Finite Group Databasebeta

← C2×#11737281 #14222151

Subgroups — C2×#11737281 #14222151

Order 1792.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90274C211yesmaximal, characteristic
2C2×#90263C211yesmaximal, characteristic
3C2×C7×#441C211yesmaximal, characteristic, complemented
4C2×#89958C211yesmaximal, characteristic
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×C4×#1144C211yesmaximal, characteristic, complemented
7C2×C4×#1144C211yesmaximal, characteristic, complemented
8#11737281C2116yesmaximal, direct product factor
9C2×#89629C211yesmaximal, characteristic, complemented
10C2×#89639C211yesmaximal, characteristic
11C2×#89565C211yesmaximal, characteristic, complemented
12C2×#89587C211yesmaximal, characteristic
13C2×#89580C211yesmaximal, characteristic
14C2×#89571C211yesmaximal, characteristic, complemented
15C2×#89488C211yesmaximal, characteristic, complemented
16C2×#89481C211yesmaximal, characteristic
17C22×Q8×D7C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6507C2211yescharacteristic
24C22×#1144C2211yescharacteristic
25C22×#1144C2211yescharacteristic
26C22×Dic28C2211yescharacteristic
27#90274—24no—
28#90274C2218yes—
29#90263—24no—
30#90263C2218yes—
31C2×#6461—21no—
32C2×#6460C2211yescharacteristic
33C2×#6455—21no—
34C2×#6455C2211yescharacteristic
35C2×#6453C2211yescharacteristic
36C2×#6452—21no—
37C2×#6450—21no—
38C2×#6450C2211yescharacteristic
39C2×#6439—21no—
40C2×#6435—21no—
41C2×#6435C2211yescharacteristic
42C2×#6433—21no—
43C2×C4×Dic14—21no—
44C2×C4×Dic14C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C7×#441C2218yescomplemented
47C2×C7×#106C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53#89958C2218yes—
54#89954C2218yescomplemented
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×#6391C2211yescharacteristic
58C2×#6390C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62C4×#1144C2218yescomplemented
63C4×#1144C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×C4×C7⋊C8C2211yescharacteristic
69#89639C2218yes—
70#89629C2218yescomplemented
71#89587C2218yes—
72#89580C2218yes—
73#89571C2218yescomplemented
74#89565C2218yescomplemented
75#89488C2218yescomplemented
76#89481C2218yes—
77C2×#3127—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C2×Q8×D7—24no—
81C2×Q8×D7—22no—
82C2×Q8×D7—24no—
83C2×Q8×D7C2314yes—
84C22×C4×D7—21no—
85C22×C4×D7C2311yescharacteristic
86C22×Dic14—21no—
87C22×Dic14C2311yescharacteristic
88C22×Dic14C2311yescharacteristic
89C2×C7×Q16—24no—
90C2×C7×Q16C2314yes—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C4×C7×Q8—22no—
94C4×C7×Q8—22no—
95C4×C7×Q8C2314yes—
96C4×C7×Q8C2314yes—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C42×C7—21no—
102C2×C42×C7—21no—
103C2×C42×C7C2311yescharacteristic
104#6509—22no—
105#6509C2314yes—
106Q8×Dic7—22no—
107Q8×Dic7C2314yes—
108#6507—22no—
109#6507C2314yes—
110C2×#1144—24no—
111C2×#1144—24no—
112C2×#1144C2314yes—
113C2×#1144C2314yes—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4D411yescharacteristic
118C2×(C2×D7)⋊C4D411yescharacteristic
119C2×C4⋊Dic7—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4D411yescharacteristic
132C2×Dic7⋊C4D411yescharacteristic
133C2×C4×Dic7—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C2×Dic28—24no—
142C2×Dic28C2314yes—
143#6461—28no—
144#6460—22no—
145#6460C2314yes—
146#6455—22no—
147#6455—28no—
148#6455C2314yes—
149#6453—22no—
150#6453C2314yes—
151#6452—28no—
152#6450—28no—
