Finite Group Databasebeta

← C2×#22600693 #32875871

Subgroups — C2×#22600693 #32875871

Order 18176.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986704C211yesmaximal, characteristic, complemented
2C2×#17986650C211yesmaximal, characteristic
3#22600693C2116yesmaximal, direct product factor
4C2×#17986396C211yesmaximal, characteristic, complemented
5C2×#17986319C211yesmaximal, characteristic, complemented
6C2×#17986317C211yesmaximal, characteristic, complemented
7C2×#17986331C211yesmaximal, characteristic, complemented
8C2×#17986329C211yesmaximal, characteristic, complemented
9C2×#17986283C211yesmaximal, characteristic, complemented
10C2×#17986288C211yesmaximal, characteristic, complemented
11C2×#17986229C211yesmaximal, characteristic, complemented
12C2×#17986228C211yesmaximal, characteristic, complemented
13C2×#17986086C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D71C211yesmaximal, characteristic, complemented
15C2×#106×D71C211yesmaximal, characteristic, complemented
16C22×#106×C71C211yesmaximal, characteristic, complemented
17C22×#11765865—21no—
18C22×#11765854C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20#17986704—24no—
21#17986704C2218yescomplemented
22#17986650—24no—
23#17986650C2218yes—
24C2×#14556127C2211yescharacteristic
25C2×#14556127C2211yescharacteristic
26C2×#14556118—21no—
27C2×#14556113—21no—
28C2×#14556111—21no—
29C2×#14556108C2211yescharacteristic
30C2×#14556107—21no—
31C2×#14556107C2211yescharacteristic
32C2×#14556106—21no—
33C2×#14556106—21no—
34C2×#14556103C2211yescharacteristic
35C2×#14556102C2211yescharacteristic
36C2×#14556093C2211yescharacteristic
37C2×#14556090C2211yescharacteristic
38C2×C4×C22⋊D71—21no—
39C2×C4×C22⋊D71C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42#17986396C2218yescomplemented
43#17986331C2218yescomplemented
44#17986329C2218yescomplemented
45#17986319C2218yescomplemented
46#17986317C2218yescomplemented
47#17986288C2218yescomplemented
48#17986283C2218yescomplemented
49#17986229C2218yescomplemented
50#17986228C2218yescomplemented
51#17986086C2218yescomplemented
52C8×C22⋊D71C2218yescomplemented
53C2×#14556060C2211yescharacteristic
54C2×#14556059C2211yescharacteristic
55C2×#14556059C2211yescharacteristic
56C2×#14556059C2211yescharacteristic
57C2×#14556059C2211yescharacteristic
58#106×D71C2218yescomplemented
59C2×Dic71⋊C8C2211yescharacteristic
60C2×#14556053C2211yescharacteristic
61C2×#14556051C2211yescharacteristic
62C2×#14556051C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C23×C8×C71C2211yescharacteristic
70C22×C4⋊C4×C71C2211yescharacteristic
71C22×C4⋊C4×C71C2211yescharacteristic
72C2×#106×C71C2211yescharacteristic
73C2×#106×C71C2211yescharacteristic
74C2×#106×C71C2211yescharacteristic
75C2×#106×C71C2211yescharacteristic
76C2×#106×C71C2218yescomplemented
77C2×#11765865—28no—
78C2×#11765865—48no—
79C22×Dic142—21no—
