Finite Group Databasebeta

← C2×#11741145 #14233593

Subgroups — C2×#11741145 #14233593

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×#557C211yesmaximal, characteristic, complemented
2C2×#90275C211yesmaximal, characteristic
3#11741145C2116yesmaximal, direct product factor
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89861C211yesmaximal, characteristic
6C2×#89835C211yesmaximal, characteristic, complemented
7C2×#89838C211yesmaximal, characteristic
8C2×#89841C211yesmaximal, characteristic, complemented
9C2×#89840C211yesmaximal, characteristic
10C2×#89803C211yesmaximal, characteristic, complemented
11C2×#89800C211yesmaximal, characteristic
12C2×#89800C211yesmaximal, characteristic
13C2×#89798C211yesmaximal, characteristic
14C2×#89796C211yesmaximal, characteristic, complemented
15C2×#89802C211yesmaximal, characteristic, complemented
16C2×C4×#1144C211yesmaximal, characteristic, complemented
17C7×#557—24no—
18C7×#557C2218yescomplemented
19C2×C7×C4⋊Q8—21no—
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×#125—21no—
22C2×C7×#125—21no—
23C2×C7×#125C2211yescharacteristic
24C2×C7×#125C2211yescharacteristic
25C2×C4×C7×Q8—21no—
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×Q8C2211yescharacteristic
29C2×C4×C7×Q8C2211yescharacteristic
30C2×#6509—21no—
31C22×#1144C2211yescharacteristic
32C22×#1144C2211yescharacteristic
33C22×#1143C2211yescharacteristic
34#90275—24no—
35#90275C2218yes—
36C2×#6461—21no—
37C2×#6461—21no—
38C2×#6455—21no—
39C2×#6438C2211yescharacteristic
40C2×#6438C2211yescharacteristic
41C2×C4×D28C2211yescharacteristic
42C2×#6432C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46#89863C2218yescomplemented
47#89861C2218yes—
48#89841C2218yescomplemented
49#89840C2218yes—
50#89838C2218yes—
51#89835C2218yescomplemented
52#89803C2218yescomplemented
53#89802C2218yescomplemented
54C4×#1144C2218yescomplemented
55#89800C2218yes—
56#89800C2218yes—
57#89798C2218yes—
58#89796C2218yescomplemented
59C2×#6384C2211yescharacteristic
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6383C2211yescharacteristic
67C2×#6383C2211yescharacteristic
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×Q8—21no—
79C22×C7×Q8D411yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×D28C2311yescharacteristic
82C22×C4×D7—21no—
83C22×Dic14C2311yescharacteristic
84C22×Dic14C2311yescharacteristic
85C7×C4⋊Q8—28no—
86C7×C4⋊Q8—22no—
87C7×C4⋊Q8C2314yes—
88C7×#125—28no—
89C7×#125—28no—
90C7×#125—22no—
91C7×#125—22no—
92C7×#125C2314yes—
93C7×#125C2314yes—
94C4×C7×Q8—28no—
95C4×C7×Q8—22no—
96C4×C7×Q8—22no—
97C4×C7×Q8—22no—
98C4×C7×Q8D414yes—
99C4×C7×Q8C2314yes—
100C4×C7×Q8C2314yes—
101C4×C7×Q8C2314yes—
102C4×C7×Q8C2314yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4D411yescharacteristic
112C2×C7×C4⋊C4D411yescharacteristic
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C42×C7—21no—
118C2×C42×C7—21no—
119C2×C42×C7—21no—
120C2×C42×C7C2311yescharacteristic
121C2×C42×C7C2311yescharacteristic
