Finite Group Databasebeta

← C2×#11741123 #14233587

Subgroups — C2×#11741123 #14233587

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#556C211yesmaximal, characteristic
2C2×#90258C211yesmaximal, characteristic, complemented
3#11741123C2116yesmaximal, direct product factor
4C2×#89862C211yesmaximal, characteristic, complemented
5C2×#89854C211yesmaximal, characteristic, complemented
6C2×#89826C211yesmaximal, characteristic
7C2×#89826C211yesmaximal, characteristic
8C2×#89827C211yesmaximal, characteristic
9C2×#89828C211yesmaximal, characteristic
10C2×#89796C211yesmaximal, characteristic, complemented
11C2×#89794C211yesmaximal, characteristic, complemented
12C2×#89793C211yesmaximal, characteristic, complemented
13C2×#89802C211yesmaximal, characteristic, complemented
14C2×C4×#1144C211yesmaximal, characteristic, complemented
15C2×#89781C211yesmaximal, characteristic
16C2×#89790C211yesmaximal, characteristic
17C7×#556—24no—
18C7×#556C2218yes—
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#126—21no—
21C2×C7×#126—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×#124C2211yescharacteristic
24C2×C7×C22⋊Q8—21no—
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117—21no—
30C2×#6507—21no—
31C22×#1144C2211yescharacteristic
32C22×#1144C2211yescharacteristic
33C22×#1142C2211yescharacteristic
34#90258—24no—
35#90258C2218yescomplemented
36C2×#6452—21no—
37C2×#6452—21no—
38C2×#6450—21no—
39C2×#6433C2211yescharacteristic
40C2×#6433C2211yescharacteristic
41C2×#6432C2211yescharacteristic
42C2×C4×Dic14C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46C2×#6409C2211yescharacteristic
47C2×#6409C2211yescharacteristic
48C2×#6409C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89862C2218yescomplemented
55#89854C2218yescomplemented
56#89828C2218yes—
57#89827C2218yes—
58#89826C2218yes—
59#89826C2218yes—
60#89802C2218yescomplemented
61C4×#1144C2218yescomplemented
62#89796C2218yescomplemented
63#89794C2218yescomplemented
64#89793C2218yescomplemented
65#89790C2218yes—
66#89781C2218yes—
67C2×#6384C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×C4⋊(C7⋊C8)C2211yescharacteristic
72C2×C4⋊(C7⋊C8)C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×#6377C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3377—71nomaximal, Sylow
78C22×C7×Q8D411yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C22×Dic14—21no—
84C22×Dic14C2311yescharacteristic
85C7×C4⋊Q8—22no—
86C7×C4⋊Q8C2314yes—
87C7×#126—28no—
88C7×#126—28no—
89C7×#124—22no—
90C7×#124—22no—
91C7×#124C2314yes—
92C7×#124C2314yes—
93C7×C22⋊Q8—28no—
94C4×C7×Q8—22no—
95C4×C7×Q8—22no—
96C4×C7×Q8D414yes—
97C4×C7×Q8C2314yes—
98C4×C7×Q8C2314yes—
99C4×C7×Q8C2314yes—
100C4×C7×D4—22no—
101C4×C7×D4C2314yes—
102C7×#117—28no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4D411yescharacteristic
108C2×C7×C4⋊C4D411yescharacteristic
109C2×C7×C4⋊C4D411yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C42×C7—21no—
117C2×C42×C7—21no—
118C2×C42×C7C2311yescharacteristic
119C2×C42×C7C2311yescharacteristic
120C2×C42×C7C2311yescharacteristic
121#6507—28no—
122C2×#1144—24no—
123C2×#1144—24no—
124C2×#1144C2314yes—
125C2×#1144C2314yes—
126C2×#1142—24no—
127C2×#1142C2314yes—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6452—28no—
147#6452—28no—
148#6450—28no—
149#6433—22no—
150#6433—22no—
151#6433C2314yes—
152#6433C2314yes—
153#6432—22no—
154#6432C2314yes—
155C4×Dic14—22no—
156C4×Dic14—22no—