153#6450—22no—
154#6450C2314yes—
155#6439—28no—
156#6435—28no—
157#6435D414yes—
158#6435C2314yes—
159#6433—28no—
160C4×Dic14—22no—
161C4×Dic14—22no—
162C4×Dic14—28no—
163C4×Dic14C2314yes—
164C4×Dic14C2314yes—
165C7×#106C2314yes—
166C7×#103C2314yes—
167C7×#103C2314yes—
168C7×#97C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171(C2×D7)⋊C8C2314yes—
172(C2×D7)⋊C8C2314yes—
173#6391C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182C4×C7⋊C8C2314yes—
183C2×#541—71no—
184C2×#519—71no—
185#3127—716no—
186C2×#485—71no—
187C2×#485—71no—
188C2×#479—71no—
189C2×#479—71no—
190C2×#462—71no—
191C2×#462—71no—
192C2×#451—71no—
193C2×#451—71no—
194C2×#441—71no—
195C2×#441D711yescharacteristic, complemented
196C2×C4×Q16—71no—
197C2×C4×Q16—71no—
198C2×#433—71no—
199C23×D7C2×D411yescharacteristic
200C2×C7×Q8—21no—
201C2×C7×Q8—21no—
202C2×C7×Q8—22no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8#4114yes—
206C2×C7×Q8C2412yes—
207C2×C7×Q8C2412yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C22×Dic7C2×D411yescharacteristic
222Q8×D7—216no—
223Q8×D7—28no—
224Q8×D7—28no—
225C2×C4×D7—28no—
226C2×C4×D7—24no—
227C2×C4×D7—22no—
228C2×C4×D7—22no—
229C2×C4×D7C2×D412yes—
230C2×C4×D7C2412yes—
231C2×Dic14—28no—
232C2×Dic14—21no—
233C2×Dic14—22no—
234C2×Dic14—24no—
235C2×Dic14—22no—
236C2×Dic14—22no—
237C2×Dic14—21no—
238C2×Dic14#4114yes—
239C2×Dic14C2412yes—
240C2×Dic14C2412yes—
241C7×Q16—28no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8C2412yes—
245C2×C7×C8C2412yes—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C42×C7—24no—
253C42×C7—24no—
254C42×C7C2×D412yes—
255C42×C7C2412yes—
256#1144—28no—
257#1144—28no—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4—24no—
260(C2×D7)⋊C4—24no—
261(C2×D7)⋊C4C2×D414yes—
262(C2×D7)⋊C4C2×D414yes—
263C4⋊Dic7—21no—
264C4⋊Dic7—21no—
265C4⋊Dic7—24no—
266C4⋊Dic7—24no—
267C4⋊Dic7—24no—
268C4⋊Dic7C2412yes—
269C4⋊Dic7C2412yes—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4C2×D414yes—
278Dic7⋊C4C2×D414yes—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7C2×D412yes—
285C4×Dic7C2412yes—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—22no—
288C2×C7⋊C8C2412yes—
289C2×C7⋊C8C2412yes—
290Dic28—28no—
291C23×Q8—71no—
292C22×Q16—71no—
293C22×Q16—71no—
294C22×Q16—71no—
295C22×Q16C2×D711yescharacteristic
296#541—78no—
297#541—144no—
298C2×C4⋊Q8—71no—
299C2×#126—141no—
300C2×#126—141no—
301C2×#125—71no—
302C2×#125—141no—
303C2×#125—141no—
304C2×C22⋊Q8—71no—
305C2×C22⋊Q8—71no—
306#519—78no—
307#519—144no—
308C2×C4×Q8—71no—
309C2×C4×Q8—71no—
310C2×C4×Q8—71no—
311C2×C4×Q8—71no—
312C2×C4×Q8—141no—
313C2×C4×Q8—141no—
314C2×C4×Q8C2×D711yescharacteristic
315C2×C4×Q8C2×D711yescharacteristic
316C2×#117—71no—
317C2×#117—71no—
318C2×#117—141no—
319C2×#117—141no—
320#485—78no—
321#485—78no—
322#479—78no—
323#479—78no—
324#462—78no—
325#462—78no—
326#451—78no—
327#451—78no—
328#441—78no—
329#441C2×D718yescomplemented
330C4×Q16—78no—
331C4×Q16—78no—
332#433—78no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#106—71no—
336C2×#106C2×D711yescharacteristic
337C2×C4⋊C8—71no—
338C2×C4⋊C8—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103C2×D711yescharacteristic
346C2×#103C2×D711yescharacteristic
347C2×C22⋊C8—71no—
348C2×C22⋊C8—71no—
349C2×#97C2×D711yescharacteristic
350C2×C4×C8—71no—
351C23×C7C22×D411yescharacteristic
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7C22×D412yes—
356C7×Q8—24no—
