Finite Group Databasebeta

← C2×#11738022 #14226649

Subgroups — C2×#11738022 #14226649

Order 1792.

1898 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90371C211yesmaximal, characteristic
2C2×#90269C211yesmaximal, characteristic, complemented
3C2×C7×#464C211yesmaximal, characteristic, complemented
4C2×#89961C211yesmaximal, characteristic, complemented
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89946C211yesmaximal, characteristic
7C2×#89934C211yesmaximal, characteristic, complemented
8C2×#89826C211yesmaximal, characteristic, complemented
9C2×#89794C211yesmaximal, characteristic, complemented
10#11738022C2116yesmaximal, direct product factor
11C2×#89601C211yesmaximal, characteristic, complemented
12C2×#89609C211yesmaximal, characteristic, complemented
13C2×#89588C211yesmaximal, characteristic, complemented
14C2×#89566C211yesmaximal, characteristic, complemented
15C2×#89552C211yesmaximal, characteristic
16C2×#89533C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C2×C7×#124C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C2×#6507C2211yescharacteristic
25C22×#1144C2211yescharacteristic
26C2×#6501C2211yescharacteristic
27C2×D4×Dic7C2211yescharacteristic
28C22×#1142C2211yescharacteristic
29C22×#1131C2211yescharacteristic
30C22×#1131C2211yescharacteristic
31#90371—24no—
32#90371C2218yes—
33#90269—24no—
34#90269C2218yescomplemented
35C2×#6460C2211yescharacteristic
36C2×#6459—21no—
37C2×#6452—21no—
38C2×#6451C2211yescharacteristic
39C2×#6446—21no—
40C2×(C22⋊D7)⋊C4—21no—
41C2×#6442—21no—
42C2×#6440—21no—
43C2×#6435—21no—
44C2×C42×D7C2211yescharacteristic
45C2×#6433C2211yescharacteristic
46C2×C4×Dic14—21no—
47C2×C4×Dic14C2211yescharacteristic
48C7×#464C2218yescomplemented
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6406C2211yescharacteristic
56#89961C2218yescomplemented
57#89954C2218yescomplemented
58#89946C2218yes—
59#89934C2218yescomplemented
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66#89826C2218yescomplemented
67#89794C2218yescomplemented
68C2×#6382C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×C4⋊(C7⋊C8)C2211yescharacteristic
71#89609C2218yescomplemented
72#89601C2218yescomplemented
73#89588C2218yescomplemented
74#89566C2218yescomplemented
75#89552C2218yes—
76#89533C2218yescomplemented
77C2×#3252—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C22×C22⋊D7—21no—
82C23×Dic7—21no—
83C22×C4×D7D411yescharacteristic
84C22×C4×D7D411yescharacteristic
85C22×C4×D7C2311yescharacteristic
86C22×Dic14—21no—
87C22×Dic14C2311yescharacteristic
88C2×C7×Q16—42no—
89C2×C7×Q16C2314yes—
90C2×C7×SD16—42no—
91C2×C7×SD16C2314yes—
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×#124—22no—
95C7×#124C2314yes—
96C4×C7×Q8—22no—
97C4×C7×Q8C2314yes—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4—21no—
102C2×C42×C7—21no—
103C2×C42×C7C2311yescharacteristic
104C2×C22⋊Dic7—21no—
105C2×C22⋊Dic7—21no—
106#6509—22no—
107#6509—22no—
108#6509C2314yes—
109#6509C2314yes—
110Q8×Dic7—22no—
111Q8×Dic7C2314yes—
112#6507—22no—
113#6507C2314yes—
114C2×#1144—42no—
115C2×#1144C2314yes—
116#6501—22no—
117#6501C2314yes—
118D4×Dic7—22no—
119D4×Dic7C2314yes—
120C2×#1142—42no—
121C2×#1142C2314yes—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7C2311yescharacteristic
128C2×C4⋊Dic7C2311yescharacteristic
129C2×C4⋊Dic7C2311yescharacteristic
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
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×C4×Dic7—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7D411yescharacteristic