80C22×Dic142—21no—
81C22×Dic142C2311yescharacteristic
82C22×D284—21no—
83C22×D284C2311yescharacteristic
84C22×C22⋊D71—21no—
85C22×C22⋊D71D411yescharacteristic
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71C2311yescharacteristic
90C2×#11765854—24no—
91C2×#11765854C2314yes—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C2×C8×D71—24no—
95C2×C8×D71C2314yes—
96#14556127—22no—
97#14556127—22no—
98#14556127C2314yes—
99#14556127C2314yes—
100#14556118—28no—
101#14556113—28no—
102#14556111—28no—
103#14556108—22no—
104#14556108C2314yes—
105#14556107—28no—
106#14556107—22no—
107#14556107C2314yes—
108#14556106—28no—
109#14556106—28no—
110#14556103—22no—
111#14556103C2314yes—
112#14556102—22no—
113#14556102C2314yes—
114#14556093—22no—
115#14556093C2314yes—
116#14556090—22no—
117#14556090C2314yes—
118C4×C22⋊D71—28no—
119C4×C22⋊D71D414yes—
120C4×C22⋊D71C2314yes—
121C2×C4⋊Dic71—21no—
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×D71—22no—
133C4⋊C4×D71C2314yes—
134C4⋊C4×D71C2314yes—
135C2×C22⋊Dic71—21no—
136C2×C22⋊Dic71D411yescharacteristic
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4D411yescharacteristic
142C2×C4×Dic71—21no—
143C2×C4×Dic71C2311yescharacteristic
144#14556060C2314yes—
145#14556059C2314yes—
146#14556059C2314yes—
147#14556059C2314yes—
148#14556059C2314yes—
149Dic71⋊C8C2314yes—
150#14556053C2314yes—
151#14556051C2314yes—
152#14556051C2314yes—
153#14556050C2314yes—
154#14556048C2314yes—
155#14556048C2314yes—
156C22⋊(C71⋊C8)C2314yes—
157(C2×D71)⋊C8C2314yes—
158C8×Dic71C2314yes—
159C23×C4×C71—21no—
160C23×C4×C71—21no—
161C23×C4×C71C2311yescharacteristic
162C22×C8×C71—24no—
163C22×C8×C71C2314yes—
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C2×C4⋊C4×C71—22no—
167C2×C4⋊C4×C71—22no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71C2314yes—
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C4⋊C4×C71C2314yes—
176#106×C71C2314yes—
177#106×C71C2314yes—
178#106×C71C2314yes—
179#106×C71C2314yes—
180C23×D71—21no—
181C23×D71C2×D411yescharacteristic
182#11765865—432no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—21no—
186C2×Dic142—24no—
187C2×Dic142—24no—
188C2×Dic142—44no—
189C2×Dic142—82no—
190C2×Dic142C2412yes—
191C2×D284—22no—
192C2×D284—22no—
193C2×D284—24no—
194C2×D284—21no—
195C2×D284—44no—
196C2×D284C2412yes—
197C2×C22⋊D71—24no—
198C2×C22⋊D71—44no—
199C2×C22⋊D71SD1618yescomplemented
200C2×C22⋊D71C2×D414yes—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—21no—
204C22×Dic71C2×D411yescharacteristic
205C22×Dic71C2×D411yescharacteristic
206C22×Dic71C2×D411yescharacteristic
207C2×C4×D71—22no—
208C2×C4×D71—22no—
209C2×C4×D71—24no—
210C2×C4×D71—24no—
211C2×C4×D71—24no—
212C2×C4×D71—44no—
213C2×C4×D71—44no—
214C2×C4×D71—82no—
215C2×C4×D71C2×D412yes—
216C2×C4×D71C2412yes—
217#11765854—28no—
218C2×C71⋊C8—22no—
219C2×C71⋊C8—22no—
220C2×C71⋊C8C2412yes—
