Finite Group Databasebeta

← C2×#22599222 #32868138

Subgroups — C2×#22599222 #32868138

Order 18176.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986577C211yesmaximal, characteristic
2#22599222C2116yesmaximal, direct product factor
3C2×#17986332C211yesmaximal, characteristic, complemented
4C2×#17986340C211yesmaximal, characteristic, complemented
5C2×#17986323C211yesmaximal, characteristic, complemented
6C2×#17986327C211yesmaximal, characteristic, complemented
7C2×#17986255C211yesmaximal, characteristic, complemented
8C2×#17986247C211yesmaximal, characteristic, complemented
9C2×#17986238C211yesmaximal, characteristic, complemented
10C2×#17986230C211yesmaximal, characteristic, complemented
11C2×#17986159C211yesmaximal, characteristic, complemented
12C2×#17986159C211yesmaximal, characteristic, complemented
13C2×#17986155C211yesmaximal, characteristic, complemented
14C2×#17986138C211yesmaximal, characteristic, complemented
15C2×#17985966C211yesmaximal, characteristic, complemented
16C2×#536×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765855C2211yescharacteristic
20C22×#11765852C2211yescharacteristic
21C22×#11765852C2211yescharacteristic
22C22×#11765849C2211yescharacteristic
23C23×C71⋊C8C2211yescharacteristic
24#17986577—24no—
25#17986577C2218yes—
26C2×#14556107C2211yescharacteristic
27C2×#14556107C2211yescharacteristic
28C2×#14556104—21no—
29C2×#14556102C2211yescharacteristic
30C2×#14556102C2211yescharacteristic
31C2×#14556100—21no—
32C2×#14556100—21no—
33C2×#14556099—21no—
34C22×C4⋊Dic71C2211yescharacteristic
35#17986340C2218yescomplemented
36#17986332C2218yescomplemented
37#17986327C2218yescomplemented
38#17986323C2218yescomplemented
39#17986255C2218yescomplemented
40#17986247C2218yescomplemented
41#17986238C2218yescomplemented
42#17986230C2218yescomplemented
43#17986159C2218yescomplemented
44#17986159C2218yescomplemented
45#17986155C2218yescomplemented
46#17986138C2218yescomplemented
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59#17985966C2218yescomplemented
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×C22⋊(C71⋊C8)C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65C23×Q8×C71C2211yescharacteristic
66#536×C71—24no—
67#536×C71C2218yescomplemented
68C2×C4⋊Q8×C71—21no—
69C2×#124×C71—21no—
70C2×#123×C71—21no—
71C2×#123×C71—21no—
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×C22⋊Q8×C71C2211yescharacteristic
74C2×C22⋊Q8×C71C2211yescharacteristic
75C2×C22⋊Q8×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C2×#11765865—22no—
78C2×#11765865—42no—
79C2×#11765865—42no—
80C2×#11765865C2314yes—
81C22×Dic142C2311yescharacteristic
82C22×D284C2311yescharacteristic
83C22×C22⋊D71—21no—
84C22×C22⋊D71—21no—
85C22×C22⋊D71—21no—
86C23×Dic71—21no—
87C22×C4×D71—21no—
88C2×#11765855—42no—
89C2×#11765855—42no—
90C2×#11765855C2314yes—
91C2×#11765855C2314yes—
92C2×#11765852—42no—
93C2×#11765852—42no—
94C2×#11765852C2314yes—
95C2×#11765852C2314yes—
96C2×#11765849—42no—
97C2×#11765849C2314yes—
