C71—22no—
241C2×Q8×C71—22no—
242C2×Q8×C71C2412yes—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—24no—
250C22×C4×C71—82no—
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D412yes—
253C22×C4×C71C2412yes—
254C22×C4×C71C2411yescharacteristic
255C2×C8×C71—22no—
256C2×C8×C71—22no—
257C2×C8×C71C2412yes—
258C2×C8×C71C2412yes—
259C4⋊C4×C71—21no—
260C4⋊C4×C71—24no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—24no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71C2412yes—
265C4⋊C4×C71C2412yes—
266C4⋊C4×C71C2412yes—
267C22⋊C4×C71—24no—
268C23×C71—22no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71C22×D412yes—
272C23×C71C22×D411yescharacteristic
273C22×D71—22no—
274C22×D71—22no—
275C22×D71—22no—
276C22×D71C22×D412yes—
277Q8×C71—22no—
278Q8×C71—22no—
279Q8×C71—42no—
280C2×C4×C71—22no—
281C2×C4×C71—24no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—42no—
289C2×C4×C71—42no—
290C2×C4×C71—42no—
291C2×C4×C71—42no—
292C2×C4×C71—84no—
293C2×C4×C71C22×D412yes—
294C2×C4×C71C22×D411yescharacteristic
295C2×C4×C71C2×#4112yes—
296C2×C4×C712−1+412yes—
297C2×C4×C71C2511yescharacteristic
298C22⋊D71—28no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—42no—
306C2×Dic71—42no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309C2×Dic71#13714yes—
310C2×Dic71C22×D412yes—
311C2×Dic71C22×D412yes—
312C2×Dic71C22×D412yes—
313C4×D71—24no—
314C4×D71—22no—
315C4×D71—22no—
316C4×D71—84no—
317Dic142—22no—
318Dic142—22no—
319Dic142—42no—
320Dic142—48no—
321Dic142—84no—
322C8×C71—22no—
323C8×C71—22no—
324C71⋊C8—22no—
325C71⋊C8C2×#4114yes—
326C22×C71—22no—
327C22×C71—22no—
328C22×C71—22no—
329C22×C71—44no—
330C22×C71#54712yes—
331C22×C71C2×#13712yes—
332C22×C71#57712yes—
333C22×C71C23×D411yescharacteristic
334C2×D71—22no—
335C2×D71—22no—
336C2×D71—22no—
337C2×D71—44no—
338C4×C71—22no—
339C4×C71—42no—
340C4×C71—42no—
341C4×C71—42no—
342C4×C71—42no—
343C4×C71#54712yes—
344C4×C71C22×#4111yescharacteristic
345C4×C71C2×2−1+411yescharacteristic
346Dic71—22no—
347Dic71—22no—
348Dic71—42no—
349Dic71—42no—
350Dic71—42no—
351Dic71—42no—
352Dic71C2×#13714yes—
353C2×#3356—711nomaximal, Sylow
354C2×C71—42no—
355C2×C71#335614yescomplemented
356C2×C71C2×#54711yescharacteristic
357C2×C71C22×#13711yescharacteristic
358C2×C71C2×#57711yescharacteristic
359D71—42no—
360C2×#556—711no—
361C2×#554—711no—
362#3356—7116no—
363C2×#498—711no—
364C2×#485—711no—
365C2×#485—711no—
366C2×#483—711no—
367C2×#483D7111yescharacteristic, complemented
368C2×#477—711no—
369C2×#475—711no—
370C2×#470—711no—
371C2×#470—711no—
372C2×C4×Q16—711no—
373C2×#436—711no—
374C2×#428—711no—
375C2×#428—711no—
376C71C2×#335611yescharacteristic, complemented, Sylow
377C22×Q16—711no—
378C22×M16—711no—
379C22×M16—711no—
380#556—718no—
381#556—1424no—
382#554—718no—
383#554—1424no—
384C2×C4⋊Q8—711no—
385C2×C4⋊Q8—711no—
386C2×#126—1421no—
387C2×#126—1421no—
388C2×#125—1421no—
389C2×#124—1421no—
390C2×C22⋊Q8—711no—
391C2×C22⋊Q8—711no—
392C2×C22⋊Q8—711no—
393C2×C22⋊Q8—1421no—
394C2×C22⋊Q8—1421no—
395C2×C22⋊Q8C2×D7111yescharacteristic
396C2×C4×Q8—711no—
397C2×C4×Q8—711no—
398C2×C4×Q8—1421no—
399C2×C4×D4—711no—
400C2×C4×D4—1421no—
401C2×#117—711no—
402C2×#117—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4C2×D7111yescharacteristic
405#498—718no—
406#485—718no—
407#485—718no—
408#483—718no—
409#483C2×D7118yescomplemented
410#477—718no—