141C2×C4×Dic7D411yescharacteristic
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C2×#1131—42no—
146C2×#1131—42no—
147C2×#1131C2314yes—
148C2×#1131C2314yes—
149#6460—22no—
150#6460C2314yes—
151#6459—28no—
152#6452—28no—
153#6451—22no—
154#6451C2314yes—
155#6446—28no—
156(C22⋊D7)⋊C4—28no—
157#6442—28no—
158#6440—28no—
159#6435—28no—
160C42×D7D414yes—
161C42×D7C2314yes—
162#6433—22no—
163#6433C2314yes—
164C4×Dic14—22no—
165C4×Dic14—28no—
166C4×Dic14C2314yes—
167C7×C4⋊C8C2314yes—
168C7×#103C2314yes—
169C7×#102C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6409C2314yes—
173#6406C2314yes—
174#6392C2314yes—
175#6391C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#533—71no—
184C2×#529—71no—
185#3252—716no—
186C2×#479—71no—
187C2×#479—71no—
188C2×#477—71no—
189C2×#476—71no—
190C2×#470—71no—
191C2×#470—71no—
192C2×#468—71no—
193C2×#468—71no—
194C2×#464—71no—
195C2×#464D711yescharacteristic, complemented
196C2×#462—71no—
197C2×#461—71no—
198C2×#423—71no—
199C24×C7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8—22no—
207C2×C7×Q8C2412yes—
208C2×C7×Q8C2412yes—
209C2×C7×D4—21no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4C2412yes—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—24no—
220C2×C22⋊D7—44no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—24no—
226C22×Dic7—44no—
227C22×Dic7C2×D411yescharacteristic
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C2×C4×D7—22no—
231C2×C4×D7—22no—
232C2×C4×D7—24no—
233C2×C4×D7—42no—
234C2×C4×D7C2×D412yes—
235C2×C4×D7C2×D414yes—
236C2×C4×D7C2×D414yes—
237C2×C4×D7C2412yes—
238C2×Dic14—22no—
239C2×Dic14—22no—
240C2×Dic14—21no—
241C2×Dic14—24no—
242C2×Dic14—44no—
243C2×Dic14C2412yes—
244C7×Q16—44no—
245C7×SD16—44no—
246C2×C7×C8—22no—
247C2×C7×C8—22no—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—24no—
252C7×C4⋊C4C2412yes—
253C7×C22⋊C4—24no—
254C7×C22⋊C4—24no—
255C42×C7—24no—
256C42×C7C2×D412yes—
257C42×C7C2412yes—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260#1144—44no—
261#1142—44no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272C4⋊Dic7C2412yes—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281C4×Dic7—24no—
282C4×Dic7—24no—
283C4×Dic7C2×D414yes—
284C4×Dic7C2×D412yes—
285C4×Dic7C2×D414yes—
286C4×Dic7C2412yes—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8C2412yes—
290C2×C7⋊C8C2412yes—
291#1131—44no—
292#1131—44no—
293C22×Q16—71no—
294C22×Q16C2×D711yescharacteristic
295C22×SD16—71no—
296C22×SD16C2×D711yescharacteristic
297C22×M16—71no—
298C22×M16—71no—
299#533—78no—
300#533—144no—
301C2×C4⋊Q8—71no—
302C2×C4⋊Q8—71no—
303#529—78no—
304#529—144no—
305C2×#126—141no—
306C2×#125—71no—
307C2×#125—141no—
308C2×#124C2×D711yescharacteristic
309C2×#123—141no—
310C2×C22⋊Q8—71no—
311C2×C22⋊Q8—71no—
312C2×C22⋊Q8—71no—
313C2×C22⋊Q8—141no—
314C2×#121—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8—71no—
317C2×C4×Q8—141no—
318C2×C4×Q8C2×D711yescharacteristic
319C2×C4×D4—71no—
320C2×C4×D4—141no—
321C2×#117—141no—
322C2×#117—141no—
323C22×C42—71no—
324#479—78no—
325#479—78no—
326#477—78no—
327#476—78no—
328#470—78no—
329#470—78no—
330#468—78no—
331#468—78no—
332#464—78no—
333#464C2×D718yescomplemented
334#462—78no—
335#461—78no—
336C2×#107—71no—
337C2×#107—71no—
338C2×#106—71no—
339C2×#106—71no—
340#423—78no—
341C2×C4⋊C8—71no—
342C2×C4⋊C8—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8C2×D711yescharacteristic