122C2×C42×C7C2311yescharacteristic
123#6509—28no—
124C2×#1144—24no—
125C2×#1144—24no—
126C2×#1144C2314yes—
127C2×#1144C2314yes—
128C2×#1143—24no—
129C2×#1143C2314yes—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7C2311yescharacteristic
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7—21no—
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146#6461—28no—
147#6461—28no—
148#6455—28no—
149#6438—22no—
150#6438—22no—
151#6438C2314yes—
152#6438C2314yes—
153C4×D28—22no—
154C4×D28C2314yes—
155#6432—22no—
156#6432C2314yes—
157C4×Dic14—22no—
158C4×Dic14—22no—
159C4×Dic14C2314yes—
160C4×Dic14C2314yes—
161#6409C2314yes—
162#6384C2314yes—
163#6384C2314yes—
164#6384C2314yes—
165#6384C2314yes—
166#6384C2314yes—
167#6384C2314yes—
168#6383C2314yes—
169#6383C2314yes—
170#6383C2314yes—
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×#557D711yescharacteristic, complemented
181C2×#556—71no—
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—
196C23×D7—21no—
197C2×C7×Q8—21no—
198C2×C7×Q8—24no—
199C2×C7×Q8—22no—
200C2×C7×Q8—42no—
201C2×C7×Q8—44no—
202C2×C7×Q8C2×D414yes—
203C2×C7×Q8#4114yes—
204C2×C7×Q8C2412yes—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2411yescharacteristic
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C2×D28—22no—
220C2×D28—22no—
221C2×D28—21no—
222C2×D28C2412yes—
223C2×C4×D7—24no—
224C2×C4×D7—44no—
225C2×Dic14—22no—
226C2×Dic14—22no—
227C2×Dic14—22no—
228C2×Dic14—22no—
229C2×Dic14—21no—
230C2×Dic14—21no—
231C2×Dic14C2412yes—
232C2×Dic14C2412yes—
233C7×C4⋊C4—24no—
234C7×C4⋊C4—24no—
235C7×C4⋊C4—24no—
236C7×C4⋊C4—24no—
237C7×C4⋊C4—24no—
238C7×C4⋊C4—24no—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—24no—
241C7×C4⋊C4—21no—
242C7×C4⋊C4—21no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4C2×D414yes—
245C7×C4⋊C4C2×D414yes—
246C7×C4⋊C4C2×D414yes—
247C7×C4⋊C4C2412yes—
248C7×C4⋊C4C2412yes—
249C7×C4⋊C4C2412yes—
250C42×C7—24no—
251C42×C7—24no—
252C42×C7—24no—
253C42×C7C2×D412yes—
254C42×C7C2×D412yes—
255C42×C7C2×D412yes—
256C42×C7C2412yes—
257C42×C7C2412yes—
258C42×C7C2412yes—
259#1144—28no—
260#1144—28no—
261#1143—28no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267C4⋊Dic7—21no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7C2412yes—
271Dic7⋊C4—24no—
272Dic7⋊C4—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—24no—
287#557C2×D718yescomplemented
288#556—78no—
289#556—144no—
290C2×C4⋊Q8—21no—
291C2×C4⋊Q8—71no—
292C2×C4⋊Q8C2×D711yescharacteristic
293C2×#126—141no—
294C2×#126—141no—
295C2×#125—21no—
296C2×#125—21no—
297C2×#125C2×D711yescharacteristic
298C2×#125C2×D711yescharacteristic
299C2×#124—71no—
300C2×#124—71no—
301C2×C22⋊Q8—141no—
302C2×C4×Q8—21no—
303C2×C4×Q8—71no—
304C2×C4×Q8—71no—
305C2×C4×Q8C2×D711yescharacteristic
306C2×C4×Q8C2×D711yescharacteristic
307C2×C4×Q8C2×D711yescharacteristic
308C2×C4×Q8C2×D711yescharacteristic
309C2×C4×D4—71no—
310C2×#117—141no—
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×C7C22×D411yescharacteristic
