Finite Group Databasebeta

← C2×#22599449 #32868847

Subgroups — C2×#22599449 #32868847

Order 18176.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986620C211yesmaximal, characteristic, complemented
2#22599449C2116yesmaximal, direct product factor
3C2×#17986391C211yesmaximal, characteristic, complemented
4C2×#17986381C211yesmaximal, characteristic, complemented
5C2×#17986358C211yesmaximal, characteristic, complemented
6C2×#17986349C211yesmaximal, characteristic, complemented
7C2×#17986218C211yesmaximal, characteristic, complemented
8C2×#17986206C211yesmaximal, characteristic, complemented
9C2×#17986211C211yesmaximal, characteristic, complemented
10C2×#17986201C211yesmaximal, characteristic, complemented
11C2×#17986161C211yesmaximal, characteristic, complemented
12C2×#17986144C211yesmaximal, characteristic
13C2×#17986155C211yesmaximal, characteristic, complemented
14C2×#17986138C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#536×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765855C2211yescharacteristic
20C22×#11765853C2211yescharacteristic
21C22×#11765852C2211yescharacteristic
22C22×#11765852C2211yescharacteristic
23C22×#11765852C2211yescharacteristic
24C22×#11765850C2211yescharacteristic
25#17986620—24no—
26#17986620C2218yescomplemented
27C2×#14556128C2211yescharacteristic
28C2×#14556123—21no—
29C2×#14556116C2211yescharacteristic
30C2×#14556114—21no—
31C2×#14556110—21no—
32C2×#14556107C2211yescharacteristic
33C2×#14556106—21no—
34C2×#14556102C2211yescharacteristic
35C2×C4×Dic142C2211yescharacteristic
36C2×C4×D284C2211yescharacteristic
37#17986391C2218yescomplemented
38#17986381C2218yescomplemented
39#17986358C2218yescomplemented
40#17986349C2218yescomplemented
41#17986218C2218yescomplemented
42#17986211C2218yescomplemented
43#17986206C2218yescomplemented
44#17986201C2218yescomplemented
45#17986161C2218yescomplemented
46#17986155C2218yescomplemented
47#17986144C2218yes—
48#17986138C2218yescomplemented
49#17986060C2218yescomplemented
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65C23×Q8×C71C2211yescharacteristic
66#536×C71—24no—
67#536×C71C2218yescomplemented
68C2×C4⋊Q8×C71C2211yescharacteristic
69C2×C4⋊Q8×C71C2211yescharacteristic
70C2×#124×C71C2211yescharacteristic
71C2×#124×C71C2211yescharacteristic
72C2×#123×C71—21no—
73C2×#123×C71—21no—
74C2×C22⋊Q8×C71—21no—
75C2×C22⋊Q8×C71—21no—
76C2×#117×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C2×#11765855—42no—
83C2×#11765855—42no—
84C2×#11765855—42no—
85C2×#11765855C2314yes—
86C2×#11765855C2314yes—
87C2×#11765855C2314yes—
88C2×#11765853—42no—
89C2×#11765853C2314yes—
90C2×#11765852—42no—
91C2×#11765852—42no—
92C2×#11765852—42no—
93C2×#11765852C2314yes—
94C2×#11765852C2314yes—
95C2×#11765852C2314yes—
96C2×#11765850—42no—
97C2×#11765850C2314yes—
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102#14556128—22no—
103#14556128C2314yes—
