Finite Group Databasebeta

← C2×#22600951 #32876186

Subgroups — C2×#22600951 #32876186

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×#17986717C211yesmaximal, characteristic
2C2×#17986704C211yesmaximal, characteristic
3#22600951C2116yesmaximal, direct product factor
4C2×#17986396C211yesmaximal, characteristic, complemented
5C2×#17986342C211yesmaximal, characteristic, complemented
6C2×#17986340C211yesmaximal, characteristic, complemented
7C2×#17986331C211yesmaximal, characteristic, complemented
8C2×#17986329C211yesmaximal, characteristic, complemented
9C2×#17986293C211yesmaximal, characteristic, complemented
10C2×#17986283C211yesmaximal, characteristic, complemented
11C2×#17986258C211yesmaximal, characteristic, complemented
12C2×#17986257C211yesmaximal, characteristic, complemented
13C2×#17986093C211yesmaximal, characteristic, complemented
14C2×#17986075C211yesmaximal, characteristic
15C2×#17986040C211yesmaximal, characteristic, complemented
16C2×#428×C71C211yesmaximal, characteristic, complemented
17C22×Dic284C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19#17986717—24no—
20#17986717C2218yes—
21#17986704—24no—
22#17986704C2218yes—
23C2×#14556127C2211yescharacteristic
24C2×#14556127C2211yescharacteristic
25C2×#14556122—21no—
26C2×#14556121—21no—
27C2×#14556118—21no—
28C2×#14556114—21no—
29C2×#14556108C2211yescharacteristic
30C2×#14556108C2211yescharacteristic
31C2×#14556107—21no—
32C2×#14556107C2211yescharacteristic
33C2×#14556107C2211yescharacteristic
34C2×#14556106—21no—
35C2×C4×Dic142—21no—
36C2×#14556093C2211yescharacteristic
37C2×#14556093C2211yescharacteristic
38C2×C4×C22⋊D71—21no—
39C2×C4×C22⋊D71C2211yescharacteristic
40C2×#14556086C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42#17986396C2218yescomplemented
43#17986342C2218yescomplemented
44#17986340C2218yescomplemented
45#17986331C2218yescomplemented
46#17986329C2218yescomplemented
47#17986293C2218yescomplemented
48#17986283C2218yescomplemented
49#17986258C2218yescomplemented
50#17986257C2218yescomplemented
51#17986093C2218yescomplemented
52#17986075C2218yes—
53#17986040C2218yescomplemented
54C2×#14556061C2211yescharacteristic
55C2×#14556060C2211yescharacteristic
56C2×#14556059C2211yescharacteristic
57C2×#14556059C2211yescharacteristic
58C2×#14556059C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×#14556053C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556051C2211yescharacteristic
63C2×#14556051C2211yescharacteristic
64C2×#14556051C2211yescharacteristic
65C2×#14556051C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C2×#117×C71C2211yescharacteristic
71C22×C4⋊C4×C71C2211yescharacteristic
72#428×C71C2218yescomplemented
73C2×#107×C71C2211yescharacteristic
74C2×#107×C71C2211yescharacteristic
75C2×#106×C71C2211yescharacteristic
76C2×#106×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C22×Dic142C2311yescharacteristic
81C22×C22⋊D71D411yescharacteristic
82C22×C4×D71—21no—
83C22×C4×D71C2311yescharacteristic
84C2×Dic284—24no—
85C2×Dic284C2314yes—
86C2×#11765848—24no—
87C2×#11765848C2314yes—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90#14556127—22no—
91#14556127—22no—
92#14556127C2314yes—
93#14556127C2314yes—
94#14556122—28no—
95#14556121—28no—
96#14556118—28no—
97#14556114—28no—
98#14556108—22no—
99#14556108—22no—
100#14556108C2314yes—
101#14556108C2314yes—
102#14556107—28no—
103#14556107—22no—
104#14556107—22no—
105#14556107C2314yes—
106#14556107C2314yes—
107#14556106—28no—
108C4×Dic142—28no—
109#14556093—22no—
110#14556093—22no—
111#14556093C2314yes—
112#14556093C2314yes—
113C4×C22⋊D71—28no—
114C4×C22⋊D71D414yes—
115C4×C22⋊D71C2314yes—
116#14556086—22no—
117#14556086C2314yes—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×Dic71⋊C4—21no—
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4D411yescharacteristic
130C4⋊C4×D71—22no—
131C4⋊C4×D71C2314yes—
132C2×C22⋊Dic71—21no—
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71D411yescharacteristic
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4D411yescharacteristic
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71C2311yescharacteristic
143#14556061C2314yes—
144#14556060C2314yes—
145#14556059C2314yes—
146#14556059C2314yes—