98C22×C71⋊C8—42no—
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103C22×C71⋊C8C2314yes—
104#14556107—22no—
105#14556107—22no—
106#14556107C2314yes—
107#14556107C2314yes—
108#14556104—28no—
109#14556102—22no—
110#14556102—22no—
111#14556102C2314yes—
112#14556102C2314yes—
113#14556100—28no—
114#14556100—28no—
115#14556099—28no—
116C2×C4⋊Dic71—22no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71C2314yes—
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×Dic71⋊C4—21no—
122C2×Dic71⋊C4—21no—
123C2×C22⋊Dic71—21no—
124C2×C22⋊Dic71—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×(C2×D71)⋊C4—21no—
127#14556061C2314yes—
128#14556061C2314yes—
129#14556059C2314yes—
130#14556059C2314yes—
131#14556052C2314yes—
132#14556052C2314yes—
133#14556052C2314yes—
134#14556052C2314yes—
135#14556051C2314yes—
136#14556051C2314yes—
137#14556048C2314yes—
138#14556048C2314yes—
139C22⋊(C71⋊C8)C2314yes—
140C22⋊(C71⋊C8)C2314yes—
141C22⋊(C71⋊C8)C2314yes—
142C22⋊(C71⋊C8)C2314yes—
143C2×#41×C71—42no—
144C2×#41×C71—42no—
145C2×#41×C71D414yes—
146C2×#41×C71C2314yes—
147C22×Q8×C71—21no—
148C22×Q8×C71—22no—
149C22×Q8×C71—42no—
150C22×Q8×C71—42no—
151C22×Q8×C71D411yescharacteristic
152C22×Q8×C71C2311yescharacteristic
153C22×Q8×C71C2311yescharacteristic
154C22×Q8×C71C2314yes—
155C22×D4×C71D411yescharacteristic
156C22×D4×C71D411yescharacteristic
157C22×D4×C71D411yescharacteristic
158C23×C4×C71—21no—
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C4⋊Q8×C71—28no—
163#124×C71—28no—
164#123×C71—28no—
165#123×C71—28no—
166C22⋊Q8×C71—22no—
167C22⋊Q8×C71—22no—
168C22⋊Q8×C71—22no—
169C22⋊Q8×C71—22no—
170C22⋊Q8×C71C2314yes—
171C22⋊Q8×C71C2314yes—
172C22⋊Q8×C71C2314yes—
173C22⋊Q8×C71C2314yes—
174#117×C71—22no—
175#117×C71C2314yes—
176C2×C4⋊C4×C71—21no—
177C2×C4⋊C4×C71—21no—
178C2×C4⋊C4×C71—21no—
179C2×C4⋊C4×C71—21no—
180C2×C4⋊C4×C71C2311yescharacteristic
181C2×C4⋊C4×C71C2311yescharacteristic
182C2×C22⋊C4×C71—21no—
183C2×C22⋊C4×C71—21no—
184C2×C22⋊C4×C71—21no—
185C2×C22⋊C4×C71—21no—
186C2×C22⋊C4×C71—21no—
187C2×C42×C71—21no—
188C23×D71—21no—
189#11765865—44no—
190#11765865—44no—
191#11765865—48no—
192C2×Dic142—22no—
193C2×Dic142—22no—
194C2×Dic142—21no—
195C2×Dic142C2412yes—
196C2×D284—22no—
197C2×D284—22no—
198C2×D284—21no—
199C2×D284C2412yes—
200C2×C22⋊D71—24no—
201C2×C22⋊D71—24no—
202C2×C22⋊D71—24no—
203C2×C22⋊D71—44no—
204C2×C22⋊D71—82no—
205C2×C22⋊D71—82no—
206C22×Dic71—21no—
207C22×Dic71—21no—
208C22×Dic71—21no—
209C22×Dic71—24no—
210C22×Dic71—82no—
211C2×C4×D71—24no—
212C2×C4×D71—44no—
213#11765855—44no—
214#11765855—44no—
215#11765852—44no—
216#11765852—44no—
217#11765849—44no—
218C2×C71⋊C8—22no—
219C2×C71⋊C8—22no—
220C2×C71⋊C8—22no—
221C2×C71⋊C8—22no—
222C2×C71⋊C8—44no—
223C2×C71⋊C8C2412yes—
224C2×C71⋊C8C2412yes—
225C2×C71⋊C8C2412yes—
226C2×C71⋊C8C2412yes—
227C4⋊Dic71—24no—
228C4⋊Dic71—21no—
229C4⋊Dic71—21no—
230C4⋊Dic71C2412yes—
231C4⋊Dic71C2412yes—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234C22⋊Dic71—24no—