411#475—718no—
412#470—718no—
413#470—718no—
414C4×Q16—718no—
415#436—718no—
416#428—718no—
417#428—718no—
418C2×#107—711no—
419C2×#107—711no—
420C2×#107—711no—
421C2×#106—711no—
422C2×#106—711no—
423C2×#106—711no—
424C2×#106—711no—
425C2×#106C2×D7111yescharacteristic
426C2×#106C2×D7111yescharacteristic
427C2×C4⋊C8—711no—
428C2×#103—711no—
429C2×#103—711no—
430C2×#103—711no—
431C2×#103—711no—
432C2×#103C2×D7111yescharacteristic
433C2×#103C2×D7111yescharacteristic
434C2×C22⋊C8—711no—
435C2×C22⋊C8C2×D7111yescharacteristic
436C2×C4×C8—711no—
437C22×Q8—711no—
438C22×Q8—1421no—
439C22×Q8—1421no—
440C22×Q8C22×D7111yescharacteristic
441C22×D4—711no—
442C23×C4—21no—
443C23×C4—711no—
444C23×C4—1421no—
445C23×C4C22×D7111yescharacteristic
446C2×Q16—714no—
447C2×Q16—1424no—
448C2×M16—714no—
449C2×M16—714no—
450C2×M16—1424no—
451C2×M16—1424no—
452C22×C8—711no—
453C22×C8—711no—
454C22×C8C22×D7111yescharacteristic
455C22×C8C22×D7111yescharacteristic
456C4⋊Q8—714no—
457C4⋊Q8—714no—
458C4⋊Q8—1422no—
459C4⋊Q8—1422no—
460#126—1428no—
461#126—1428no—
462#125—1428no—
463#124—1428no—
464C22⋊Q8—22no—
465C22⋊Q8—714no—
466C22⋊Q8—714no—
467C22⋊Q8—714no—
468C22⋊Q8—1428no—
469C22⋊Q8—1428no—
470C22⋊Q8—1422no—
471C22⋊Q8—1422no—
472C22⋊Q8—1422no—
473C22⋊Q8C22×D7114yes—
474C4×Q8—714no—
475C4×Q8—714no—
476C4×Q8—1422no—
477C4×Q8—1422no—
478C4×Q8—1428no—
479C4×D4—714no—
480C4×D4—714no—
481C4×D4—1428no—
482#117—714no—
483#117—714no—
484#117—1422no—
485#117—1422no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—711no—
490C2×C4⋊C4—711no—
491C2×C4⋊C4—711no—
492C2×C4⋊C4—711no—
493C2×C4⋊C4—714no—
494C2×C4⋊C4—1422no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4—1421no—
498C2×C4⋊C4—1421no—
499C2×C4⋊C4—1421no—
500C2×C4⋊C4—1421no—
501C2×C4⋊C4—1421no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4C22×D7111yescharacteristic
504C2×C4⋊C4C22×D7111yescharacteristic
505C2×C4⋊C4C22×D7114yes—
506C2×C4⋊C4C22×D7111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—711no—
509C2×C22⋊C4—711no—
510C2×C22⋊C4—1421no—
511C2×C22⋊C4—1421no—
512C2×C22⋊C4—1421no—
513C2×C22⋊C4—1421no—
514C2×C22⋊C4—1421no—
515C2×C42—711no—
516C2×C42—1421no—
517C2×C42—1421no—
518C2×C42—1421no—
519C2×C42—1421no—
520#107—714no—
521#107—714no—
522#107—714no—
523#106—714no—
524#106—714no—
525#106—714no—
526#106—714no—
527#106C22×D7114yes—
528#106C22×D7114yes—
529C4⋊C8—714no—
530#103—714no—
531#103—714no—
532#103—714no—
533#103—714no—
534#103C22×D7114yes—
535#103C22×D7114yes—
536C22⋊C8—714no—
537C22⋊C8C22×D7114yes—
538C4×C8—714no—
539C24—711no—
540C24D4×D7111yescharacteristic
541C2×Q8—21no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—2844no—
545C2×Q8—5682no—
546C2×Q8—712no—
547C2×Q8—1424no—
548C2×Q8—1424no—
549C2×Q8—1422no—
550C2×Q8—1422no—
551C2×Q8—1421no—
552C2×Q8C23×D7112yes—
553C2×D4—714no—
554C2×D4—1424no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—82no—
563C22×C4—5682no—
564C22×C4—711no—
565C22×C4—711no—
566C22×C4—711no—
567C22×C4—712no—
568C22×C4—712no—
569C22×C4—1424no—
570C22×C4—1421no—
571C22×C4—1421no—
572C22×C4—1421no—
573C22×C4—1421no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4D4×D7112yes—
577C22×C4D4×D7111yescharacteristic
578C22×C4C23×D7112yes—
579C22×C4C23×D7111yescharacteristic
580Q16—1428no—
581M16—1428no—
582M16—1428no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—714no—
586C2×C8—712no—