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#103—71no—
350C2×#103C2×D711yescharacteristic
351C2×#102—71no—
352C2×#102C2×D711yescharacteristic
353C23×C7—22no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7C22×D412yes—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—22no—
366C7×Q8—42no—
367C7×Q8—42no—
368C7×D4—22no—
369C7×D4—22no—
370C7×D4—42no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7H(5,𝔽2)12yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C22⋊D7—48no—
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×Dic7—48no—
397C2×Dic7#13714yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401C4×D7—24no—
402C4×D7—22no—
403C4×D7—22no—
404C4×D7—28no—
405C4×D7—44no—
406Dic14—22no—
407Dic14—22no—
408Dic14—48no—
409Dic14—42no—
410C7×C8—22no—
411C7×C8—22no—
412C7⋊C8—22no—
413C7⋊C8—22no—
414C22×Q8—71no—
415C22×Q8—141no—
416C22×Q8C22×D711yescharacteristic
417C22×Q8C22×D711yescharacteristic
418C22×D4—141no—
419C22×D4C22×D711yescharacteristic
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—141no—
424C2×Q16—42no—
425C2×Q16—74no—
426C2×Q16—282no—
427C2×Q16C22×D714yes—
428C2×SD16—42no—
429C2×SD16—74no—
430C2×SD16—282no—
431C2×SD16C22×D714yes—
432C2×M16—74no—
433C2×M16—74no—
434C2×M16—282no—
435C2×M16—282no—
436C22×C8—71no—
437C22×C8—71no—
438C22×C8C22×D711yescharacteristic
439C22×C8C22×D711yescharacteristic
440C4⋊Q8—74no—
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443C4⋊Q8—142no—
444#126—148no—
445#125—74no—
446#125—148no—
447#125—142no—
448#124—22no—
449#124C22×D714yes—
450#123—148no—
451C22⋊Q8—74no—
452C22⋊Q8—74no—
453C22⋊Q8—74no—
454C22⋊Q8—142no—
455C22⋊Q8—148no—
456C22⋊Q8—142no—
457C22⋊Q8—142no—
458#121—74no—
459#121—142no—
460C4×Q8—22no—
461C4×Q8—74no—
462C4×Q8—74no—
463C4×Q8—148no—
464C4×Q8—142no—
465C4×Q8—142no—
466C4×Q8C22×D714yes—
467C4×D4—74no—
468C4×D4—142no—
469C4×D4—148no—
470#117—148no—
471#117—148no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4C22×D711yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C42—21no—
495C2×C42—71no—
496C2×C42—71no—
497C2×C42—71no—
498C2×C42—74no—
499C2×C42—74no—
500C2×C42—141no—
501C2×C42—141no—
502C2×C42C22×D711yescharacteristic
503#107—74no—
504#107—74no—
505#106—74no—
506#106—74no—
507C4⋊C8—74no—
508C4⋊C8—74no—
509C4⋊C8—74no—
510C4⋊C8C22×D714yes—
511#103—74no—
512#103—74no—
513#103—74no—
514#103—74no—
515#103—74no—
516#103C22×D714yes—
517#102—74no—
518#102C22×D714yes—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—84no—
523C22×C7#53712yes—
524C22×C7C2×#13712yes—
525C22×C7#57512yes—
526C22×C7C23×D411yescharacteristic
527C2×D7—22no—
528C2×D7—22no—
529C2×D7—22no—
530C2×D7—44no—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#53712yes—
537C4×C7C2×H(5,𝔽2)11yescharacteristic
538C4×C7C2×2−1+411yescharacteristic
539Dic7—22no—
540Dic7—22no—
541Dic7—42no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7C2×#13714yes—
546C24—21no—
547C24—71no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—72no—
555C2×Q8—144no—
556C2×Q8—141no—
557C2×Q8—142no—
558C2×Q8—142no—
559C2×Q8—284no—
560C2×Q8C23×D712yes—
561C2×Q8C23×D712yes—
562C2×D4—21no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—144no—
566C2×D4—284no—
567C2×D4C23×D712yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—71no—
572C22×C4—71no—
573C22×C4—71no—
574C22×C4—74no—
575C22×C4—72no—
576C22×C4—72no—
577C22×C4—74no—
578C22×C4—144no—
579C22×C4—144no—
580C22×C4—142no—
581C22×C4—142no—
582C22×C4—141no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—282no—
