Finite Group Databasebeta

← C2×#11739436 #14232342

Subgroups — C2×#11739436 #14232342

Order 1792.

1878 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×#90421C211yesmaximal, characteristic
2C2×#90385C211yesmaximal, characteristic
3C2×C7×#501C211yesmaximal, characteristic, complemented
4C2×#89866C211yesmaximal, characteristic, complemented
5C2×#89835C211yesmaximal, characteristic, complemented
6#11739436C2116yesmaximal, direct product factor
7C2×#89656C211yesmaximal, characteristic, complemented
8C2×#89660C211yesmaximal, characteristic, complemented
9C2×#89659C211yesmaximal, characteristic, complemented
10C2×#89653C211yesmaximal, characteristic, complemented
11C2×#89634C211yesmaximal, characteristic, complemented
12C2×#89634C211yesmaximal, characteristic, complemented
13C2×#89640C211yesmaximal, characteristic, complemented
14C2×D7×#106C211yesmaximal, characteristic, complemented
15C2×#89488C211yesmaximal, characteristic, complemented
16C2×#89478C211yesmaximal, characteristic
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C7×#125C2211yescharacteristic
19C2×#6509—21no—
20C2×#6509—21no—
21C22×Dic28C2211yescharacteristic
22C22×#1131C2211yescharacteristic
23C22×C8×D7C2211yescharacteristic
24#90421—24no—
25#90421C2218yes—
26#90385—24no—
27#90385C2218yes—
28C2×#6461—21no—
29C2×#6460C2211yescharacteristic
30C2×#6460C2211yescharacteristic
31C2×#6460C2211yescharacteristic
32C2×#6460C2211yescharacteristic
33C2×#6457—21no—
34C2×#6456—21no—
35C2×#6455—21no—
36C2×#6455C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×#6453—21no—
41C2×#6453—21no—
42C2×C4×D28C2211yescharacteristic
43C2×C4×Dic14C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#501C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×(C2×D7)⋊C8C2211yescharacteristic
52C2×(C2×D7)⋊C8C2211yescharacteristic
53C2×#6391C2211yescharacteristic
54C2×#6390C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56#89866C2218yescomplemented
57#89835C2218yescomplemented
58C2×#6384C2211yescharacteristic
59C2×#6384C2211yescharacteristic
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89660C2218yescomplemented
68#89659C2218yescomplemented
69#89656C2218yescomplemented
70#89653C2218yescomplemented
71#89640C2218yescomplemented
72#89634C2218yescomplemented
73#89634C2218yescomplemented
74D7×#106C2218yescomplemented
75#89488C2218yescomplemented
76#89478C2218yes—
77C2×#3344—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×D28D411yescharacteristic
80C22×C4×D7—21no—
81C22×C4×D7—21no—
82C22×C4×D7—21no—
83C22×C4×D7C2311yescharacteristic
84C22×C4×D7C2311yescharacteristic
85C22×Dic14C2311yescharacteristic
86C22×Dic14C2311yescharacteristic
87C22×C7×C8C2311yescharacteristic
88C22×C7×C8C2311yescharacteristic
89C7×C4⋊Q8—22no—
90C7×C4⋊Q8C2314yes—
91C7×#125—22no—
92C7×#125C2314yes—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C42×C7C2311yescharacteristic
101#6509—28no—
102#6509—28no—
103C2×(C2×D7)⋊C4—21no—
104C2×(C2×D7)⋊C4—21no—
105C2×(C2×D7)⋊C4—21no—
106C2×(C2×D7)⋊C4—21no—
107C2×(C2×D7)⋊C4—21no—
108C2×(C2×D7)⋊C4D411yescharacteristic
109C2×(C2×D7)⋊C4D411yescharacteristic
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—21no—
112C2×C4⋊Dic7—21no—
113C2×C4⋊Dic7—21no—
114C2×C4⋊Dic7D411yescharacteristic
115C2×C4⋊Dic7C2311yescharacteristic
116C2×C4⋊Dic7C2311yescharacteristic
117C2×Dic7⋊C4—21no—
118C2×Dic7⋊C4—21no—
119C2×Dic7⋊C4—21no—
120C2×Dic7⋊C4—21no—
121C2×Dic7⋊C4—21no—
122C2×C4×Dic7—21no—
123C2×C4×Dic7—21no—
124C2×C4×Dic7—21no—
125C22×C7⋊C8C2311yescharacteristic
126C22×C7⋊C8C2311yescharacteristic
127C2×Dic28—24no—