587C2×C8—712no—
588C2×C8—1422no—
589C2×C8C23×D7112yes—
590C2×C8C23×D7112yes—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—714no—
597C4⋊C4—712no—
598C4⋊C4—712no—
599C4⋊C4—712no—
600C4⋊C4—1424no—
601C4⋊C4—1424no—
602C4⋊C4—1424no—
603C4⋊C4—1424no—
604C4⋊C4—1424no—
605C4⋊C4—1424no—
606C4⋊C4—1424no—
607C4⋊C4—1424no—
608C4⋊C4—1421no—
609C4⋊C4—1421no—
610C4⋊C4—1421no—
611C4⋊C4C23×D7112yes—
612C4⋊C4C23×D7112yes—
613C4⋊C4C23×D7112yes—
614C22⋊C4—24no—
615C22⋊C4—714no—
616C22⋊C4—714no—
617C22⋊C4—1424no—
618C22⋊C4—1424no—
619C22⋊C4—1424no—
620C22⋊C4—1424no—
621C22⋊C4—1424no—
622C42—712no—
623C42—712no—
624C42—1424no—
625C42—1424no—
626C42—1424no—
627C42—1424no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—712no—
632C23—1422no—
633C23—1422no—
634C23—1422no—
635C23C2×D4×D7112yes—
636C23C2×D4×D7111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—2848no—
641Q8—2842no—
642Q8—5684no—
643Q8—1422no—
644Q8—1422no—
645D4—1428no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—2842no—
660C2×C4—2842no—
661C2×C4—2842no—
662C2×C4—2842no—
663C2×C4—5684no—
664C2×C4—712no—
665C2×C4—714no—
666C2×C4—712no—
667C2×C4—712no—
668C2×C4—1422no—
669C2×C4—1422no—
670C2×C4—1422no—
671C2×C4—1422no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4—1424no—
677C2×C4C2×D4×D7112yes—
678C2×C4C2×D4×D7111yescharacteristic
679C2×C4#41×D7112yes—
680C2×C4#1455617512yes—
681C2×C4C24×D7111yescharacteristic
682C8—22no—
683C8—22no—
684C8—714no—
685C8—1422no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—2844no—
691C22—1422no—
692C22—1422no—
693C22—1422no—
694C22#1798664712yes—
695C22#137×D7112yes—
696C22#1798680512yes—
697C22C22×D4×D7111yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—2842no—
704C4—2842no—
705C4—2842no—
706C4—2842no—
707C4—714no—
708C4—1422no—
709C4—1422no—
710C4#1798664712yes—
711C4C2×#41×D7111yescharacteristic
712C4C2×#1455617511yescharacteristic
713C2—42no—
714C2—2842no—
715C2#2260094814yesdirect product factor
716C2C2×#1798664711yescharacteristic
717C2C2×#137×D7111yescharacteristic
718C2C2×#1798680511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#483×C71C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
hypercenterC2×#483D71
hypocenterC71C2×#3356
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #22600948C2direct (N × H)
4. C2×#17986396C2semidirect
5. C2×#17986343C2semidirect
6. C2×#17986341C2semidirect
7. C2×#17986328C2semidirect
8. C2×#17986292C2semidirect
9. C2×#17986283C2semidirect
10. C2×#17986256C2semidirect
11. C2×#17986255C2semidirect
12. C2×#17986091C2semidirect
14. C2×#17986039C2semidirect
15. C2×#17986038C2semidirect
16. C2×#483×C71C2semidirect
43. #17986396C22semidirect
44. #17986343C22semidirect
45. #17986341C22semidirect
46. #17986328C22semidirect
47. #17986292C22semidirect
48. #17986283C22semidirect
49. #17986256C22semidirect
50. #17986255C22semidirect
51. #17986091C22semidirect
53. #17986039C22semidirect
54. #17986038C22semidirect
71. #483×C71C22semidirect
355. C2×C71#3356semidirect
367. C2×#483D71semidirect
376. C71C2×#3356semidirect
409. #483C2×D71semidirect
715. C2#22600948direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867202
C2×#179867042
#226009482
C2×#179863962
C2×#179863432
C2×#179863412
C2×#179863282
C2×#179862922
C2×#179862832
C2×#179862562
C2×#179862552
C2×#179860912
C2×#179860742
C2×#179860392
C2×#179860382
C2×#483×C712
C2×#335671