104#14556123—28no—
105#14556116—22no—
106#14556116C2314yes—
107#14556114—28no—
108#14556110—28no—
109#14556107—22no—
110#14556107C2314yes—
111#14556106—28no—
112#14556102—22no—
113#14556102C2314yes—
114C4×Dic142—22no—
115C4×Dic142C2314yes—
116C4×D284—22no—
117C4×D284C2314yes—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×Dic71⋊C4—21no—
122C2×Dic71⋊C4—21no—
123C2×C22⋊Dic71—21no—
124C2×(C2×D71)⋊C4—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×(C2×D71)⋊C4—21no—
127C2×(C2×D71)⋊C4—21no—
128C2×C4×Dic71—21no—
129C4⋊(C71⋊C8)C2314yes—
130C4⋊(C71⋊C8)C2314yes—
131#14556052C2314yes—
132#14556052C2314yes—
133#14556052C2314yes—
134#14556052C2314yes—
135#14556052C2314yes—
136#14556052C2314yes—
137#14556049C2314yes—
138#14556049C2314yes—
139C22⋊(C71⋊C8)C2314yes—
140C22⋊(C71⋊C8)C2314yes—
141#14556039C2314yes—
142C4×C71⋊C8C2314yes—
143C2×#41×C71—22no—
144C2×#41×C71—42no—
145C2×#41×C71—42no—
146C2×#41×C71C2314yes—
147C22×Q8×C71—21no—
148C22×Q8×C71—22no—
149C22×Q8×C71—42no—
150C22×Q8×C71—42no—
151C22×Q8×C71C2311yescharacteristic
152C22×Q8×C71C2311yescharacteristic
153C22×Q8×C71C2311yescharacteristic
154C22×Q8×C71C2314yes—
155C22×D4×C71—21no—
156C22×D4×C71C2311yescharacteristic
157C23×C4×C71—21no—
158C23×C4×C71—21no—
159C23×C4×C71C2311yescharacteristic
160C4⋊Q8×C71—22no—
161C4⋊Q8×C71—22no—
162C4⋊Q8×C71C2314yes—
163C4⋊Q8×C71C2314yes—
164#124×C71—22no—
165#124×C71—22no—
166#124×C71C2314yes—
167#124×C71C2314yes—
168#123×C71—28no—
169#123×C71—28no—
170C22⋊Q8×C71—28no—
171C22⋊Q8×C71—28no—
172#117×C71D414yes—
173#117×C71C2314yes—
174C2×C4⋊C4×C71—21no—
175C2×C4⋊C4×C71—21no—
176C2×C4⋊C4×C71—21no—
177C2×C4⋊C4×C71—21no—
178C2×C4⋊C4×C71D411yescharacteristic
179C2×C4⋊C4×C71D411yescharacteristic
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71—21no—
182C2×C22⋊C4×C71—21no—
183C2×C22⋊C4×C71—21no—
184C2×C22⋊C4×C71D411yescharacteristic
185C2×C22⋊C4×C71D411yescharacteristic
186C2×C42×C71C2311yescharacteristic
187C2×C42×C71C2311yescharacteristic
188C23×D71—21no—
189C2×Dic142—22no—
190C2×Dic142—22no—
191C2×Dic142—21no—
192C2×Dic142—24no—
193C2×Dic142—82no—
194C2×Dic142C2412yes—
195C2×D284—22no—
196C2×D284—22no—
197C2×D284—21no—
198C2×D284C2412yes—
199C2×C22⋊D71—24no—
200C2×C22⋊D71—82no—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—21no—
204C2×C4×D71—24no—
205C2×C4×D71—82no—
206#11765855—44no—
207#11765855—44no—
208#11765855—44no—
209#11765853—44no—
210#11765852—44no—
211#11765852—44no—
212#11765852—44no—
213#11765850—44no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8—22no—
216C2×C71⋊C8—22no—
217C2×C71⋊C8—22no—
218C2×C71⋊C8C2412yes—
219C2×C71⋊C8C2412yes—
220C2×C71⋊C8C2412yes—
221C2×C71⋊C8C2412yes—
222C4⋊Dic71—24no—
223C4⋊Dic71—21no—
224C4⋊Dic71—21no—
225C4⋊Dic71C2412yes—
226C4⋊Dic71C2412yes—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229C22⋊Dic71—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4—24no—