128C2×Dic28C2314yes—
129C2×#1131—24no—
130C2×#1131C2314yes—
131C2×C8×D7—24no—
132C2×C8×D7C2314yes—
133#6461—28no—
134#6460—22no—
135#6460—22no—
136#6460—22no—
137#6460—22no—
138#6460C2314yes—
139#6460C2314yes—
140#6460C2314yes—
141#6460C2314yes—
142#6457—28no—
143#6456—28no—
144#6455—22no—
145#6455—28no—
146#6455C2314yes—
147D7×C4⋊C4—22no—
148D7×C4⋊C4—22no—
149D7×C4⋊C4—22no—
150D7×C4⋊C4C2314yes—
151D7×C4⋊C4C2314yes—
152D7×C4⋊C4C2314yes—
153#6453—28no—
154#6453—28no—
155C4×D28D414yes—
156C4×D28C2314yes—
157C4×Dic14—22no—
158C4×Dic14—22no—
159C4×Dic14C2314yes—
160C4×Dic14C2314yes—
161C7×#107C2314yes—
162C7×#107C2314yes—
163C7×#106C2314yes—
164C7×#106C2314yes—
165C7×#97C2314yes—
166(C2×D7)⋊C8C2314yes—
167(C2×D7)⋊C8C2314yes—
168#6391C2314yes—
169#6390C2314yes—
170#6390C2314yes—
171#6384C2314yes—
172#6384C2314yes—
173#6384C2314yes—
174#6384C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6382C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C2×#554—71no—
181C2×#552—71no—
182#3344—716no—
183C2×#501D711yescharacteristic, complemented
184C2×#484—71no—
185C2×#485—71no—
186C2×#483—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#475—71no—
190C2×#470—71no—
191C2×#467—71no—
192C2×#441—71no—
193C2×#435—71no—
194C2×#428—71no—
195C22×#106—71no—
196C23×D7C2×D411yescharacteristic
197C23×D7C2×D411yescharacteristic
198C2×C7×Q8—24no—
199C2×C7×Q8—82no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2411yescharacteristic
207C22×Dic7—21no—
208C22×Dic7—21no—
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7C2×D411yescharacteristic
212C22×Dic7C2×D411yescharacteristic
213C2×D28—24no—
214C2×D28C2×D414yes—
215C2×C4×D7—22no—
216C2×C4×D7—22no—
217C2×C4×D7—22no—
218C2×C4×D7—22no—
219C2×C4×D7—24no—
220C2×C4×D7—24no—
221C2×C4×D7—24no—
222C2×C4×D7—44no—
223C2×C4×D7—82no—
224C2×C4×D7—82no—
225C2×C4×D7C2×D412yes—
226C2×C4×D7C2×D412yes—
227C2×C4×D7C2412yes—
228C2×C4×D7C2412yes—
229C2×Dic14—22no—
230C2×Dic14—22no—
231C2×Dic14—22no—
232C2×Dic14—22no—
233C2×Dic14—21no—
234C2×Dic14—21no—
235C2×Dic14C2412yes—
236C2×Dic14C2412yes—
237C2×C7×C8—22no—
238C2×C7×C8#4114yes—
239C2×C7×C8C2412yes—
240C2×C7×C8C2412yes—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4—21no—
246C7×C4⋊C4—21no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4C2412yes—
249C7×C4⋊C4C2412yes—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C42×C7C2×D412yes—
253C42×C7C2412yes—
254(C2×D7)⋊C4—24no—
255(C2×D7)⋊C4—24no—
256(C2×D7)⋊C4—24no—
257(C2×D7)⋊C4—24no—
258(C2×D7)⋊C4—24no—
259(C2×D7)⋊C4C2×D414yes—
260(C2×D7)⋊C4C2×D414yes—
261C4⋊Dic7—21no—
262C4⋊Dic7—21no—
263C4⋊Dic7—24no—
264C4⋊Dic7—24no—
265C4⋊Dic7—24no—
266C4⋊Dic7—24no—
267C4⋊Dic7C2×D414yes—
268C4⋊Dic7C2412yes—
269C4⋊Dic7C2412yes—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275C4×Dic7—24no—
276C4×Dic7—24no—
277C4×Dic7—24no—
278C2×C7⋊C8—22no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8C2412yes—
281C2×C7⋊C8C2412yes—
282Dic28—28no—
283#1131—28no—
284C8×D7—28no—
285C22×Q16—71no—
286C22×M16—71no—
287C23×C8—71no—
288#554—78no—
289#554—144no—
290#552—78no—
291#552—144no—
292C2×C4⋊Q8C2×D711yescharacteristic
293C2×#126—141no—
294C2×#125—141no—
295C2×#125—141no—
296C2×#125C2×D711yescharacteristic
297C2×#123—141no—
298C2×C22⋊Q8—71no—
299C2×C22⋊Q8—71no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×C4×Q8—71no—
305C2×C4×Q8—71no—
306C2×C4×D4—71no—
307C2×C4×D4—141no—
308C2×#117—71no—
309C2×#117—141no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313#501C2×D718yescomplemented
314#485—78no—
315#484—78no—
316#483—78no—
317#483—78no—
318#479—78no—
319#475—78no—