221C2×C71⋊C8C2412yes—
222C8×D71—28no—
223C4⋊Dic71—21no—
224C4⋊Dic71—21no—
225C4⋊Dic71—24no—
226C4⋊Dic71C2412yes—
227C4⋊Dic71C2412yes—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4—24no—
231Dic71⋊C4—24no—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234Dic71⋊C4C2×D414yes—
235C22⋊Dic71—24no—
236C22⋊Dic71C2×D414yes—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4—24no—
239(C2×D71)⋊C4—24no—
240(C2×D71)⋊C4—24no—
241(C2×D71)⋊C4C2×D414yes—
242C4×Dic71—24no—
243C4×Dic71C2×D412yes—
244C4×Dic71C2412yes—
245C24×C71C2×D411yescharacteristic
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—24no—
253C22×C4×C71—24no—
254C22×C4×C71—44no—
255C22×C4×C71—82no—
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2411yescharacteristic
260C2×C8×C71—22no—
261C2×C8×C71—28no—
262C2×C8×C71#4114yescomplemented
263C2×C8×C71C2412yes—
264C2×C8×C71C2412yes—
265C4⋊C4×C71—21no—
266C4⋊C4×C71—21no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71—24no—
269C4⋊C4×C71—24no—
270C4⋊C4×C71—21no—
271C4⋊C4×C71C2412yes—
272C4⋊C4×C71C2412yes—
273C4⋊C4×C71C2412yes—
274C4⋊C4×C71C2412yes—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71C2×SD1614yes—
278C23×C71C22×D412yes—
279C23×C71C22×D411yescharacteristic
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—42no—
284C22×D71—42no—
285C22×D71—42no—
286C22×D71C2×SD1614yes—
287C22×D71C22×D412yes—
288C2×C4×C71—22no—
289C2×C4×C71—24no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—42no—
297C2×C4×C71—42no—
298C2×C4×C71—48no—
299C2×C4×C71—42no—
300C2×C4×C71—42no—
301C2×C4×C71—84no—
302C2×C4×C71C22×D412yes—
303C2×C4×C71C22×D411yescharacteristic
304C2×C4×C71C2×#4112yes—
305C2×C4×C712−1+412yes—
306C2×C4×C71C2511yescharacteristic
307C22⋊D71—48no—
308C22⋊D71C2×SD16116yescomplemented
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—42no—
315C2×Dic71—42no—
316C2×Dic71—42no—
317C2×Dic71C2×SD1614yes—
318C2×Dic71C22×D412yes—
319C2×Dic71C22×D412yes—
320C2×Dic71C22×D412yes—
321D284—22no—
322D284—22no—
323D284—48no—
324D284—42no—
325C4×D71—24no—
326C4×D71—22no—
327C4×D71—22no—
328C4×D71—48no—
329C4×D71—48no—
330C4×D71—84no—
331Dic142—22no—
332Dic142—22no—
333Dic142—42no—
334Dic142—48no—
335Dic142—84no—
336C8×C71—22no—
337C8×C71C2×#4114yescomplemented
338C71⋊C8—22no—
339C71⋊C8—22no—
340C22×C71—28no—
341C22×C71—22no—
342C22×C71—22no—
343C22×C71#54712yes—
344C22×C71C22×SD1614yes—
345C22×C71C22×SD1612yes—
346C22×C71#57712yes—
347C22×C71C23×D411yescharacteristic
348C2×D71—28no—
349C2×D71—22no—
350C2×D71—22no—
351C2×D71—42no—
352C2×D71—42no—
353C2×D71—42no—
354C2×D71—84no—
355C2×D71C22×SD1614yes—
356C4×C71—22no—
357C4×C71—42no—
358C4×C71—42no—
359C4×C71—42no—
360C4×C71—42no—
361C4×C71#54712yes—
362C4×C71C22×#4111yescharacteristic
363C4×C71C2×2−1+411yescharacteristic
364Dic71—22no—
365Dic71—22no—
366Dic71—42no—
367Dic71—42no—
368Dic71—42no—
369Dic71C22×SD1614yes—