357C7×Q8—22no—
358C7×Q8—22no—
359C7×Q8—22no—
360C7×Q8—42no—
361C7×Q8C2×#4114yes—
362C2×C4×C7—24no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D412yes—
374C2×C4×C7C22×D411yescharacteristic
375C2×C4×C7C2×#4112yes—
376C2×C4×C7C2×#4112yes—
377C2×C4×C7C2511yescharacteristic
378C2×Dic7—22no—
379C2×Dic7—24no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7C22×D412yes—
390C2×Dic7C22×D412yes—
391C2×Dic7C22×D412yes—
392C4×D7—216no—
393C4×D7—24no—
394C4×D7—22no—
395C4×D7—22no—
396Dic14—216no—
397Dic14—24no—
398Dic14—22no—
399Dic14—22no—
400Dic14—22no—
401Dic14—42no—
402Dic14C2×#4114yes—
403C7×C8—22no—
404C7×C8—22no—
405C7⋊C8—22no—
406C7⋊C8—22no—
407C22×Q8—74no—
408C22×Q8—71no—
409C22×Q8—71no—
410C22×Q8—141no—
411C22×Q8—142no—
412C22×Q8—144no—
413C22×Q8—144no—
414C22×Q8C22×D711yescharacteristic
415C22×Q8C22×D711yescharacteristic
416C23×C4—71no—
417C23×C4—141no—
418C2×Q16—24no—
419C2×Q16—74no—
420C2×Q16—74no—
421C2×Q16—74no—
422C2×Q16—144no—
423C2×Q16—144no—
424C2×Q16—144no—
425C2×Q16C22×D714yes—
426C22×C8—71no—
427C22×C8—71no—
428C22×C8C22×D711yescharacteristic
429C22×C8C22×D711yescharacteristic
430C4⋊Q8—74no—
431C4⋊Q8—142no—
432#126—148no—
433#126—148no—
434#125—74no—
435#125—148no—
436#125—142no—
437#125—148no—
438C22⋊Q8—74no—
439C22⋊Q8—74no—
440C22⋊Q8—142no—
441C22⋊Q8—142no—
442C4×Q8—22no—
443C4×Q8—22no—
444C4×Q8—74no—
445C4×Q8—74no—
446C4×Q8—74no—
447C4×Q8—74no—
448C4×Q8—148no—
449C4×Q8—142no—
450C4×Q8—142no—
451C4×Q8—148no—
452C4×Q8—142no—
453C4×Q8—142no—
454C4×Q8C22×D714yes—
455C4×Q8C22×D714yes—
456#117—74no—
457#117—74no—
458#117—74no—
459#117—148no—
460#117—148no—
461#117—142no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—71no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4—141no—
473C2×C4⋊C4—141no—
474C2×C4⋊C4—141no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4C22×D711yescharacteristic
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C22⋊C4—71no—
481C2×C22⋊C4—71no—
482C2×C22⋊C4—141no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4—141no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—71no—
488C2×C42—141no—
489C2×C42—141no—
490C2×C42—141no—
491C2×C42—141no—
492C2×C42—141no—
493C2×C42C22×D711yescharacteristic
494#107—74no—
495#107—74no—
496#106—74no—
497#106C22×D714yes—
498C4⋊C8—74no—
499C4⋊C8—74no—
500#103—74no—
501#103—74no—
502#103—74no—
503#103—74no—
504#103—74no—
505#103—74no—
506#103C22×D714yes—
507#103C22×D714yes—
508C22⋊C8—74no—
509C22⋊C8—74no—
510#97C22×D714yes—
511C4×C8—74no—
512C22×C7#52512yes—
513C22×C7#57812yes—
514C22×C7#57812yes—
515C22×C7C23×D411yescharacteristic
516C2×D7—22no—
517C2×D7—22no—
518C2×D7—22no—
519C2×D7—44no—
520C4×C7—24no—
521C4×C7—22no—
522C4×C7—22no—
523C4×C7—42no—
524C4×C7—42no—
525C4×C7—42no—
526C4×C7#52512yes—
527C4×C7C22×#4111yescharacteristic
528C4×C7C22×#4111yescharacteristic
529Dic7—22no—
530Dic7—24no—
531Dic7—22no—
532Dic7—22no—
533Dic7—42no—
534Dic7—42no—
535Dic7—42no—
536C24—71no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—74no—
543C2×Q8—72no—
544C2×Q8—72no—
545C2×Q8—144no—
546C2×Q8—148no—
547C2×Q8—148no—
548C2×Q8—1416no—
549C2×Q8—148no—
550C2×Q8—142no—
551C2×Q8—141no—
552C2×Q8—141no—
553C2×Q8—142no—
554C2×Q8—142no—
555C2×Q8#115714yes—
556C2×Q8C23×D712yes—
557C2×Q8C23×D712yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—71no—
563C22×C4—71no—
564C22×C4—71no—
565C22×C4—72no—
566C22×C4—72no—
567C22×C4—144no—
568C22×C4—148no—
569C22×C4—141no—