320#470—78no—
321#467—78no—
322#441—78no—
323#435—78no—
324#428—78no—
325C2×#107—71no—
326C2×#107C2×D711yescharacteristic
327C2×#107C2×D711yescharacteristic
328C2×#106—71no—
329C2×#106—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—78no—
333C2×#106C2×D711yescharacteristic
334C2×#106C2×D711yescharacteristic
335C2×C4⋊C8—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×C22⋊C8—71no—
343C2×C22⋊C8—71no—
344C2×#97C2×D711yescharacteristic
345C23×C7C22×D411yescharacteristic
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7#13714yes—
352C22×D7C22×D412yes—
353C22×D7C22×D412yes—
354C7×Q8—84no—
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—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7C22×D412yes—
366C2×C4×C7C22×D412yes—
367C2×C4×C7C22×D411yescharacteristic
368C2×C4×C7C2×#4112yes—
369C2×C4×C72−1+412yes—
370C2×C4×C7C2511yescharacteristic
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—42no—
378C2×Dic7—42no—
379C2×Dic7—42no—
380C2×Dic7—42no—
381C2×Dic7C22×D412yes—
382C2×Dic7C22×D412yes—
383D28—28no—
384C4×D7—24no—
385C4×D7—24no—
386C4×D7—22no—
387C4×D7—22no—
388C4×D7—22no—
389C4×D7—22no—
390C4×D7—48no—
391C4×D7—84no—
392C4×D7—84no—
393Dic14—22no—
394Dic14—22no—
395Dic14—22no—
396Dic14—22no—
397Dic14—42no—
398Dic14—42no—
399C7×C8—22no—
400C7×C8C2×#4114yes—
401C7⋊C8—22no—
402C7⋊C8—22no—
403C22×Q8—21no—
404C22×Q8—71no—
405C22×Q8—71no—
406C22×D4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4—141no—
412C2×Q16—74no—
413C2×Q16—144no—
414C2×M16—74no—
415C2×M16—144no—
416C22×C8—71no—
417C22×C8—71no—
418C22×C8—74no—
419C22×C8—144no—
420C22×C8C22×D711yescharacteristic
421C22×C8C22×D711yescharacteristic
422C4⋊Q8—22no—
423C4⋊Q8C22×D714yes—
424#126—148no—
425#125—22no—
426#125—148no—
427#125—148no—
428#125C22×D714yes—
429#123—148no—
430C22⋊Q8—74no—
431C22⋊Q8—74no—
432C22⋊Q8—74no—
433C22⋊Q8—74no—
434C22⋊Q8—148no—
435C22⋊Q8—148no—
436C22⋊Q8—142no—
437C22⋊Q8—142no—
438C22⋊Q8—142no—
439C22⋊Q8—142no—
440C4×Q8—74no—
441C4×Q8—74no—
442C4×Q8—142no—
443C4×Q8—142no—
444C4×D4—74no—
445C4×D4—74no—
446C4×D4—148no—
447#117—74no—
448#117—148no—
449#117—142no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—142no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4—141no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4C22×D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—71no—
476C2×C22⋊C4—71no—
477C2×C22⋊C4—141no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C42—141no—
483C2×C42—141no—
484C2×C42—141no—
485C2×C42C22×D711yescharacteristic
486#107—74no—
487#107C22×D714yes—
488#107C22×D714yes—
489#106—74no—
490#106—74no—
491#106—74no—
492#106—74no—
493#106C22×D714yes—
494#106C22×D714yes—
495C4⋊C8—74no—
496#103—74no—
497#103—74no—
498#103—74no—
499#103—74no—
500#103—74no—
501#103—74no—
502C22⋊C8—74no—
503C22⋊C8—74no—
504#97C22×D714yes—
505C22×C7#54712yes—
506C22×C7C2×#13712yes—
507C22×C7#57712yes—
508C22×C7C23×D411yescharacteristic
509C2×D7—28no—
510C2×D7—22no—
511C2×D7—22no—
512C2×D7—22no—
513C2×D7—22no—
514C2×D7—22no—
515C2×D7—44no—
516C2×D7C2×#13714yes—
517C4×C7—22no—
518C4×C7—22no—
519C4×C7—42no—
520C4×C7—42no—
521C4×C7—42no—
522C4×C7—42no—
523C4×C7#54712yes—
524C4×C7C22×#4111yescharacteristic
525C4×C7C2×2−1+411yescharacteristic
526Dic7—22no—
527Dic7—22no—
528Dic7—42no—
529Dic7—42no—
530Dic7—42no—
531Dic7—42no—
532C24—71no—
533C24—71no—
534C2×Q8—24no—
535C2×Q8—72no—
536C2×Q8—72no—
537C2×Q8—82no—
538C2×Q8—141no—
539C2×Q8—141no—
540C2×Q8—142no—
541C2×Q8—142no—
542C2×Q8—142no—
543C2×Q8—142no—
544C2×D4—74no—
545C2×D4—144no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—71no—
