Finite Group Databasebeta

← C2×#11737622 #14222146

Subgroups — C2×#11737622 #14222146

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×#90503C211yesmaximal, characteristic
2C2×#90316C211yesmaximal, characteristic
3C2×C7×#451C211yesmaximal, characteristic
4C2×#90000C211yesmaximal, characteristic
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89954C211yesmaximal, characteristic, complemented
7C2×#89956C211yesmaximal, characteristic, complemented
8C2×Q16×Dic7C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic
10#11737622C2116yesmaximal, direct product factor
11C2×#89568C211yesmaximal, characteristic, complemented
12C2×#89571C211yesmaximal, characteristic, complemented
13C2×#89561C211yesmaximal, characteristic, complemented
14C2×#89562C211yesmaximal, characteristic, complemented
15C2×#89495C211yesmaximal, characteristic
16C2×#89492C211yesmaximal, characteristic
17C23×C7×Q8C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×Q16C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21#90503—24no—
22#90503C2218yes—
23C2×Q8×Dic7—21no—
24C2×Q8×Dic7—21no—
25C2×Q8×Dic7C2211yescharacteristic
26C2×Q8×Dic7C2211yescharacteristic
27C2×Q8×Dic7C2211yescharacteristic
28C2×Q8×Dic7C2211yescharacteristic
29C2×Q8×Dic7C2211yescharacteristic
30C2×#6507C2211yescharacteristic
31C22×#1144C2211yescharacteristic
32C22×#1144C2211yescharacteristic
33C2×#6489—21no—
34C2×#6489—21no—
35C2×#6489C2211yescharacteristic
36C2×#6489C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38#90316—24no—
39#90316C2218yes—
40C2×#6453—21no—
41C2×#6453C2211yescharacteristic
42C2×#6452—21no—
43C2×#6450C2211yescharacteristic
44C2×#6442—21no—
45C2×#6442—21no—
46C7×#451C2218yes—
47C2×C7×#103C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50#90000C2218yes—
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89956C2218yescomplemented
57Q16×Dic7C2218yescomplemented
58#89954C2218yescomplemented
59#89954C2218yescomplemented
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6389C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66C2×Dic7⋊C8C2211yescharacteristic
67C2×C8×Dic7C2211yescharacteristic
68#89817C2218yes—
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89571C2218yescomplemented
72#89568C2218yescomplemented
73#89562C2218yescomplemented
74#89561C2218yescomplemented
75#89495C2218yes—
76#89492C2218yes—
77C2×#3127—71nomaximal, Sylow
78C22×C7×Q8—24no—
79C22×C7×Q8—24no—
80C22×C7×Q8—21no—
81C22×C7×Q8—22no—
82C22×C7×Q8C2314yes—
83C22×C7×Q8C2311yescharacteristic
84C22×C7×Q8C2311yescharacteristic
85C22×C7×Q8C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7C2311yescharacteristic
88C22×Dic14C2311yescharacteristic
89C2×C7×Q16—24no—
90C2×C7×Q16—24no—
91C2×C7×Q16C2314yes—
92C2×C7×Q16C2314yes—
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8C2314yes—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C22⋊Dic7—21no—
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7D411yescharacteristic
103C2×C22⋊Dic7D411yescharacteristic
104Q8×Dic7—28no—
105Q8×Dic7—28no—
106Q8×Dic7—22no—
107Q8×Dic7—22no—
108Q8×Dic7—22no—
109Q8×Dic7—22no—
110Q8×Dic7—22no—
111Q8×Dic7C2314yes—
112Q8×Dic7C2314yes—
113Q8×Dic7C2314yes—
114Q8×Dic7C2314yes—