235C22⋊Dic71—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238C24×C71C2×D411yescharacteristic
239C24×C71C2×D411yescharacteristic
240C24×C71C2×D411yescharacteristic
241#41×C71—48no—
242#41×C71—44no—
243#41×C71—44no—
244C2×Q8×C71—21no—
245C2×Q8×C71—21no—
246C2×Q8×C71—24no—
247C2×Q8×C71—22no—
248C2×Q8×C71—22no—
249C2×Q8×C71—22no—
250C2×Q8×C71—22no—
251C2×Q8×C71—42no—
252C2×Q8×C71—44no—
253C2×Q8×C71—44no—
254C2×Q8×C71—44no—
255C2×Q8×C71—48no—
256C2×Q8×C71C2×D414yes—
257C2×Q8×C71C2412yes—
258C2×Q8×C71C2412yes—
259C2×D4×C71—42no—
260C2×D4×C71—42no—
261C2×D4×C71—42no—
262C2×D4×C71C2×D414yes—
263C2×D4×C71C2×D414yes—
264C2×D4×C71C2×D414yes—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71—21no—
275C22×C4×C71—24no—
276C22×C4×C71—44no—
277C22×C4×C71C2×D411yescharacteristic
278C22×C4×C71C2×D412yes—
279C22×C4×C71C2×D411yescharacteristic
280C22×C4×C71C2×D411yescharacteristic
281C22×C4×C71C2×D412yes—
282C22×C4×C71C2×D412yes—
283C22×C4×C71C2412yes—
284C22×C4×C71C2412yes—
285C22×C4×C71C2412yes—
286C22×C4×C71C2411yescharacteristic
287C4⋊C4×C71—24no—
288C4⋊C4×C71—24no—
289C4⋊C4×C71—24no—
290C4⋊C4×C71—24no—
291C4⋊C4×C71—21no—
292C4⋊C4×C71—21no—
293C4⋊C4×C71C2412yes—
294C4⋊C4×C71C2412yes—
295C22⋊C4×C71—24no—
296C22⋊C4×C71—24no—
297C22⋊C4×C71—24no—
298C22⋊C4×C71—24no—
299C22⋊C4×C71—24no—
300C42×C71—24no—
301C23×C71—22no—
302C23×C71—22no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71C22×D412yes—
311C23×C71C22×D412yes—
312C23×C71C22×D412yes—
313C23×C71C22×D411yescharacteristic
314C22×D71—22no—
315C22×D71—42no—
316C22×D71—42no—
317C22×D71—42no—
318Q8×C71—22no—
319Q8×C71—22no—
320Q8×C71—22no—
321Q8×C71—22no—
322Q8×C71—44no—
323Q8×C71—48no—
324Q8×C71—42no—
325Q8×C71—42no—
326D4×C71—44no—
327D4×C71—44no—
328D4×C71—44no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—24no—
333C2×C4×C71—24no—
334C2×C4×C71—24no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
337C2×C4×C71—22no—
338C2×C4×C71—22no—
339C2×C4×C71—22no—
340C2×C4×C71—22no—
341C2×C4×C71—22no—
342C2×C4×C71—22no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—48no—
346C2×C4×C71—42no—
347C2×C4×C71—42no—
348C2×C4×C71—42no—
349C2×C4×C71—42no—
350C2×C4×C71C22×D412yes—
351C2×C4×C71C22×D412yes—
352C2×C4×C71C22×D412yes—
353C2×C4×C71C22×D411yescharacteristic
354C2×C4×C71H(5,𝔽2)12yes—
355C2×C4×C71H(5,𝔽2)12yes—
356C2×C4×C71C2511yescharacteristic
357C22⋊D71—48no—
358C22⋊D71—84no—
359C22⋊D71—84no—
360C2×Dic71—22no—
361C2×Dic71—22no—
362C2×Dic71—22no—
363C2×Dic71—42no—
364C2×Dic71—42no—
365C2×Dic71—42no—
366C2×Dic71—84no—
367D284—22no—
368D284—22no—
369D284—42no—
370C4×D71—48no—
371Dic142—22no—
372Dic142—22no—
373Dic142—42no—
374C71⋊C8—22no—
375C71⋊C8—22no—
376C71⋊C8—22no—
377C71⋊C8—22no—
378C22×C71—22no—
379C22×C71—22no—
380C22×C71—22no—
381C22×C71—22no—
382C22×C71—22no—
383C22×C71—22no—
384C22×C71—22no—
385C22×C71—22no—
386C22×C71—22no—
387C22×C71—44no—
388C22×C71—44no—
389C22×C71—44no—
390C22×C71#53412yes—
391C22×C71#57712yes—
392C22×C71#57812yes—