157C4×Dic14—22no—
158C4×Dic14C2314yes—
159C4×Dic14C2314yes—
160C4×Dic14C2314yes—
161#6409C2314yes—
162#6409C2314yes—
163#6409C2314yes—
164#6409C2314yes—
165#6409C2314yes—
166#6409C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169#6406C2314yes—
170#6384C2314yes—
171#6382C2314yes—
172#6381C2314yes—
173#6381C2314yes—
174C4⋊(C7⋊C8)C2314yes—
175C4⋊(C7⋊C8)C2314yes—
176C4⋊(C7⋊C8)C2314yes—
177#6377C2314yes—
178#6377C2314yes—
179C4×C7⋊C8C2314yes—
180C2×#557—71no—
181C2×#556D711yescharacteristic
182#3377—716no—
183C2×#491—71no—
184C2×#489—71no—
185C2×#488—71no—
186C2×#479—71no—
187C2×#477—71no—
188C2×#478—71no—
189C2×#464—71no—
190C2×#464—71no—
191C2×#462—71no—
192C2×#446—71no—
193C2×#441—71no—
194C2×#440—71no—
195C2×C4×Q16—71no—
196C24×C7—21no—
197C2×C7×Q8—21no—
198C2×C7×Q8—21no—
199C2×C7×Q8—22no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8—42no—
204C2×C7×Q8C2×D414yes—
205C2×C7×Q8C2412yes—
206C2×C7×Q8C2412yes—
207C2×C7×D4—21no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4C2412yes—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—24no—
215C22×C4×C7—44no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2411yescharacteristic
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C2×Dic14—21no—
228C2×Dic14—22no—
229C2×Dic14—24no—
230C2×Dic14—44no—
231C2×Dic14#4114yes—
232C2×Dic14C2412yes—
233C7×C4⋊C4—24no—
234C7×C4⋊C4—24no—
235C7×C4⋊C4—24no—
236C7×C4⋊C4—24no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4C2×D414yes—
239C7×C4⋊C4C2×D414yes—
240C7×C4⋊C4C2×D414yes—
241C7×C4⋊C4C2412yes—
242C7×C22⋊C4—24no—
243C7×C22⋊C4—24no—
244C7×C22⋊C4—24no—
245C7×C22⋊C4—24no—
246C7×C22⋊C4—24no—
247C42×C7—24no—
248C42×C7—24no—
249C42×C7C2×D412yes—
250C42×C7C2×D412yes—
251C42×C7C2×D412yes—
252C42×C7C2412yes—
253C42×C7C2412yes—
254C42×C7C2412yes—
255#1144—28no—
256#1144—28no—
257#1142—28no—
258C4⋊Dic7—21no—
259C4⋊Dic7—21no—
260C4⋊Dic7—21no—
261C4⋊Dic7—24no—
262C4⋊Dic7C2412yes—
263C4⋊Dic7C2412yes—
264C4⋊Dic7C2412yes—
265Dic7⋊C4—24no—
266Dic7⋊C4—24no—
267Dic7⋊C4—24no—
268Dic7⋊C4—24no—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272C4×Dic7—24no—
273C4×Dic7—24no—
274C4×Dic7—24no—
275C2×C7⋊C8—22no—
276C2×C7⋊C8—22no—
277C2×C7⋊C8—22no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8C2412yes—
280C2×C7⋊C8C2412yes—
281C2×C7⋊C8C2412yes—
282C2×C7⋊C8C2412yes—
283C22×Q16—71no—
284C22×Q16—71no—
285C22×SD16—71no—
286#557—78no—
287#557—144no—
288#556—24no—
289#556C2×D718yes—
290C2×C4⋊Q8—71no—
291C2×C4⋊Q8—141no—
292C2×C4⋊Q8C2×D711yescharacteristic
293C2×#126—21no—
294C2×#126—21no—
295C2×#125—71no—
296C2×#125—71no—
297C2×#125—141no—
298C2×#125—141no—
299C2×#124C2×D711yescharacteristic
300C2×#124C2×D711yescharacteristic
301C2×C22⋊Q8—21no—
302C2×C4×Q8—71no—
303C2×C4×Q8—71no—
304C2×C4×Q8—71no—
305C2×C4×Q8—141no—
306C2×C4×Q8C2×D711yescharacteristic
307C2×C4×Q8C2×D711yescharacteristic
308C2×C4×Q8C2×D711yescharacteristic
309C2×C4×D4C2×D711yescharacteristic
310C2×#117—21no—
311#491—78no—
312#489—78no—
313#488—78no—
314#479—78no—
315#478—78no—
316#477—78no—
317#464—78no—
318#464—78no—
319#462—78no—
320#446—78no—
321#441—78no—
322#440—78no—
323C4×Q16—78no—
324C2×#107—71no—
325C2×#107—71no—
326C2×#106—71no—
327C2×C4⋊C8—71no—
328C2×C4⋊C8—71no—
329C2×C4⋊C8—71no—
330C2×#103—71no—
331C2×#103—71no—
332C2×#103—71no—
333C2×#103—71no—
334C2×#103—71no—
335C2×#103—71no—
336C2×#103—71no—
337C2×#102—71no—
338C2×#102—71no—
339C2×#102—71no—
340C2×#97—71no—
341C2×#97—71no—