115Q8×Dic7C2314yes—
116#6507—22no—
117#6507C2314yes—
118C2×#1144—24no—
119C2×#1144—24no—
120C2×#1144C2314yes—
121C2×#1144C2314yes—
122#6489—22no—
123#6489—28no—
124#6489—28no—
125#6489D414yes—
126#6489C2314yes—
127#6489C2314yes—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7—21no—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7—21no—
134C2×C4⋊Dic7D411yescharacteristic
135C2×C4⋊Dic7D411yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139#6487—22no—
140#6487C2314yes—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×C4×Dic7—21no—
147C2×C4×Dic7—21no—
148C2×C4×Dic7—21no—
149C2×C4×Dic7—21no—
150C2×C4×Dic7—21no—
151C2×C4×Dic7—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7C2311yescharacteristic
154C2×C4×Dic7C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C22×C7⋊C8C2311yescharacteristic
157#6453—28no—
158#6453—22no—
159#6453C2314yes—
160#6452—28no—
161#6450—22no—
162#6450C2314yes—
163#6442—28no—
164#6442—28no—
165C7×#103C2314yes—
166C7×#103C2314yes—
167C7×C22⋊C8C2314yes—
168#6409C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172C22⋊(C7⋊C8)C2314yes—
173#6392C2314yes—
174#6391C2314yes—
175#6390C2314yes—
176#6390C2314yes—
177#6389C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180C8×Dic7C2314yes—
181#6382C2314yes—
182#6381C2314yes—
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×#451D711yescharacteristic
194C2×#441—71no—
195C2×#441—71no—
196C2×C4×Q16—71no—
197C2×C4×Q16—71no—
198C2×#433—71no—
199C24×C7C2×D411yescharacteristic
200C2×C7×Q8—216no—
201C2×C7×Q8—28no—
202C2×C7×Q8—28no—
203C2×C7×Q8—28no—
204C2×C7×Q8—24no—
205C2×C7×Q8—21no—
206C2×C7×Q8—21no—
207C2×C7×Q8—21no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8#4114yes—
213C2×C7×Q8#4114yes—
214C2×C7×Q8C2412yes—
215C2×C7×Q8C2412yes—
216C2×C7×Q8C2412yes—
217C22×C4×C7—28no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—24no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2411yescharacteristic
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235C22×Dic7C2×D411yescharacteristic
236C22×Dic7C2×D411yescharacteristic
237C2×Dic14—22no—
238C2×Dic14—22no—
239C2×Dic14—21no—
240C2×Dic14C2412yes—
241C7×Q16—28no—
242C7×Q16—28no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8C2412yes—
246C2×C7×C8C2412yes—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4C2412yes—
250C7×C22⋊C4—24no—
251C22⋊Dic7—24no—
252C22⋊Dic7—24no—
253C22⋊Dic7C2×D414yes—
254C22⋊Dic7C2×D414yes—
255#1144—28no—
256#1144—28no—
257C4⋊Dic7—21no—
258C4⋊Dic7—21no—
259C4⋊Dic7—21no—
260C4⋊Dic7—24no—
261C4⋊Dic7—24no—
262C4⋊Dic7—24no—
263C4⋊Dic7—24no—
264C4⋊Dic7—24no—
265C4⋊Dic7—24no—
266C4⋊Dic7C2×D414yes—
267C4⋊Dic7C2×D414yes—
268C4⋊Dic7C2412yes—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276C4×Dic7—24no—
277C4×Dic7—24no—
278C4×Dic7—24no—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7C2×D412yes—
284C4×Dic7C2×D412yes—
285C4×Dic7C2412yes—
286C4×Dic7C2412yes—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291C23×Q8C2×D711yescharacteristic
292C22×Q16—71no—
293C22×Q16—71no—
294C22×Q16C2×D711yescharacteristic
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⋊Q8C2×D711yescharacteristic