551C22×C4—71no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—144no—
557C22×C4—144no—
558C22×C4—144no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—284no—
568C22×C4—562no—
569C22×C4—562no—
570C22×C4D4×D711yescharacteristic
571C22×C4D4×D711yescharacteristic
572C22×C4C23×D711yescharacteristic
573Q16—148no—
574M16—148no—
575C2×C8—22no—
576C2×C8—72no—
577C2×C8—72no—
578C2×C8—142no—
579C2×C8—142no—
580C2×C8—148no—
581C2×C8#116114yes—
582C2×C8C23×D712yes—
583C2×C8C23×D712yes—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—74no—
592C4⋊C4—72no—
593C4⋊C4—72no—
594C4⋊C4—144no—
595C4⋊C4—144no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4C23×D712yes—
606C4⋊C4C23×D712yes—
607C4⋊C4C23×D712yes—
608C4⋊C4C23×D712yes—
609C22⋊C4—74no—
610C22⋊C4—74no—
611C22⋊C4—144no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C42—144no—
617C42—144no—
618C42—144no—
619C42D4×D712yes—
620C42C23×D712yes—
621C2×C7#334414yescomplemented
622C2×C7C2×#54711yescharacteristic
623C2×C7C22×#13711yescharacteristic
624C2×C7C2×#57711yescharacteristic
625D7—24no—
626D7—42no—
627C23—74no—
628C23—72no—
629C23—72no—
630C23—142no—
631C23—142no—
632C23—142no—
633C23—142no—
634C23—142no—
635C23C2×D4×D711yescharacteristic
636Q8—84no—
637Q8—142no—
638Q8—142no—
639Q8—142no—
640Q8—142no—
641Q8—282no—
642Q8—282no—
643D4—148no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—72no—
655C2×C4—72no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—144no—
659C2×C4—144no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—288no—
669C2×C4—282no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—564no—
674C2×C4—564no—
675C2×C4C2×D4×D712yes—
676C2×C4C2×D4×D712yes—
677C2×C4C2×D4×D711yescharacteristic
678C2×C4C2×#116112yes—
679C2×C4#655112yes—
680C2×C4C24×D711yescharacteristic
681C8—22no—
682C8—142no—
683C8—142no—
684C8C2×#116114yes—
685C7C2×#334411yescharacteristic, complemented, Sylow
686C22—74no—
687C22—142no—
688C22—148no—
689C22—142no—
690C22—142no—
691C22—142no—
692C22—142no—
693C22—284no—
694C22#9041712yes—
695C22#9046612yes—
696C22D7×#13712yes—
697C22C22×D4×D711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4#9041712yes—
711C4C22×#116111yescharacteristic
712C4C2×#655111yescharacteristic
713C2—144no—
714C2—282no—
715C2#1173943614yesdirect product factor
716C2C2×#9041711yescharacteristic
717C2C2×#9046611yescharacteristic
718C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#501C2
socleC23×C7C22×D4
prime radicalC22×D28D4
hypercenterC2×#501D7
hypocenterC7C2×#3344
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. C2×C7×#501C2semidirect
4. C2×#89866C2semidirect
5. C2×#89835C2semidirect
6. #11739436C2direct (N × H)
7. C2×#89656C2semidirect
8. C2×#89660C2semidirect
9. C2×#89659C2semidirect
10. C2×#89653C2semidirect
11. C2×#89634C2semidirect
12. C2×#89634C2semidirect
13. C2×#89640C2semidirect
14. C2×D7×#106C2semidirect
15. C2×#89488C2semidirect
45. C7×#501C22semidirect
56. #89866C22semidirect
57. #89835C22semidirect
67. #89660C22semidirect
68. #89659C22semidirect
69. #89656C22semidirect
70. #89653C22semidirect
71. #89640C22semidirect
72. #89634C22semidirect
73. #89634C22semidirect
74. D7×#106C22semidirect
75. #89488C22semidirect
183. C2×#501D7semidirect
313. #501C2×D7semidirect
621. C2×C7#3344semidirect
685. C7C2×#3344semidirect
715. C2#11739436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904212
C2×#903852
C2×C7×#5012
C2×#898662
C2×#898352
#117394362
C2×#896562
C2×#896602
C2×#896592
C2×#896532
C2×#896342
C2×#896402
C2×D7×#1062
C2×#894882
C2×#894782
C2×#33447