393C22×C71C23×D411yescharacteristic
394C2×D71—42no—
395C2×D71—42no—
396C2×D71—42no—
397C2×D71—84no—
398C4×C71—22no—
399C4×C71—22no—
400C4×C71—22no—
401C4×C71—42no—
402C4×C71—42no—
403C4×C71—42no—
404C4×C71—42no—
405C4×C71#53412yes—
406C4×C71C2×H(5,𝔽2)11yescharacteristic
407C4×C71C2×H(5,𝔽2)11yescharacteristic
408Dic71—42no—
409Dic71—42no—
410Dic71—42no—
411C2×#3201—711nomaximal, Sylow
412C2×C71—42no—
413C2×C71—42no—
414C2×C71—42no—
415C2×C71#320114yescomplemented
416C2×C71C2×#53411yescharacteristic
417C2×C71C2×#57711yescharacteristic
418C2×C71C2×#57811yescharacteristic
419D71—82no—
420C2×#537—711no—
421C2×#536D7111yescharacteristic, complemented
422#3201—7116no—
423C2×#484—711no—
424C2×#485—711no—
425C2×#482—711no—
426C2×#483—711no—
427C2×#470—711no—
428C2×#468—711no—
429C2×#467—711no—
430C2×#465—711no—
431C2×#452—711no—
432C2×#452—711no—
433C2×#451—711no—
434C2×#448—711no—
435C2×#408—711no—
436C71C2×#320111yescharacteristic, complemented, Sylow
437C22×#41—711no—
438C22×#41C2×D7111yescharacteristic
439C23×Q8C2×D7111yescharacteristic
440C22×Q16—711no—
441C22×Q16—711no—
442C22×SD16—711no—
443C22×SD16—711no—
444C22×M16—711no—
445C23×C8—711no—
446#537—718no—
447#537—1424no—
448#536—24no—
449#536C2×D7118yescomplemented
450C2×C4⋊Q8—21no—
451C2×#124—21no—
452C2×#123—21no—
453C2×#123—21no—
454C2×C22⋊Q8—711no—
455C2×C22⋊Q8—711no—
456C2×C22⋊Q8—1421no—
457C2×C22⋊Q8C2×D7111yescharacteristic
458C2×C22⋊Q8C2×D7111yescharacteristic
459C2×C22⋊Q8C2×D7111yescharacteristic
460C2×C22⋊Q8C2×D7111yescharacteristic
461C2×#121—711no—
462C2×#121—711no—
463C2×#121—1421no—
464C2×#121—1421no—
465C2×#121—1421no—
466C2×#117C2×D7111yescharacteristic
467C22×C4⋊C4—711no—
468#485—718no—
469#484—718no—
470#483—718no—
471#482—718no—
472#470—718no—
473#468—718no—
474#467—718no—
475#465—718no—
476#452—718no—
477#452—718no—
478#451—718no—
479#448—718no—
480C2×#107—711no—
481C2×#107—711no—
482C2×#106—711no—
483C2×#106—711no—
484C2×#103—711no—
485C2×#103—711no—
486C2×#103—711no—
487C2×#103—711no—
488C2×#103—711no—
489C2×#103—711no—
490C2×#102—711no—
491C2×#102—711no—
492#408—718no—
493C2×C22⋊C8—711no—
494C2×C22⋊C8—711no—
495C2×C22⋊C8—711no—
496C2×C22⋊C8—711no—
497C2×#41—42no—
498C2×#41—42no—
499C2×#41—2842no—
500C2×#41—2842no—
501C2×#41—714no—
502C2×#41—1422no—
503C2×#41C22⋊D7114yes—
504C2×#41C22×D7114yes—
505C22×Q8—21no—
506C22×Q8—22no—
507C22×Q8—42no—
508C22×Q8—42no—
509C22×Q8—711no—
510C22×Q8C22⋊D7111yescharacteristic
511C22×Q8C22×D7111yescharacteristic
512C22×Q8C22×D7111yescharacteristic
513C22×Q8C22×D7114yes—
514C22×D4—711no—
515C22×D4—1421no—
516C22×D4—1421no—
517C22×D4—1421no—
518C22×D4C22⋊D7111yescharacteristic
519C22×D4C22⋊D7111yescharacteristic
520C22×D4C22⋊D7111yescharacteristic
521C23×C4—21no—
522C23×C4—1421no—
523C23×C4—1421no—
524C23×C4C22×D7111yescharacteristic
525C23×C4C22×D7111yescharacteristic
526C23×C4C22×D7111yescharacteristic
527C2×Q16—2842no—
528C2×Q16—2842no—
529C2×Q16—714no—
530C2×Q16—714no—
531C2×SD16—2842no—