234C4×Dic71—24no—
235C24×C71—21no—
236C24×C71C2×D411yescharacteristic
237#41×C71—44no—
238#41×C71—44no—
239#41×C71—48no—
240C2×Q8×C71—24no—
241C2×Q8×C71—21no—
242C2×Q8×C71—21no—
243C2×Q8×C71—21no—
244C2×Q8×C71—22no—
245C2×Q8×C71—22no—
246C2×Q8×C71—22no—
247C2×Q8×C71—22no—
248C2×Q8×C71—22no—
249C2×Q8×C71—22no—
250C2×Q8×C71—44no—
251C2×Q8×C71—44no—
252C2×Q8×C71—44no—
253C2×Q8×C71—48no—
254C2×Q8×C71C2412yes—
255C2×Q8×C71C2412yes—
256C2×Q8×C71C2412yes—
257C2×D4×C71—24no—
258C2×D4×C71—21no—
259C2×D4×C71—22no—
260C2×D4×C71—22no—
261C2×D4×C71—44no—
262C2×D4×C71C2412yes—
263C22×C4×C71—22no—
264C22×C4×C71—22no—
265C22×C4×C71—21no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—24no—
269C22×C4×C71—24no—
270C22×C4×C71—44no—
271C22×C4×C71—44no—
272C22×C4×C71C2×D411yescharacteristic
273C22×C4×C71C2×D411yescharacteristic
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2×D411yescharacteristic
277C22×C4×C71C2×D412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2411yescharacteristic
280C4⋊C4×C71—24no—
281C4⋊C4×C71—24no—
282C4⋊C4×C71—24no—
283C4⋊C4×C71—24no—
284C4⋊C4×C71C2×D414yes—
285C4⋊C4×C71C2×D414yes—
286C22⋊C4×C71—24no—
287C22⋊C4×C71—24no—
288C22⋊C4×C71—24no—
289C22⋊C4×C71—24no—
290C22⋊C4×C71C2×D414yes—
291C22⋊C4×C71C2×D414yes—
292C42×C71C2×D412yes—
293C42×C71C2×D412yes—
294C42×C71C2412yes—
295C42×C71C2412yes—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—22no—
300C23×C71—42no—
301C23×C71—42no—
302C23×C71—42no—
303C23×C71C22×D412yes—
304C23×C71C22×D411yescharacteristic
305C22×D71—22no—
306C22×D71—42no—
307C22×D71—42no—
308C22×D71—42no—
309Q8×C71—22no—
310Q8×C71—22no—
311Q8×C71—22no—
312Q8×C71—22no—
313Q8×C71—22no—
314Q8×C71—22no—
315Q8×C71—48no—
316Q8×C71—42no—
317Q8×C71—42no—
318Q8×C71—42no—
319D4×C71—22no—
320D4×C71—22no—
321D4×C71—48no—
322D4×C71—42no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—24no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—48no—
335C2×C4×C71—48no—
336C2×C4×C71—42no—
337C2×C4×C71—42no—
338C2×C4×C71—42no—
339C2×C4×C71C22×D412yes—
340C2×C4×C71C22×D412yes—
341C2×C4×C71C22×D412yes—
342C2×C4×C71C22×D412yes—
343C2×C4×C71C22×D412yes—
344C2×C4×C71C22×D411yescharacteristic
345C2×C4×C71H(5,𝔽2)12yes—
346C2×C4×C71H(5,𝔽2)12yes—
347C2×C4×C71C2511yescharacteristic
348C22⋊D71—84no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—42no—
353C2×Dic71—42no—
354C2×Dic71—42no—
355D284—22no—
356D284—22no—
357D284—42no—
358C4×D71—84no—
359Dic142—22no—
360Dic142—22no—
361Dic142—42no—
362Dic142—84no—
363C71⋊C8—22no—
364C71⋊C8—22no—
365C71⋊C8—22no—
366C71⋊C8—22no—
367C22×C71—22no—
368C22×C71—22no—
369C22×C71—22no—
370C22×C71—44no—
371C22×C71—42no—
372C22×C71—42no—
373C22×C71—42no—
374C22×C71—84no—
375C22×C71#53512yes—
376C22×C71#57712yes—
377C22×C71#57812yes—
378C22×C71C23×D411yescharacteristic
379C2×D71—42no—
380C2×D71—42no—
381C2×D71—42no—
382C2×D71—84no—
383C4×C71—22no—
384C4×C71—22no—