344C22×D7—22no—
345C22×D7—42no—
346C22×D7—42no—
347C22×D7—42no—
348C7×Q8—24no—
349C7×Q8—22no—
350C7×Q8—44no—
351C7×Q8—48no—
352C7×Q8C2×#4114yes—
353C2×C4×C7—24no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
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—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7C22×D412yes—
368C2×C4×C7C22×D412yes—
369C2×C4×C7C22×D412yes—
370C2×C4×C7C22×D412yes—
371C2×C4×C7C22×D412yes—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D411yescharacteristic
374C2×C4×C7C2×#4112yes—
375C2×C4×C72−1+412yes—
376C2×C4×C7C2511yescharacteristic
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—42no—
381C2×Dic7—42no—
382C2×Dic7—42no—
383D28—22no—
384D28—22no—
385D28—42no—
386C4×D7—48no—
387Dic14—22no—
388Dic14—22no—
389Dic14—22no—
390Dic14—22no—
391Dic14—42no—
392Dic14—42no—
393C7⋊C8—22no—
394C7⋊C8—22no—
395C7⋊C8—22no—
396C7⋊C8—22no—
397C22×Q8—21no—
398C22×Q8—71no—
399C22×Q8—71no—
400C22×Q8C22⋊D711yescharacteristic
401C22×Q8C22×D711yescharacteristic
402C22×D4—71no—
403C23×C4—141no—
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—28no—
415C4⋊Q8—22no—
416C4⋊Q8—74no—
417C4⋊Q8—142no—
418C4⋊Q8C22×D714yes—
419#126—148no—
420#126—148no—
421#125—28no—
422#125—28no—
423#125—22no—
424#125—22no—
425#125C22×D714yes—
426#125C22×D714yes—
427#124—74no—
428#124—74no—
429#124—142no—
430#124—142no—
431C22⋊Q8—148no—
432C4×Q8—28no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—74no—
437C4×Q8—74no—
438C4×Q8—142no—
439C4×Q8—142no—
440C4×Q8C22⋊D714yes—
441C4×Q8C22×D714yes—
442C4×Q8C22×D714yes—
443C4×Q8C22×D714yes—
444C4×Q8C22×D714yes—
445C4×D4—74no—
446C4×D4—142no—
447#117—148no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—71no—
457C2×C4⋊C4—141no—
458C2×C4⋊C4—141no—
459C2×C4⋊C4—141no—
460C2×C4⋊C4—141no—
461C2×C4⋊C4C22⋊D711yescharacteristic
462C2×C4⋊C4C22⋊D711yescharacteristic
463C2×C4⋊C4C22⋊D711yescharacteristic
464C2×C4⋊C4C22×D711yescharacteristic
465C2×C4⋊C4C22×D711yescharacteristic
466C2×C4⋊C4C22×D711yescharacteristic
467C2×C22⋊C4—141no—
468C2×C22⋊C4—141no—
469C2×C22⋊C4—141no—
470C2×C22⋊C4—141no—
471C2×C22⋊C4—141no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
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#54812yes—
500C22×C7#57512yes—
501C22×C7#57812yes—
502C22×C7C23×D411yescharacteristic
503C2×D7—42no—
504C2×D7—42no—
505C2×D7—42no—
506C2×D7—84no—
507C4×C7—24no—
508C4×C7—22no—
509C4×C7—22no—
510C4×C7—22no—
511C4×C7—22no—
512C4×C7—22no—
513C4×C7—22no—
514C4×C7—42no—
515C4×C7—42no—
516C4×C7—42no—
517C4×C7#54812yes—
518C4×C7C22×#4111yescharacteristic
519C4×C7C2×2−1+411yescharacteristic
520Dic7—42no—
521Dic7—42no—
522Dic7—42no—
523C24—141no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—24no—
527C2×Q8—42no—
528C2×Q8—44no—
529C2×Q8—72no—
530C2×Q8—72no—
531C2×Q8—141no—
532C2×Q8—141no—
533C2×Q8—142no—
534C2×Q8—142no—
535C2×Q8—142no—
536C2×Q8—142no—
537C2×Q8#116114yes—
538C2×Q8C2×C22⋊D714yes—
539C2×Q8C23×D712yes—
540C2×D4—72no—