532C2×SD16—2842no—
533C2×SD16—714no—
534C2×SD16—714no—
535C2×M16—2842no—
536C2×M16—714no—
537C22×C8—2842no—
538C22×C8—714no—
539C22×C8—711no—
540C22×C8—711no—
541C22×C8—711no—
542C22×C8—711no—
543C4⋊Q8—28no—
544#124—28no—
545#123—28no—
546#123—28no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—714no—
552C22⋊Q8—714no—
553C22⋊Q8—1428no—
554C22⋊Q8—1422no—
555C22⋊Q8—1422no—
556C22⋊Q8C22×D7114yes—
557C22⋊Q8C22×D7114yes—
558C22⋊Q8C22×D7114yes—
559C22⋊Q8C22×D7114yes—
560#121—714no—
561#121—714no—
562#121—1428no—
563#121—1428no—
564#121—1428no—
565#121—1422no—
566#121—1422no—
567#117—22no—
568#117C22×D7114yes—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—711no—
574C2×C4⋊C4—711no—
575C2×C4⋊C4—714no—
576C2×C4⋊C4—1421no—
577C2×C4⋊C4—1422no—
578C2×C4⋊C4—1421no—
579C2×C4⋊C4—1421no—
580C2×C4⋊C4C22×D7111yescharacteristic
581C2×C4⋊C4C22×D7111yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—1421no—
588C2×C22⋊C4—1421no—
589C2×C22⋊C4—1421no—
590C2×C22⋊C4—1421no—
591C2×C42—21no—
592#107—714no—
593#107—714no—
594#106—714no—
595#106—714no—
596#103—714no—
597#103—714no—
598#103—714no—
599#103—714no—
600#103—714no—
601#103—714no—
602#102—714no—
603#102—714no—
604C22⋊C8—714no—
605C22⋊C8—714no—
606C22⋊C8—714no—
607C22⋊C8—714no—
608C24—1421no—
609C24C2×C22⋊D7111yescharacteristic
610C24C2×C22⋊D7111yescharacteristic
611C24C2×C22⋊D7111yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—2848no—
616#41—2844no—
617#41—2844no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—24no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—42no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—48no—
630C2×Q8—712no—
631C2×Q8—1422no—
632C2×Q8—1422no—
633C2×Q8—1421no—
634C2×Q8C2×C22⋊D7114yes—
635C2×Q8C23×D7112yes—
636C2×Q8C23×D7112yes—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—2844no—
641C2×D4—5682no—
642C2×D4—5682no—
643C2×D4—712no—
644C2×D4—1424no—
645C2×D4—1424no—
646C2×D4—1424no—
647C2×D4—1421no—
648C2×D4—1422no—
649C2×D4—1422no—
650C2×D4C2×C22⋊D7114yes—
651C2×D4C2×C22⋊D7114yes—
652C2×D4C2×C22⋊D7114yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—44no—
665C22×C4—2844no—
666C22×C4—5682no—
667C22×C4—1421no—
668C22×C4—1421no—
669C22×C4—1421no—
670C22×C4—1424no—
671C22×C4—1424no—
672C22×C4C2×C22⋊D7112yes—
673C22×C4C2×C22⋊D7112yes—
674C22×C4C2×C22⋊D7112yes—
675C22×C4C2×C22⋊D7111yescharacteristic
676C22×C4C2×C22⋊D7111yescharacteristic
677C22×C4C2×C22⋊D7111yescharacteristic
678C22×C4C23×D7112yes—
679C22×C4C23×D7112yes—
680C22×C4C23×D7112yes—
681C22×C4C23×D7111yescharacteristic
682Q16—2844no—
683Q16—2844no—
684SD16—2844no—
685SD16—2844no—
686M16—2844no—
687C2×C8—2844no—
688C2×C8—712no—
689C2×C8—712no—
690C2×C8—712no—
691C2×C8—712no—
692C2×C8—1422no—
693C2×C8—1422no—
694C2×C8—1422no—
695C2×C8—1422no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—712no—
703C4⋊C4—712no—
704C4⋊C4—1424no—
705C4⋊C4—1424no—
706C4⋊C4—1424no—
707C4⋊C4—1421no—
708C4⋊C4—1421no—
709C4⋊C4C23×D7112yes—