370C2×#3335—711nomaximal, Sylow
371C2×C71—24no—
372C2×C71#333514yescomplemented
373C2×C71C2×#54711yescharacteristic
374C2×C71C23×SD1611yescharacteristic
375C2×C71C2×#57711yescharacteristic
376D71—24no—
377D71—82no—
378C2×#554—711no—
379C2×#547—711no—
380#3335—7116no—
381C2×#498—711no—
382C2×#481—711no—
383C2×#481—711no—
384C2×#483—711no—
385C2×#483—711no—
386C2×#475—711no—
387C2×#476—711no—
388C2×#465—711no—
389C2×#465—711no—
390C2×C4×SD16—711no—
391C2×C8×D4—711no—
392C22×#106—711no—
393C22×#106D7111yescharacteristic, complemented
394C71C2×#333511yescharacteristic, complemented, Sylow
395C22×#41—1421no—
396C22×SD16—711no—
397C23×C8—711no—
398C23×C8C2×D7111yescharacteristic
399#554—718no—
400#554—1424no—
401#547—718no—
402#547—1424no—
403C2×C4⋊Q8—711no—
404C2×C4⋊Q8—711no—
405C2×#125—1421no—
406C2×#123—1421no—
407C2×#123—1421no—
408C2×C22⋊Q8—711no—
409C2×C22⋊Q8—711no—
410C2×C22⋊Q8—1421no—
411C2×C22⋊Q8—1421no—
412C2×C22⋊Q8—1421no—
413C2×#121—711no—
414C2×#121—711no—
415C2×C4×Q8—711no—
416C2×C4×D4—711no—
417C2×C4×D4—711no—
418C2×C4×D4—1421no—
419C22×C4⋊C4—711no—
420C22×C4⋊C4—711no—
421C22×C4⋊C4C2×D7111yescharacteristic
422C22×C4⋊C4C2×D7111yescharacteristic
423#498—718no—
424#483—718no—
425#483—718no—
426#481—718no—
427#481—718no—
428#476—718no—
429#475—718no—
430#465—718no—
431#465—718no—
432C4×SD16—718no—
433C8×D4—718no—
434C2×#106—711no—
435C2×#106—711no—
436C2×#106—711no—
437C2×#106—711no—
438C2×#106—711no—
439C2×#106—718no—
440C2×#106C2×D7111yescharacteristic
441C2×#106C2×D7111yescharacteristic
442C2×#106C2×D7111yescharacteristic
443C2×#106C2×D7111yescharacteristic
444C2×#106C2×D7118yescomplemented
445C2×C4⋊C8—711no—
446C2×#103—711no—
447C2×#103—711no—
448C2×#103—711no—
449C2×#102—711no—
450C2×#102—711no—
451C2×#102—711no—
452C2×C22⋊C8—711no—
453C2×C22⋊C8—711no—
454C2×C4×C8—711no—
455C2×#41—2848no—
456C2×#41—1428no—
457C22×Q8—711no—
458C22×Q8—1421no—
459C22×Q8—1421no—
460C22×D4—711no—
461C22×D4—711no—
462C22×D4—1421no—
463C22×D4—1421no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—711no—
467C23×C4—1421no—
468C23×C4—1421no—
469C23×C4—1421no—
470C23×C4C22×D7111yescharacteristic
471C2×SD16—714no—
472C2×SD16—1424no—
473C22×C8—24no—
474C22×C8—711no—
475C22×C8—711no—
476C22×C8—714no—
477C22×C8—1424no—
478C22×C8C22×D7111yescharacteristic
479C22×C8C22×D7114yes—
480C22×C8C22×D7111yescharacteristic
481C4⋊Q8—714no—
482C4⋊Q8—714no—
483C4⋊Q8—1422no—
484C4⋊Q8—1422no—
485#125—1428no—
486#123—1428no—
487#123—1428no—
488C22⋊Q8—714no—
489C22⋊Q8—714no—
490C22⋊Q8—1428no—
491C22⋊Q8—1428no—
492C22⋊Q8—1428no—
493C22⋊Q8—1422no—
494C22⋊Q8—1422no—
495#121—714no—
496#121—714no—
497#121—1422no—
498#121—1422no—
499C4×Q8—714no—
500C4×Q8—1422no—
501C4×D4—714no—
502C4×D4—714no—
503C4×D4—714no—
504C4×D4—1422no—
505C4×D4—1428no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—711no—
512C2×C4⋊C4—711no—