570C22×C4—142no—
571C22×C4—142no—
572C22×C4—141no—
573C22×C4—141no—
574C22×C4—141no—
575C22×C4D4×D711yescharacteristic
576C22×C4D4×D711yescharacteristic
577C22×C4C23×D711yescharacteristic
578Q16—28no—
579Q16—148no—
580Q16—148no—
581Q16—148no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—72no—
585C2×C8—72no—
586C2×C8—142no—
587C2×C8—142no—
588C2×C8C23×D712yes—
589C2×C8C23×D712yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—74no—
595C4⋊C4—74no—
596C4⋊C4—72no—
597C4⋊C4—72no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—144no—
604C4⋊C4—144no—
605C4⋊C4—144no—
606C4⋊C4—144no—
607C4⋊C4—144no—
608C4⋊C4—141no—
609C4⋊C4—141no—
610C4⋊C4C23×D712yes—
611C4⋊C4C23×D712yes—
612C22⋊C4—74no—
613C22⋊C4—74no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C22⋊C4—144no—
617C42—24no—
618C42—24no—
619C42—72no—
620C42—72no—
621C42—144no—
622C42—144no—
623C42—144no—
624C42—144no—
625C42—144no—
626C42D4×D712yes—
627C42C23×D712yes—
628C2×C7#312714yescomplemented
629C2×C7C2×#52511yescharacteristic
630C2×C7C2×#57811yescharacteristic
631C2×C7C2×#57811yescharacteristic
632D7—42no—
633C23—72no—
634C23—142no—
635C23—142no—
636C23—142no—
637C23C2×D4×D711yescharacteristic
638Q8—24no—
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—74no—
644Q8—1416no—
645Q8—144no—
646Q8—142no—
647Q8—142no—
648Q8—142no—
649Q8—282no—
650Q8C2×#115714yes—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—72no—
662C2×C4—72no—
663C2×C4—72no—
664C2×C4—1416no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—144no—
669C2×C4—142no—
670C2×C4—144no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—142no—
675C2×C4—142no—
676C2×C4—282no—
677C2×C4—282no—
678C2×C4—282no—
679C2×C4C2×#115712yes—
680C2×C4C2×D4×D712yes—
681C2×C4C2×D4×D712yes—
682C2×C4C2×D4×D711yescharacteristic
683C2×C4D7×#4112yes—
684C2×C4C24×D711yescharacteristic
685C8—22no—
686C8—22no—
687C8—142no—
688C8—142no—
689C7C2×#312711yescharacteristic, complemented, Sylow
690C22—142no—
691C22—142no—
692C22—142no—
693C22—284no—
694C22#9023812yes—
695C22#9047012yes—
696C22#9047012yes—
697C22C22×D4×D711yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—142no—
705C4—142no—
706C4—142no—
707C4—144no—
708C4—282no—
709C4—282no—
710C4—282no—
711C4#9023812yes—
712C4C22×#115711yescharacteristic
713C4C2×D7×#4111yescharacteristic
714C2—282no—
715C2#1173728114yesdirect product factor
716C2C2×#9023811yescharacteristic
717C2C2×#9047011yescharacteristic
718C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#441C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#441D7
hypocenterC7C2×#3127
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×C7×#441C2semidirect
5. C2×#89954C2semidirect
6. C2×C4×#1144C2semidirect
7. C2×C4×#1144C2semidirect
8. #11737281C2direct (N × H)
9. C2×#89629C2semidirect
11. C2×#89565C2semidirect
14. C2×#89571C2semidirect
15. C2×#89488C2semidirect
46. C7×#441C22semidirect
54. #89954C22semidirect
62. C4×#1144C22semidirect
63. C4×#1144C22semidirect
70. #89629C22semidirect
73. #89571C22semidirect
74. #89565C22semidirect
75. #89488C22semidirect
195. C2×#441D7semidirect
329. #441C2×D7semidirect
628. C2×C7#3127semidirect
689. C7C2×#3127semidirect
715. C2#11737281direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902742
C2×#902632
C2×C7×#4412
C2×#899582
C2×#899542
C2×C4×#11442
#117372812
C2×#896292
C2×#896392
C2×#895652
C2×#895872
C2×#895802
C2×#895712
C2×#894882
C2×#894812
C2×#31277