385C4×C71—22no—
386C4×C71—22no—
387C4×C71—22no—
388C4×C71—42no—
389C4×C71—42no—
390C4×C71—42no—
391C4×C71#53512yes—
392C4×C71C2×H(5,𝔽2)11yescharacteristic
393C4×C71C2×H(5,𝔽2)11yescharacteristic
394Dic71—42no—
395Dic71—42no—
396Dic71—42no—
397C2×#3225—711nomaximal, Sylow
398C2×C71—42no—
399C2×C71—82no—
400C2×C71#322514yescomplemented
401C2×C71C2×#53511yescharacteristic
402C2×C71C2×#57711yescharacteristic
403C2×C71C2×#57811yescharacteristic
404D71—82no—
405C2×#542—711no—
406C2×#536D7111yescharacteristic, complemented
407#3225—7116no—
408C2×#497—711no—
409C2×#495—711no—
410C2×#489—711no—
411C2×#487—711no—
412C2×#464—711no—
413C2×#462—711no—
414C2×#463—711no—
415C2×#461—711no—
416C2×#452—711no—
417C2×#449—711no—
418C2×#451—711no—
419C2×#448—711no—
420C2×#433—711no—
421C71C2×#322511yescharacteristic, complemented, Sylow
422C22×#41C2×D7111yescharacteristic
423C23×Q8C2×D7111yescharacteristic
424C22×Q16—711no—
425C22×Q16—711no—
426C22×Q16—711no—
427C22×SD16—711no—
428C22×SD16—711no—
429C22×SD16—711no—
430C22×SD16—711no—
431C22×D8—711no—
432#542—718no—
433#542—1424no—
434#536—24no—
435#536C2×D7118yescomplemented
436C2×C4⋊Q8—711no—
437C2×C4⋊Q8C2×D7111yescharacteristic
438C2×C4⋊Q8C2×D7111yescharacteristic
439C2×#126—1421no—
440C2×#124—711no—
441C2×#124—1421no—
442C2×#124C2×D7111yescharacteristic
443C2×#124C2×D7111yescharacteristic
444C2×#123—21no—
445C2×#123—21no—
446C2×#123—1421no—
447C2×C22⋊Q8—21no—
448C2×C22⋊Q8—21no—
449C2×C22⋊Q8—711no—
450C2×C22⋊Q8—1421no—
451C2×#121—711no—
452C2×C4×Q8—711no—
453C2×C4×D4—711no—
454C2×#117C2×D7111yescharacteristic
455#497—718no—
456#495—718no—
457#489—718no—
458#487—718no—
459#464—718no—
460#463—718no—
461#462—718no—
462#461—718no—
463#452—718no—
464#451—718no—
465#449—718no—
466#448—718no—
467#433—718no—
468C2×C4⋊C8—711no—
469C2×C4⋊C8—711no—
470C2×#103—711no—
471C2×#103—711no—
472C2×#103—711no—
473C2×#103—711no—
474C2×#103—711no—
475C2×#103—711no—
476C2×#102—711no—
477C2×#102—711no—
478C2×C22⋊C8—711no—
479C2×C22⋊C8—711no—
480C2×#97—711no—
481C2×C4×C8—711no—
482C2×#41—22no—
483C2×#41—42no—
484C2×#41—42no—
485C2×#41C22×D7114yes—
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—42no—
489C22×Q8—42no—
490C22×Q8—711no—
491C22×Q8—1421no—
492C22×Q8C22×D7111yescharacteristic
493C22×Q8C22×D7111yescharacteristic
494C22×Q8C22×D7111yescharacteristic
495C22×Q8C22×D7114yes—
496C22×D4—21no—
497C22×D4—711no—
498C22×D4—1421no—
499C22×D4C22×D7111yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—1421no—
503C23×C4C22×D7111yescharacteristic
504C2×Q16—2842no—
505C2×Q16—2842no—
506C2×Q16—2842no—
507C2×Q16—714no—
508C2×Q16—714no—
509C2×Q16—714no—
510C2×SD16—2842no—
511C2×SD16—2842no—
512C2×SD16—2842no—
513C2×SD16—2842no—
514C2×SD16—714no—
515C2×SD16—714no—
516C2×SD16—714no—
517C2×SD16—714no—
518C2×D8—2842no—
519C2×D8—714no—
520C22×C8—711no—
521C22×C8—711no—
522C22×C8—711no—