513C2×C4⋊C4—714no—
514C2×C4⋊C4—714no—
515C2×C4⋊C4—1422no—
516C2×C4⋊C4—1422no—
517C2×C4⋊C4—1421no—
518C2×C4⋊C4—1421no—
519C2×C4⋊C4—1421no—
520C2×C4⋊C4—1421no—
521C2×C4⋊C4—1421no—
522C2×C4⋊C4—1421no—
523C2×C4⋊C4—1421no—
524C2×C4⋊C4C22×D7111yescharacteristic
525C2×C4⋊C4C22×D7111yescharacteristic
526C2×C4⋊C4C22×D7111yescharacteristic
527C2×C4⋊C4C22×D7111yescharacteristic
528C2×C4⋊C4C22×D7114yes—
529C2×C4⋊C4C22×D7114yes—
530C2×C22⋊C4—711no—
531C2×C22⋊C4—711no—
532C2×C22⋊C4—1421no—
533C2×C22⋊C4—1421no—
534C2×C22⋊C4—1421no—
535C2×C22⋊C4—1421no—
536C2×C22⋊C4—1421no—
537C2×C42—711no—
538C2×C42—1421no—
539#106—714no—
540#106—714no—
541#106—714no—
542#106—714no—
543#106—714no—
544#106C22×D7114yes—
545#106C22×D7114yes—
546#106C22×D7114yes—
547#106C22×D7114yes—
548C4⋊C8—714no—
549#103—714no—
550#103—714no—
551#103—714no—
552#102—714no—
553#102—714no—
554#102—714no—
555C22⋊C8—714no—
556C22⋊C8—714no—
557C4×C8—714no—
558C24—711no—
559C24—1421no—
560C24D4×D7111yescharacteristic
561#41—28432no—
562C2×Q8—2844no—
563C2×Q8—5682no—
564C2×Q8—712no—
565C2×Q8—1424no—
566C2×Q8—1424no—
567C2×Q8—1422no—
568C2×Q8—1422no—
569C2×Q8—1421no—
570C2×D4—2844no—
571C2×D4—2844no—
572C2×D4—714no—
573C2×D4—718no—
574C2×D4—712no—
575C2×D4—1424no—
576C2×D4—1424no—
577C2×D4—1421no—
578C2×D4—1422no—
579C2×D4—1422no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—82no—
590C22×C4—2844no—
591C22×C4—2844no—
592C22×C4—5682no—
593C22×C4—711no—
594C22×C4—711no—
595C22×C4—711no—
596C22×C4—712no—
597C22×C4—712no—
598C22×C4—1424no—
599C22×C4—1424no—
600C22×C4—1424no—
601C22×C4—1421no—
602C22×C4—1421no—
603C22×C4—1421no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4D4×D7112yes—
607C22×C4D4×D7111yescharacteristic
608C22×C4C23×D7112yes—
609C22×C4C23×D7111yescharacteristic
610SD16—1428no—
611C2×C8—22no—
612C2×C8—28no—
613C2×C8—712no—
614C2×C8—712no—
615C2×C8—1422no—
616C2×C8—1422no—
617C2×C8—1428no—
618C2×C8#1176586514yescomplemented
619C2×C8C23×D7112yes—
620C2×C8C23×D7112yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—714no—
628C4⋊C4—712no—
629C4⋊C4—712no—
630C4⋊C4—1424no—
631C4⋊C4—1424no—
632C4⋊C4—1424no—
633C4⋊C4—1424no—
634C4⋊C4—1424no—
635C4⋊C4—1424no—
636C4⋊C4—1424no—
637C4⋊C4—1421no—
638C4⋊C4—1421no—
639C4⋊C4C23×D7112yes—
640C4⋊C4C23×D7112yes—
641C4⋊C4C23×D7112yes—
642C4⋊C4C23×D7112yes—
643C22⋊C4—714no—
644C22⋊C4—714no—
645C22⋊C4—1424no—
646C22⋊C4—1424no—
647C22⋊C4—1424no—
648C22⋊C4—1424no—
649C22⋊C4—1424no—
650C42—712no—
651C42—712no—
652C42—1424no—
653C23—22no—
654C23—22no—
655C23—2842no—
656C23—2842no—
657C23—2842no—
658C23—712no—
659C23—714no—
660C23—1422no—
661C23—1422no—
662C23—1422no—
663C23SD16×D7114yes—
664C23C2×D4×D7112yes—
665C23C2×D4×D7111yescharacteristic
666Q8—2848no—
667Q8—2842no—
668Q8—5684no—
669Q8—1422no—
670Q8—1422no—
671D4—2848no—
672D4—2848no—
673D4—2842no—
674D4—7116no—
675D4—1422no—