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—71no—
313C2×C4×Q8—71no—
314C2×C4×Q8—141no—
315C2×C4×Q8—141no—
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#451C2×D718yes—
328#441—78no—
329#441—78no—
330C4×Q16—78no—
331C4×Q16—78no—
332#433—78no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#106—71no—
336C2×#106—71no—
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⋊C8C2×D711yescharacteristic
349C2×#97—71no—
350C2×C4×C8—71no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7C22×D412yes—
355C23×C7C22×D411yescharacteristic
356C7×Q8—216no—
357C7×Q8—24no—
358C7×Q8—24no—
359C7×Q8—22no—
360C7×Q8—22no—
361C7×Q8—22no—
362C7×Q8—22no—
363C7×Q8—42no—
364C7×Q8C2×#4114yes—
365C7×Q8C2×#4114yes—
366C2×C4×C7—216no—
367C2×C4×C7—24no—
368C2×C4×C7—24no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—24no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C2×#4112yes—
382C2×C4×C7C2×#4112yes—
383C2×C4×C7C2511yescharacteristic
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400Dic14—22no—
401Dic14—22no—
402Dic14—42no—
403C7×C8—22no—
404C7×C8—22no—
405C7⋊C8—22no—
406C7⋊C8—22no—
407C22×Q8—24no—
408C22×Q8—24no—
409C22×Q8—21no—
410C22×Q8—22no—
411C22×Q8—71no—
412C22×Q8C22×D711yescharacteristic
413C22×Q8C22×D714yes—
414C22×Q8C22×D711yescharacteristic
415C22×Q8C22×D711yescharacteristic
416C23×C4—21no—
417C23×C4C22×D711yescharacteristic
418C2×Q16—24no—
419C2×Q16—24no—
420C2×Q16—74no—
421C2×Q16—74no—
422C2×Q16—144no—
423C2×Q16—144no—
424C2×Q16C22×D714yes—
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—142no—
436#125—148no—
437#125—148no—
438C22⋊Q8—22no—
439C22⋊Q8—74no—
440C22⋊Q8—142no—
441C22⋊Q8C22×D714yes—
442C4×Q8—74no—
443C4×Q8—74no—
444C4×Q8—74no—
445C4×Q8—74no—
446C4×Q8—74no—
447C4×Q8—74no—
448C4×Q8—142no—
449C4×Q8—142no—
450C4×Q8—142no—
451C4×Q8—142no—
452C4×Q8—142no—
453C4×Q8—142no—
454C4×Q8—148no—
455C4×Q8—148no—
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—71no—
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⋊C4—141no—
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—71no—
482C2×C22⋊C4—71no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4—141no—
485C2×C42—71no—
486C2×C42—71no—
487C2×C42—141no—
488C2×C42—141no—
489C2×C42—141no—
490C2×C42—141no—
491C2×C42—141no—
492C2×C42—141no—
493C2×C42—141no—
494#107—74no—
495#107—74no—
496#106—74no—
497#106—74no—
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⋊C8C22×D714yes—
510#97—74no—
511C4×C8—74no—
512C22×C7—22no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—44no—
516C22×C7#52512yes—
517C22×C7#57812yes—
518C22×C7#57812yes—
519C22×C7C23×D411yescharacteristic
520C4×C7—24no—
521C4×C7—24no—
522C4×C7—22no—
523C4×C7—42no—
524C4×C7—42no—
525C4×C7#52512yes—
526C4×C7C22×#4111yescharacteristic
527C4×C7C22×#4111yescharacteristic
528Dic7—22no—
529Dic7—22no—
530Dic7—22no—
531Dic7—22no—
532Dic7—42no—
533Dic7—42no—
534Dic7—42no—
535Dic7—42no—
536C24D4×D711yescharacteristic
537C2×Q8—216no—
538C2×Q8—28no—
539C2×Q8—28no—
540C2×Q8—28no—
541C2×Q8—24no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—72no—
550C2×Q8—141no—
551C2×Q8—142no—
552C2×Q8—142no—
553C2×Q8#115914yes—
554C2×Q8#115914yes—
555C2×Q8C23×D712yes—
556C2×Q8C23×D712yes—