147#14556059C2314yes—
148Dic71⋊C8C2314yes—
149#14556053C2314yes—
150#14556053C2314yes—
151#14556051C2314yes—
152#14556051C2314yes—
153#14556051C2314yes—
154#14556051C2314yes—
155C22⋊(C71⋊C8)C2314yes—
156(C2×D71)⋊C8C2314yes—
157C8×Dic71C2314yes—
158C23×C4×C71—21no—
159C23×C4×C71C2311yescharacteristic
160C2×M16×C71—24no—
161C2×M16×C71C2314yes—
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2311yescharacteristic
164#117×C71—22no—
165#117×C71C2314yes—
166C2×C4⋊C4×C71—22no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2314yes—
173C2×C22⋊C4×C71—21no—
174C2×C42×C71—21no—
175#107×C71C2314yes—
176#107×C71C2314yes—
177#106×C71C2314yes—
178#106×C71C2314yes—
179C23×D71C2×D411yescharacteristic
180C2×Dic142—22no—
181C2×Dic142—22no—
182C2×Dic142—22no—
183C2×Dic142—22no—
184C2×Dic142—21no—
185C2×Dic142—21no—
186C2×Dic142—24no—
187C2×Dic142—24no—
188C2×Dic142—44no—
189C2×Dic142—82no—
190C2×Dic142C2412yes—
191C2×Dic142C2412yes—
192C2×C22⋊D71—24no—
193C2×C22⋊D71C2×D414yes—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71C2×D411yescharacteristic
199C22×Dic71C2×D411yescharacteristic
200C22×Dic71C2×D411yescharacteristic
201C2×C4×D71—22no—
202C2×C4×D71—22no—
203C2×C4×D71—24no—
204C2×C4×D71—82no—
205C2×C4×D71C2×D412yes—
206C2×C4×D71C2412yes—
207Dic284—28no—
208#11765848—28no—
209C2×C71⋊C8—22no—
210C2×C71⋊C8—22no—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C4⋊Dic71—21no—
214C4⋊Dic71—21no—
215C4⋊Dic71—24no—
216C4⋊Dic71—24no—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4C2×D414yes—
227C22⋊Dic71—24no—
228C22⋊Dic71—24no—
229C22⋊Dic71C2×D414yes—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4C2×D414yes—
234C4×Dic71—24no—
235C4×Dic71—24no—
236C4×Dic71—24no—
237C4×Dic71C2×D412yes—
238C4×Dic71C2412yes—
239C24×C71C2×D411yescharacteristic
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—24no—
247C22×C4×C71—82no—
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2411yescharacteristic
252M16×C71—28no—
253C2×C8×C71—22no—
254C2×C8×C71#4114yes—
255C2×C8×C71C2412yes—
256C2×C8×C71C2412yes—
257C4⋊C4×C71—21no—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71—21no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71C2412yes—
263C4⋊C4×C71C2412yes—
264C4⋊C4×C71C2412yes—
265C4⋊C4×C71C2412yes—
266C22⋊C4×C71—24no—
267C42×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—
277C2×C4×C71—22no—
278C2×C4×C71—24no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—42no—
286C2×C4×C71—42no—
287C2×C4×C71—42no—
288C2×C4×C71—42no—
289C2×C4×C71—84no—
290C2×C4×C71C22×D412yes—
291C2×C4×C71C22×D411yescharacteristic
292C2×C4×C71C2×#4112yes—
293C2×C4×C712−1+412yes—
294C2×C4×C71C2511yescharacteristic
295C22⋊D71—28no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304C2×Dic71—42no—
305C2×Dic71—42no—
306C2×Dic71#13714yes—
307C2×Dic71C22×D412yes—
308C2×Dic71C22×D412yes—
309C2×Dic71C22×D412yes—
310C4×D71—24no—
311C4×D71—22no—
312C4×D71—22no—
313C4×D71—84no—
314Dic142—22no—
315Dic142—22no—
316Dic142—22no—
317Dic142—22no—
318Dic142—42no—
319Dic142—42no—
320Dic142—48no—
321Dic142—84no—
322C8×C71—22no—
323C8×C71C2×#4114yes—
324C71⋊C8—22no—
325C71⋊C8—22no—
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×#483—711no—
368C2×#477—711no—
369C2×#475—711no—
370C2×#470—711no—
371C2×#470—711no—
372C2×C4×Q16—711no—
373C2×#436—711no—
374C2×#428—711no—
375C2×#428D7111yescharacteristic, complemented
376C71C2×#335611yescharacteristic, complemented, Sylow
377C22×Q16—711no—
378C22×M16—711no—
379C22×M16C2×D7111yescharacteristic
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—711no—
394C2×C22⋊Q8—1421no—
395C2×C22⋊Q8—1421no—
396C2×C4×Q8—711no—
397C2×C4×Q8—711no—
398C2×C4×Q8—1421no—
399C2×C4×D4—711no—
400C2×C4×D4—1421no—
401C2×#117—711no—
402C2×#117C2×D7111yescharacteristic
403C22×C4⋊C4—711no—
404C22×C4⋊C4C2×D7111yescharacteristic
405#498—718no—
406#485—718no—
407#485—718no—
408#483—718no—
409#483—718no—
410#477—718no—
411#475—718no—
412#470—718no—
413#470—718no—
414C4×Q16—718no—
415#436—718no—
416#428—718no—
417#428C2×D7118yescomplemented
418C2×#107—711no—
419C2×#107C2×D7111yescharacteristic
420C2×#107C2×D7111yescharacteristic
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×#103—711no—
433C2×#103—711no—
434C2×C22⋊C8—711no—