523C22×C8—711no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—714no—
527C4⋊Q8—1422no—
528C4⋊Q8C22×D7114yes—
529C4⋊Q8C22×D7114yes—
530#126—1428no—
531#124—22no—
532#124—22no—
533#124—714no—
534#124—1428no—
535#124—1422no—
536#124C22×D7114yes—
537#124C22×D7114yes—
538#123—28no—
539#123—28no—
540#123—1428no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543C22⋊Q8—714no—
544C22⋊Q8—1422no—
545C22⋊Q8—1428no—
546#121—714no—
547#121—1422no—
548C4×Q8—714no—
549C4×Q8—1422no—
550C4×D4—714no—
551C4×D4—1422no—
552#117C22⋊D7114yes—
553#117C22×D7114yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—711no—
559C2×C4⋊C4—711no—
560C2×C4⋊C4—1421no—
561C2×C4⋊C4—1421no—
562C2×C4⋊C4—1421no—
563C2×C4⋊C4C22⋊D7111yescharacteristic
564C2×C4⋊C4C22⋊D7111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—1421no—
570C2×C22⋊C4—1421no—
571C2×C22⋊C4—1421no—
572C2×C22⋊C4—1421no—
573C2×C22⋊C4—1421no—
574C2×C22⋊C4C22⋊D7111yescharacteristic
575C2×C22⋊C4C22⋊D7111yescharacteristic
576C2×C42—1421no—
577C2×C42C22×D7111yescharacteristic
578C2×C42C22×D7111yescharacteristic
579C4⋊C8—714no—
580C4⋊C8—714no—
581#103—714no—
582#103—714no—
583#103—714no—
584#103—714no—
585#103—714no—
586#103—714no—
587#102—714no—
588#102—714no—
589C22⋊C8—714no—
590C22⋊C8—714no—
591#97—714no—
592C4×C8—714no—
593C24—21no—
594C24—1421no—
595C24C2×C22⋊D7111yescharacteristic
596#41—44no—
597#41—44no—
598#41—48no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—44no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—48no—
613C2×Q8—5682no—
614C2×Q8—712no—
615C2×Q8—1422no—
616C2×Q8—1422no—
617C2×Q8—1421no—
618C2×Q8—1424no—
619C2×Q8C23×D7112yes—
620C2×Q8C23×D7112yes—
621C2×Q8C23×D7112yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—5682no—
628C2×D4—712no—
629C2×D4—1424no—
630C2×D4—1421no—
631C2×D4—1422no—
632C2×D4—1422no—
633C2×D4C23×D7112yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—5682no—
644C22×C4—1421no—
645C22×C4—1421no—
646C22×C4—1421no—
647C22×C4—1424no—
648C22×C4C2×C22⋊D7112yes—
649C22×C4C2×C22⋊D7111yescharacteristic
650C22×C4C2×C22⋊D7111yescharacteristic
651C22×C4C2×C22⋊D7111yescharacteristic
652C22×C4C2×C22⋊D7111yescharacteristic
653C22×C4C2×C22⋊D7111yescharacteristic
654C22×C4C23×D7112yes—
655C22×C4C23×D7111yescharacteristic
656Q16—2844no—
657Q16—2844no—
658Q16—2844no—
659SD16—2844no—
660SD16—2844no—
661SD16—2844no—
662SD16—2844no—
663D8—2844no—
664C2×C8—712no—
665C2×C8—712no—
666C2×C8—712no—
667C2×C8—712no—
668C2×C8—1422no—
669C2×C8—1422no—
670C2×C8—1422no—
671C2×C8—1422no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—712no—
677C4⋊C4—712no—
678C4⋊C4—1424no—
679C4⋊C4—1424no—
680C4⋊C4—1421no—
681C4⋊C4—1421no—
682C4⋊C4—1424no—
683C4⋊C4C2×C22⋊D7114yes—
684C4⋊C4C2×C22⋊D7114yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—1424no—
690C22⋊C4—1424no—
691C22⋊C4—1424no—
692C22⋊C4—1424no—
693C22⋊C4—1424no—
694C22⋊C4C2×C22⋊D7114yes—
695C22⋊C4C2×C22⋊D7114yes—