676D4—1422no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—2848no—
692C2×C4—2848no—
693C2×C4—2842no—
694C2×C4—2842no—
695C2×C4—2842no—
696C2×C4—5684no—
697C2×C4—712no—
698C2×C4—714no—
699C2×C4—712no—
700C2×C4—712no—
701C2×C4—1422no—
702C2×C4—1422no—
703C2×C4—1422no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4—1422no—
708C2×C4—1424no—
709C2×C4C2×D4×D7112yes—
710C2×C4C2×D4×D7111yescharacteristic
711C2×C4C2×#1176586512yes—
712C2×C4#1455617612yes—
713C2×C4C24×D7111yescharacteristic
714C8—22no—
715C8—1422no—
716C8—1422no—
717C8C2×#1176586514yescomplemented
718C22—22no—
719C22—22no—
720C22—28no—
721C22—2842no—
722C22—2842no—
723C22—2842no—
724C22—5684no—
725C22—714no—
726C22—1422no—
727C22—1422no—
728C22—1428no—
729C22#1798665012yes—
730C22C2×SD16×D7114yes—
731C22C2×SD16×D7112yes—
732C22#1798680512yes—
733C22C22×D4×D7111yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—2842no—
740C4—2842no—
741C4—2842no—
742C4—714no—
743C4—1422no—
744C4—1422no—
745C4#1798665012yes—
746C4C22×#1176586511yescharacteristic
747C4C2×#1455617611yescharacteristic
748C2—24no—
749C2—5682no—
750C2—1424no—
751C2#2260069314yesdirect product factor
752C2C2×#1798665011yescharacteristic
753C2C22×SD16×D7111yescharacteristic
754C2C2×#1798680511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC22×#106×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986650C2
hypercenterC22×#106D71
hypocenterC71C2×#3335
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#17986704C2semidirect
3. #22600693C2direct (N × H)
4. C2×#17986396C2semidirect
5. C2×#17986319C2semidirect
6. C2×#17986317C2semidirect
7. C2×#17986331C2semidirect
8. C2×#17986329C2semidirect
9. C2×#17986283C2semidirect
10. C2×#17986288C2semidirect
11. C2×#17986229C2semidirect
12. C2×#17986228C2semidirect
13. C2×#17986086C2semidirect
14. C2×C8×C22⋊D71C2semidirect
15. C2×#106×D71C2semidirect
16. C22×#106×C71C2semidirect
21. #17986704C22semidirect
42. #17986396C22semidirect
43. #17986331C22semidirect
44. #17986329C22semidirect
45. #17986319C22semidirect
46. #17986317C22semidirect
47. #17986288C22semidirect
48. #17986283C22semidirect
49. #17986229C22semidirect
50. #17986228C22semidirect
51. #17986086C22semidirect
52. C8×C22⋊D71C22semidirect
58. #106×D71C22semidirect
76. C2×#106×C71C22semidirect
199. C2×C22⋊D71SD16semidirect
262. C2×C8×C71#41semidirect
308. C22⋊D71C2×SD16semidirect
337. C8×C71C2×#41semidirect
372. C2×C71#3335semidirect
393. C22×#106D71semidirect
394. C71C2×#3335semidirect
444. C2×#106C2×D71semidirect
618. C2×C8#11765865semidirect
717. C8C2×#11765865semidirect
751. C2#22600693direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867042
C2×#179866502
#226006932
C2×#179863962
C2×#179863192
C2×#179863172
C2×#179863312
C2×#179863292
C2×#179862832
C2×#179862882
C2×#179862292
C2×#179862282
C2×#179860862
C2×C8×C22⋊D712
C2×#106×D712
C22×#106×C712
C2×#333571