557C2×Q8C23×D712yes—
558C22×C4—28no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—71no—
567C22×C4—71no—
568C22×C4—71no—
569C22×C4—71no—
570C22×C4—141no—
571C22×C4—141no—
572C22×C4—141no—
573C22×C4—141no—
574C22×C4D4×D712yes—
575C22×C4D4×D711yescharacteristic
576C22×C4C23×D712yes—
577C22×C4C23×D711yescharacteristic
578Q16—28no—
579Q16—28no—
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—21no—
592C4⋊C4—74no—
593C4⋊C4—74no—
594C4⋊C4—72no—
595C4⋊C4—72no—
596C4⋊C4—72no—
597C4⋊C4—144no—
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⋊C4—141no—
611C4⋊C4C23×D712yes—
612C22⋊C4—24no—
613C22⋊C4—74no—
614C22⋊C4—74no—
615C22⋊C4—144no—
616C22⋊C4—144no—
617C42—72no—
618C42—72no—
619C42—72no—
620C42—72no—
621C42—144no—
622C42—144no—
623C42—144no—
624C42—144no—
625C42—144no—
626C42—144no—
627C42—144no—
628C2×C7—42no—
629C2×C7#312714yescomplemented
630C2×C7C2×#52511yescharacteristic
631C2×C7C2×#57811yescharacteristic
632C2×C7C2×#57811yescharacteristic
633C23—22no—
634C23—22no—
635C23—22no—
636C23C2×D4×D712yes—
637C23C2×D4×D711yescharacteristic
638Q8—216no—
639Q8—24no—
640Q8—24no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—142no—
647Q8—142no—
648Q8—282no—
649Q8C2×#115914yes—
650Q8C2×#115914yes—
651C2×C4—216no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—72no—
665C2×C4—72no—
666C2×C4—72no—
667C2×C4—72no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
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×C4—282no—
680C2×C4C2×D4×D712yes—
681C2×C4C2×D4×D711yescharacteristic
682C2×C4C2×#115912yes—
683C2×C4C2×#115912yes—
684C2×C4C24×D711yescharacteristic
685C8—22no—
686C8—22no—
687C8—142no—
688C8—142no—
689C7C2×#312711yescharacteristic, complemented, Sylow
690C22—22no—
691C22—22no—
692C22—22no—
693C22—44no—
694C22#9027712yes—
695C22#9045712yes—
696C22#9047012yes—
697C22C22×D4×D711yescharacteristic
698C4—24no—
699C4—24no—
700C4—22no—
701C4—42no—
702C4—42no—
703C4—142no—
704C4—142no—
705C4—142no—
706C4—142no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4—282no—
711C4#9027712yes—
712C4C22×#115911yescharacteristic
713C4C22×#115911yescharacteristic
714C2—42no—
715C2#1173762214yesdirect product factor
716C2C2×#9027711yescharacteristic
717C2C2×#9045711yescharacteristic
718C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#451C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
hypercenterC2×#451D7
hypocenterC7C2×#3127
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
5. C2×#89954C2semidirect
6. C2×#89954C2semidirect
7. C2×#89956C2semidirect
8. C2×Q16×Dic7C2semidirect
10. #11737622C2direct (N × H)
11. C2×#89568C2semidirect
12. C2×#89571C2semidirect
13. C2×#89561C2semidirect
14. C2×#89562C2semidirect
56. #89956C22semidirect
57. Q16×Dic7C22semidirect
58. #89954C22semidirect
59. #89954C22semidirect
71. #89571C22semidirect
72. #89568C22semidirect
73. #89562C22semidirect
74. #89561C22semidirect
629. C2×C7#3127semidirect
689. C7C2×#3127semidirect
715. C2#11737622direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905032
C2×#903162
C2×C7×#4512
C2×#900002
C2×#899542
C2×#899562
C2×Q16×Dic72
C2×#898172
#117376222
C2×#895682
C2×#895712
C2×#895612
C2×#895622
C2×#894952
C2×#894922
C2×#31277