342C2×C4×C8—71no—
343C23×C7—22no—
344C23×C7—42no—
345C23×C7—42no—
346C23×C7—42no—
347C23×C7C22×D411yescharacteristic
348C7×Q8—22no—
349C7×Q8—22no—
350C7×Q8—22no—
351C7×Q8—22no—
352C7×Q8—44no—
353C7×Q8—42no—
354C7×Q8—42no—
355C7×D4—22no—
356C7×D4—22no—
357C7×D4—42no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—48no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7C22×D412yes—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D412yes—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C2×#4112yes—
379C2×C4×C72−1+412yes—
380C2×C4×C7C2511yescharacteristic
381C2×Dic7—24no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389Dic14—24no—
390Dic14—22no—
391Dic14—48no—
392Dic14C2×#4114yes—
393C7⋊C8—22no—
394C7⋊C8—22no—
395C7⋊C8—22no—
396C7⋊C8—22no—
397C22×Q8—71no—
398C22×Q8—141no—
399C22×Q8C22⋊D711yescharacteristic
400C22×Q8C22×D711yescharacteristic
401C22×Q8C22×D711yescharacteristic
402C22×D4C22×D711yescharacteristic
403C23×C4—21no—
404C2×Q16—74no—
405C2×Q16—74no—
406C2×Q16—144no—
407C2×Q16—144no—
408C2×SD16—74no—
409C2×SD16—144no—
410C22×C8—71no—
411C22×C8—71no—
412C22×C8—71no—
413C22×C8—71no—
414C4⋊Q8—22no—
415C4⋊Q8—74no—
416C4⋊Q8—148no—
417C4⋊Q8—142no—
418C4⋊Q8C22×D714yes—
419#126—28no—
420#126—28no—
421#125—74no—
422#125—74no—
423#125—148no—
424#125—148no—
425#125—142no—
426#125—142no—
427#124—22no—
428#124—22no—
429#124C22×D714yes—
430#124C22×D714yes—
431C22⋊Q8—28no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×Q8—74no—
435C4×Q8—74no—
436C4×Q8—74no—
437C4×Q8—148no—
438C4×Q8—142no—
439C4×Q8—142no—
440C4×Q8—142no—
441C4×Q8C22⋊D714yes—
442C4×Q8C22×D714yes—
443C4×Q8C22×D714yes—
444C4×Q8C22×D714yes—
445C4×D4—22no—
446C4×D4C22×D714yes—
447#117—28no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—71no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—141no—
456C2×C4⋊C4—141no—
457C2×C4⋊C4—141no—
458C2×C4⋊C4—141no—
459C2×C4⋊C4—141no—
460C2×C4⋊C4—141no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4C22⋊D711yescharacteristic
464C2×C4⋊C4C22⋊D711yescharacteristic
465C2×C4⋊C4C22⋊D711yescharacteristic
466C2×C4⋊C4C22×D711yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—141no—
475C2×C42—141no—
476C2×C42—141no—
477C2×C42C22×D711yescharacteristic
478C2×C42C22×D711yescharacteristic
479C2×C42C22×D711yescharacteristic
480#107—74no—
481#107—74no—
482#106—74no—
483C4⋊C8—74no—
484C4⋊C8—74no—
485C4⋊C8—74no—
486#103—74no—
487#103—74no—
488#103—74no—
489#103—74no—
490#103—74no—
491#103—74no—
492#103—74no—
493#102—74no—
494#102—74no—
495#102—74no—
496#97—74no—
497#97—74no—
498C4×C8—74no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—84no—
503C22×C7#54812yes—
504C22×C7#57512yes—
505C22×C7#57812yes—
506C22×C7C23×D411yescharacteristic
507C4×C7—22no—
508C4×C7—22no—
509C4×C7—22no—
510C4×C7—22no—
511C4×C7—22no—
512C4×C7—22no—
513C4×C7—42no—
514C4×C7—42no—
515C4×C7—42no—
516C4×C7#54812yes—
517C4×C7C22×#4111yescharacteristic
518C4×C7C2×2−1+411yescharacteristic
519Dic7—24no—
520Dic7—42no—
521Dic7—42no—
522Dic7—42no—
523C24—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—42no—
531C2×Q8—74no—
532C2×Q8—72no—
533C2×Q8—142no—
534C2×Q8—141no—
535C2×Q8—144no—
536C2×Q8—284no—
537C2×Q8C2×C22⋊D714yes—
538C2×Q8C23×D712yes—
539C2×Q8C23×D712yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4C23×D712yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—44no—
549C22×C4—141no—
550C22×C4—141no—
551C22×C4—141no—
552C22×C4—141no—