696C42—1424no—
697C42C2×C22⋊D7112yes—
698C42C2×C22⋊D7112yes—
699C42C23×D7112yes—
700C42C23×D7112yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—2842no—
709C23—2842no—
710C23—2842no—
711C23—1422no—
712C23C22×C22⋊D7112yes—
713C23C22×C22⋊D7111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—48no—
721Q8—42no—
722Q8—42no—
723Q8—42no—
724Q8—2842no—
725Q8—5684no—
726Q8—1422no—
727Q8—1422no—
728D4—22no—
729D4—22no—
730D4—48no—
731D4—42no—
732D4—2842no—
733D4—5684no—
734D4—1422no—
735D4—1422no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—2842no—
755C2×C4—5684no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4C22×C22⋊D7112yes—
760C2×C4C22×C22⋊D7112yes—
761C2×C4C22×C22⋊D7112yes—
762C2×C4C22×C22⋊D7112yes—
763C2×C4C22×C22⋊D7112yes—
764C2×C4C22×C22⋊D7111yescharacteristic
765C2×C4#1455617312yes—
766C2×C4#1455617312yes—
767C2×C4C24×D7111yescharacteristic
768C8—1422no—
769C8—1422no—
770C8—1422no—
771C8—1422no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—2842no—
781C22—2842no—
782C22—2842no—
783C22—5684no—
784C22#1798656612yes—
785C22#1798680712yes—
786C22#1798681412yes—
787C22C23×C22⋊D7111yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—2842no—
797C4—2842no—
798C4—2842no—
799C4#1798656612yes—
800C4C2×#1455617311yescharacteristic
801C4C2×#1455617311yescharacteristic
802C2—42no—
803C2—82no—
804C2—5682no—
805C2#2259944914yesdirect product factor
806C2C2×#1798656611yescharacteristic
807C2C2×#1798680711yescharacteristic
808C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#536×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986144C2
hypercenterC2×#536D71
hypocenterC71C2×#3225
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#17986620C2semidirect
2. #22599449C2direct (N × H)
3. C2×#17986391C2semidirect
4. C2×#17986381C2semidirect
5. C2×#17986358C2semidirect
6. C2×#17986349C2semidirect
7. C2×#17986218C2semidirect
8. C2×#17986206C2semidirect
9. C2×#17986211C2semidirect
10. C2×#17986201C2semidirect
11. C2×#17986161C2semidirect
13. C2×#17986155C2semidirect
14. C2×#17986138C2semidirect
15. C2×#17986060C2semidirect
16. C2×#536×C71C2semidirect
26. #17986620C22semidirect
37. #17986391C22semidirect
38. #17986381C22semidirect
39. #17986358C22semidirect
40. #17986349C22semidirect
41. #17986218C22semidirect
42. #17986211C22semidirect
43. #17986206C22semidirect
44. #17986201C22semidirect
45. #17986161C22semidirect
46. #17986155C22semidirect
48. #17986138C22semidirect
49. #17986060C22semidirect
67. #536×C71C22semidirect
400. C2×C71#3225semidirect
406. C2×#536D71semidirect
421. C71C2×#3225semidirect
435. #536C2×D71semidirect
805. C2#22599449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
#225994492
C2×#179863912
C2×#179863812
C2×#179863582
C2×#179863492
C2×#179862182
C2×#179862062
C2×#179862112
C2×#179862012
C2×#179861612
C2×#179861442
C2×#179861552
C2×#179861382
C2×#179860602
C2×#536×C712
C2×#322571