435C2×C22⋊C8—711no—
436C2×C4×C8—711no—
437C22×Q8—711no—
438C22×Q8—711no—
439C22×Q8—1421no—
440C22×Q8—1421no—
441C22×D4—711no—
442C23×C4—21no—
443C23×C4—711no—
444C23×C4—1421no—
445C23×C4C22×D7111yescharacteristic
446C2×Q16—714no—
447C2×Q16—1424no—
448C2×M16—24no—
449C2×M16—714no—
450C2×M16—1424no—
451C2×M16C22×D7114yes—
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—714no—
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⋊Q8—1422no—
474C4×Q8—714no—
475C4×Q8—714no—
476C4×Q8—1428no—
477C4×Q8—1422no—
478C4×Q8—1422no—
479C4×D4—714no—
480C4×D4—714no—
481C4×D4—1428no—
482#117—22no—
483#117—714no—
484#117—1422no—
485#117C22×D7114yes—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—711no—
490C2×C4⋊C4—711no—
491C2×C4⋊C4—714no—
492C2×C4⋊C4—1422no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4—1421no—
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⋊C4C22×D7111yescharacteristic
503C2×C4⋊C4C22×D7111yescharacteristic
504C2×C4⋊C4C22×D7114yes—
505C2×C4⋊C4C22×D7111yescharacteristic
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—21no—
516C2×C42—711no—
517C2×C42—1421no—
518C2×C42—1421no—
519C2×C42—1421no—
520#107—714no—
521#107C22×D7114yes—
522#107C22×D7114yes—
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#103—714no—
535#103—714no—
536C22⋊C8—714no—
537C22⋊C8—714no—
538C4×C8—714no—
539C24—711no—
540C24D4×D7111yescharacteristic
541C2×Q8—2844no—
542C2×Q8—5682no—
543C2×Q8—712no—
544C2×Q8—712no—
545C2×Q8—1424no—
546C2×Q8—1424no—
547C2×Q8—1422no—
548C2×Q8—1422no—
549C2×Q8—1422no—
550C2×Q8—1422no—
551C2×Q8—1421no—
552C2×Q8—1421no—
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—28no—
582M16—1428no—
583C2×C8—22no—
584C2×C8—712no—
585C2×C8—712no—
586C2×C8—1422no—
587C2×C8—1422no—
588C2×C8#1176586514yes—
589C2×C8C23×D7112yes—
590C2×C8C23×D7112yes—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—714no—
597C4⋊C4—712no—
598C4⋊C4—712no—
599C4⋊C4—1424no—
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⋊C4C23×D7112yes—
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—24no—
623C42—712no—
624C42—712no—
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—2848no—
638Q8—2842no—
639Q8—2842no—
640Q8—5684no—
641Q8—1422no—
642Q8—1422no—
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×C4C2×#1176586512yes—
680C2×C4#1455617612yes—
681C2×C4C24×D7111yescharacteristic
682C8—22no—
683C8—1422no—
684C8—1422no—
685C8C2×#1176586514yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—2844no—
691C22—1422no—
692C22—1422no—
693C22—1422no—
694C22#1798665012yes—
695C22#137×D7112yes—
696C22#1798680912yes—
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#1798665012yes—
711C4C22×#1176586511yescharacteristic
712C4C2×#1455617611yescharacteristic
713C2—42no—
714C2—2842no—
715C2#2260095114yesdirect product factor
716C2C2×#1798665011yescharacteristic
717C2C2×#137×D7111yescharacteristic
718C2C2×#1798680911yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#428×C71C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
hypercenterC2×#428D71
hypocenterC71C2×#3356
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. #22600951C2direct (N × H)
4. C2×#17986396C2semidirect
5. C2×#17986342C2semidirect
6. C2×#17986340C2semidirect
7. C2×#17986331C2semidirect
8. C2×#17986329C2semidirect
9. C2×#17986293C2semidirect
10. C2×#17986283C2semidirect
11. C2×#17986258C2semidirect
12. C2×#17986257C2semidirect
13. C2×#17986093C2semidirect
15. C2×#17986040C2semidirect
16. C2×#428×C71C2semidirect
42. #17986396C22semidirect
43. #17986342C22semidirect
44. #17986340C22semidirect
45. #17986331C22semidirect
46. #17986329C22semidirect
47. #17986293C22semidirect
48. #17986283C22semidirect
49. #17986258C22semidirect
50. #17986257C22semidirect
51. #17986093C22semidirect
53. #17986040C22semidirect
72. #428×C71C22semidirect
355. C2×C71#3356semidirect
375. C2×#428D71semidirect
376. C71C2×#3356semidirect
417. #428C2×D71semidirect
715. C2#22600951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867172
C2×#179867042
#226009512
C2×#179863962
C2×#179863422
C2×#179863402
C2×#179863312
C2×#179863292
C2×#179862932
C2×#179862832
C2×#179862582
C2×#179862572
C2×#179860932
C2×#179860752
C2×#179860402
C2×#428×C712
C2×#335671