553C22×C4C2×C22⋊D711yescharacteristic
554C22×C4C2×C22⋊D711yescharacteristic
555C22×C4C2×C22⋊D711yescharacteristic
556C22×C4C2×C22⋊D711yescharacteristic
557C22×C4C2×C22⋊D711yescharacteristic
558C22×C4C2×C22⋊D711yescharacteristic
559C22×C4C23×D711yescharacteristic
560Q16—148no—
561Q16—148no—
562SD16—148no—
563C2×C8—72no—
564C2×C8—72no—
565C2×C8—72no—
566C2×C8—72no—
567C2×C8—142no—
568C2×C8—142no—
569C2×C8—142no—
570C2×C8—142no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—72no—
577C4⋊C4—72no—
578C4⋊C4—72no—
579C4⋊C4—144no—
580C4⋊C4—144no—
581C4⋊C4—144no—
582C4⋊C4—144no—
583C4⋊C4—144no—
584C4⋊C4—144no—
585C4⋊C4—144no—
586C4⋊C4—141no—
587C4⋊C4—141no—
588C4⋊C4—141no—
589C4⋊C4—144no—
590C4⋊C4C2×C22⋊D714yes—
591C4⋊C4C2×C22⋊D714yes—
592C4⋊C4C2×C22⋊D714yes—
593C4⋊C4C23×D712yes—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C42—24no—
600C42—24no—
601C42—144no—
602C42—144no—
603C42—144no—
604C42C2×C22⋊D712yes—
605C42C2×C22⋊D712yes—
606C42C2×C22⋊D712yes—
607C42C23×D712yes—
608C42C23×D712yes—
609C42C23×D712yes—
610C2×C7—82no—
611C2×C7#337714yescomplemented
612C2×C7C2×#54811yescharacteristic
613C2×C7C2×#57511yescharacteristic
614C2×C7C2×#57811yescharacteristic
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C22×C22⋊D711yescharacteristic
620Q8—22no—
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—44no—
625Q8—42no—
626Q8—42no—
627Q8—74no—
628Q8—144no—
629Q8—142no—
630Q8—288no—
631D4—22no—
632D4—22no—
633D4—42no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—48no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—144no—
648C2×C4—142no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—282no—
653C2×C4—282no—
654C2×C4—282no—
655C2×C4D7×#4112yes—
656C2×C4#655412yes—
657C2×C4C22×C22⋊D712yes—
658C2×C4C22×C22⋊D712yes—
659C2×C4C22×C22⋊D712yes—
660C2×C4C22×C22⋊D712yes—
661C2×C4C22×C22⋊D712yes—
662C2×C4C22×C22⋊D712yes—
663C2×C4C22×C22⋊D711yescharacteristic
664C2×C4C24×D711yescharacteristic
665C8—142no—
666C8—142no—
667C8—142no—
668C8—142no—
669C7C2×#337711yescharacteristic, complemented, Sylow
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22#9051312yes—
675C22#9052212yes—
676C22#9052912yes—
677C22C23×C22⋊D711yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—144no—
688C4—282no—
689C4—282no—
690C4—282no—
691C4#9052212yes—
692C4C2×D7×#4111yescharacteristic
693C4C2×#655411yescharacteristic
694C2—82no—
695C2#1174112314yesdirect product factor
696C2C2×#9051311yescharacteristic
697C2C2×#9052211yescharacteristic
698C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#556C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×#556D7
hypocenterC7C2×#3377
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. C2×#90258C2semidirect
3. #11741123C2direct (N × H)
4. C2×#89862C2semidirect
5. C2×#89854C2semidirect
10. C2×#89796C2semidirect
11. C2×#89794C2semidirect
12. C2×#89793C2semidirect
13. C2×#89802C2semidirect
14. C2×C4×#1144C2semidirect
35. #90258C22semidirect
54. #89862C22semidirect
55. #89854C22semidirect
60. #89802C22semidirect
61. C4×#1144C22semidirect
62. #89796C22semidirect
63. #89794C22semidirect
64. #89793C22semidirect
611. C2×C7#3377semidirect
669. C7C2×#3377semidirect
695. C2#11741123direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5562
C2×#902582
#117411232
C2×#898622
C2×#898542
C2×#898262
C2×#898272
C2×#898282
C2×#897962
C2×#897942
C2×#897932
C2×#898022
C2×C4×#11442
C2×#897812
C2×#897902
C2×#33777