710C4⋊C4C23×D7112yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—1424no—
717C22⋊C4—1424no—
718C22⋊C4—1424no—
719C22⋊C4—1424no—
720C42—24no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—2842no—
731C23—2842no—
732C23—2842no—
733C23—1422no—
734C23C22×C22⋊D7112yes—
735C23C22×C22⋊D7112yes—
736C23C22×C22⋊D7112yes—
737C23C22×C22⋊D7111yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—44no—
743Q8—48no—
744Q8—42no—
745Q8—42no—
746Q8—2842no—
747Q8—1422no—
748Q8—1422no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—2848no—
753D4—2842no—
754D4—5684no—
755D4—5684no—
756D4—1422no—
757D4—1422no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—2848no—
780C2×C4—2842no—
781C2×C4—2842no—
782C2×C4—2842no—
783C2×C4—5684no—
784C2×C4—1422no—
785C2×C4—1422no—
786C2×C4—1422no—
787C2×C4C22×C22⋊D7112yes—
788C2×C4C22×C22⋊D7112yes—
789C2×C4C22×C22⋊D7112yes—
790C2×C4C22×C22⋊D7111yescharacteristic
791C2×C4#1455617312yes—
792C2×C4#1455617312yes—
793C2×C4C24×D7111yescharacteristic
794C8—1422no—
795C8—1422no—
796C8—1422no—
797C8—1422no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—2842no—
811C22—2842no—
812C22—2842no—
813C22—5684no—
814C22#1798655812yes—
815C22#1798680712yes—
816C22#1798681412yes—
817C22C23×C22⋊D7111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—2842no—
826C4—2842no—
827C4—2842no—
828C4#1798655812yes—
829C4C2×#1455617311yescharacteristic
830C4C2×#1455617311yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—5682no—
835C2#2259922214yesdirect product factor
836C2C2×#1798655811yescharacteristic
837C2C2×#1798680711yescharacteristic
838C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#536×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986577C2
hypercenterC2×#536D71
hypocenterC71C2×#3201
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. #22599222C2direct (N × H)
3. C2×#17986332C2semidirect
4. C2×#17986340C2semidirect
5. C2×#17986323C2semidirect
6. C2×#17986327C2semidirect
7. C2×#17986255C2semidirect
8. C2×#17986247C2semidirect
9. C2×#17986238C2semidirect
10. C2×#17986230C2semidirect
11. C2×#17986159C2semidirect
12. C2×#17986159C2semidirect
13. C2×#17986155C2semidirect
14. C2×#17986138C2semidirect
15. C2×#17985966C2semidirect
16. C2×#536×C71C2semidirect
35. #17986340C22semidirect
36. #17986332C22semidirect
37. #17986327C22semidirect
38. #17986323C22semidirect
39. #17986255C22semidirect
40. #17986247C22semidirect
41. #17986238C22semidirect
42. #17986230C22semidirect
43. #17986159C22semidirect
44. #17986159C22semidirect
45. #17986155C22semidirect
46. #17986138C22semidirect
59. #17985966C22semidirect
67. #536×C71C22semidirect
415. C2×C71#3201semidirect
421. C2×#536D71semidirect
436. C71C2×#3201semidirect
449. #536C2×D71semidirect
835. C2#22599222direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865772
#225992222
C2×#179863322
C2×#179863402
C2×#179863232
C2×#179863272
C2×#179862552
C2×#179862472
C2×#179862382
C2×#179862302
C2×#179861592
C2×#179861552
C2×#179861382
C2×#179859662
C2×#536×C712
C2×#320171