587C22×C4—284no—
588C22×C4D4×D711yescharacteristic
589C22×C4D4×D711yescharacteristic
590C22×C4C23×D711yescharacteristic
591Q16—44no—
592Q16—284no—
593SD16—44no—
594SD16—284no—
595M16—284no—
596M16—284no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—72no—
600C2×C8—72no—
601C2×C8—142no—
602C2×C8—142no—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—72no—
608C4⋊C4—72no—
609C4⋊C4—72no—
610C4⋊C4—144no—
611C4⋊C4—144no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—141no—
621C4⋊C4—141no—
622C4⋊C4—141no—
623C4⋊C4C23×D712yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—24no—
632C42—74no—
633C42—72no—
634C42—74no—
635C42—72no—
636C42—144no—
637C42—144no—
638C42D4×D712yes—
639C42C23×D712yes—
640C2×C7—82no—
641C2×C7#325214yescomplemented
642C2×C7C2×#53711yescharacteristic
643C2×C7C22×#13711yescharacteristic
644C2×C7C2×#57511yescharacteristic
645D7—42no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—72no—
651C23—142no—
652C23—142no—
653C23—142no—
654C23C2×D4×D711yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—42no—
660Q8—42no—
661Q8—142no—
662Q8—142no—
663Q8—288no—
664Q8—282no—
665D4—22no—
666D4—22no—
667D4—42no—
668D4—288no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—74no—
678C2×C4—72no—
679C2×C4—72no—
680C2×C4—72no—
681C2×C4—148no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—144no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—284no—
692C2×C4—288no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4C2×D4×D712yes—
698C2×C4C2×D4×D712yes—
699C2×C4C2×D4×D711yescharacteristic
700C2×C4#654812yes—
701C2×C4#655412yes—
702C2×C4C24×D711yescharacteristic
703C8—22no—
704C8—22no—
705C8—142no—
706C8—142no—
707C7C2×#325211yescharacteristic, complemented, Sylow
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—142no—
713C22—142no—
714C22—142no—
715C22—284no—
716C22#9029912yes—
717C22#9045912yes—
718C22D7×#13712yes—
719C22C22×D4×D711yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—74no—
726C4—142no—
727C4—142no—
728C4—282no—
729C4—282no—
730C4—282no—
731C4—282no—
732C4#9029912yes—
733C4C2×#654811yescharacteristic
734C4C2×#655411yescharacteristic
735C2—82no—
736C2—282no—
737C2#1173802214yesdirect product factor
738C2C2×#9029911yescharacteristic
739C2C2×#9045911yescharacteristic
740C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#464C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
hypercenterC2×#464D7
hypocenterC7C2×#3252
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×#90269C2semidirect
3. C2×C7×#464C2semidirect
4. C2×#89961C2semidirect
5. C2×#89954C2semidirect
7. C2×#89934C2semidirect
8. C2×#89826C2semidirect
9. C2×#89794C2semidirect
10. #11738022C2direct (N × H)
11. C2×#89601C2semidirect
12. C2×#89609C2semidirect
13. C2×#89588C2semidirect
14. C2×#89566C2semidirect
16. C2×#89533C2semidirect
34. #90269C22semidirect
48. C7×#464C22semidirect
56. #89961C22semidirect
57. #89954C22semidirect
59. #89934C22semidirect
66. #89826C22semidirect
67. #89794C22semidirect
71. #89609C22semidirect
72. #89601C22semidirect
73. #89588C22semidirect
74. #89566C22semidirect
76. #89533C22semidirect
195. C2×#464D7semidirect
333. #464C2×D7semidirect
641. C2×C7#3252semidirect
707. C7C2×#3252semidirect
737. C2#11738022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903712
C2×#902692
C2×C7×#4642
C2×#899612
C2×#899542
C2×#899462
C2×#899342
C2×#898262
C2×#897942
#117380222
C2×#896012
C2×#896092
C2×#895882
C2×#895662
C2×#895522
C2×#895332
C2×#32527