541C2×D4—142no—
542C2×D4—142no—
543C2×D4—141no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—141no—
549C22×C4—141no—
550C22×C4—141no—
551C22×C4—144no—
552C22×C4—284no—
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—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—72no—
583C4⋊C4—144no—
584C4⋊C4—144no—
585C4⋊C4—141no—
586C4⋊C4—144no—
587C4⋊C4—144no—
588C4⋊C4C2×C22⋊D714yes—
589C4⋊C4C2×C22⋊D714yes—
590C4⋊C4C2×C22⋊D714yes—
591C4⋊C4C23×D712yes—
592C4⋊C4C23×D712yes—
593C4⋊C4C23×D712yes—
594C22⋊C4—144no—
595C22⋊C4—144no—
596C22⋊C4—144no—
597C22⋊C4—144no—
598C22⋊C4—144no—
599C42—24no—
600C42—24no—
601C42—24no—
602C42—144no—
603C42—144no—
604C42C2×C22⋊D712yes—
605C42C2×C22⋊D712yes—
606C42C2×C22⋊D712yes—
607C42C23×D712yes—
608C42C23×D712yes—
609C42C23×D712yes—
610C2×C7#337714yescomplemented
611C2×C7C2×#54811yescharacteristic
612C2×C7C2×#57511yescharacteristic
613C2×C7C2×#57811yescharacteristic
614D7—82no—
615C23—142no—
616C23—282no—
617C23—282no—
618C23—282no—
619C23C22×C22⋊D711yescharacteristic
620Q8—24no—
621Q8—22no—
622Q8—44no—
623Q8—48no—
624Q8—142no—
625Q8—142no—
626Q8—142no—
627Q8—142no—
628Q8—282no—
629Q8—282no—
630Q8C2×#116114yes—
631D4—142no—
632D4—142no—
633D4—282no—
634C2×C4—24no—
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—22no—
644C2×C4—22no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—142no—
649C2×C4—142no—
650C2×C4—142no—
651C2×C4—288no—
652C2×C4—282no—
653C2×C4—282no—
654C2×C4—282no—
655C2×C4C2×#116112yes—
656C2×C4#655112yes—
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—282no—
671C22—282no—
672C22—282no—
673C22—564no—
674C22#9050812yes—
675C22#9051312yes—
676C22#9052912yes—
677C22C23×C22⋊D711yescharacteristic
678C4—24no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—282no—
689C4—282no—
690C4—282no—
691C4#9050812yes—
692C4C22×#116111yescharacteristic
693C4C2×#655111yescharacteristic
694C2—562no—
695C2#1174114514yesdirect product factor
696C2C2×#9050811yescharacteristic
697C2C2×#9051311yescharacteristic
698C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#557C2
socleC23×C7C22×D4
prime radicalC22×D28C23
hypercenterC2×#557D7
hypocenterC7C2×#3377
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
3. #11741145C2direct (N × H)
4. C2×#89863C2semidirect
6. C2×#89835C2semidirect
8. C2×#89841C2semidirect
10. C2×#89803C2semidirect
14. C2×#89796C2semidirect
15. C2×#89802C2semidirect
16. C2×C4×#1144C2semidirect
18. C7×#557C22semidirect
46. #89863C22semidirect
48. #89841C22semidirect
51. #89835C22semidirect
52. #89803C22semidirect
53. #89802C22semidirect
54. C4×#1144C22semidirect
58. #89796C22semidirect
180. C2×#557D7semidirect
287. #557C2×D7semidirect
610. C2×C7#3377semidirect
669. C7C2×#3377semidirect
695. C2#11741145direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
C2×#902752
#117411452
C2×#898632
C2×#898612
C2×#898352
C2×#898382
C2×#898412
C2×#898402
C2×#898032
C2×#898002
C2×#897982
C2×#897962
C2×#898022
C2×C4×#11442
C2×#33777