Finite Group Databasebeta

← C2×#11736672 #14232392

Subgroups — C2×#11736672 #14232392

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90223C211yesmaximal, characteristic, complemented
2C2×#90205C211yesmaximal, characteristic, complemented
3C2×C7×#428C211yesmaximal, characteristic, complemented
4C2×#89907C211yesmaximal, characteristic, complemented
5C2×#89899C211yesmaximal, characteristic, complemented
6C2×#89775C211yesmaximal, characteristic, complemented
7C2×#89739C211yesmaximal, characteristic, complemented
8#11736672C2116yesmaximal, direct product factor
9C2×#89662C211yesmaximal, characteristic, complemented
10C2×#89655C211yesmaximal, characteristic, complemented
11C2×#89657C211yesmaximal, characteristic, complemented
12C2×#89648C211yesmaximal, characteristic, complemented
13C2×#89643C211yesmaximal, characteristic, complemented
14C2×#89638C211yesmaximal, characteristic, complemented
15C2×#89632C211yesmaximal, characteristic, complemented
16C2×#89641C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C2×C7×#117C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C2×#6493—21no—
21C2×#6493C2211yescharacteristic
22C2×#6493C2211yescharacteristic
23C2×C4×C22⋊D7—21no—
24C2×C4×C22⋊D7C2211yescharacteristic
25C22×D56C2211yescharacteristic
26C22×C8×D7C2211yescharacteristic
27#90223—24no—
28#90223C2218yescomplemented
29#90205—24no—
30#90205C2218yescomplemented
31C2×#6461—21no—
32C2×#6458C2211yescharacteristic
33C2×#6458C2211yescharacteristic
34C2×#6457—21no—
35C2×#6456C2211yescharacteristic
36C2×#6456C2211yescharacteristic
37C2×#6455C2211yescharacteristic
38C2×#6455C2211yescharacteristic
39C2×#6453C2211yescharacteristic
40C2×#6451C2211yescharacteristic
41C2×#6448—21no—
42C2×#6447—21no—
43C2×#6438—21no—
44C2×#6435—21no—
45C7×#428C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#107C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#106C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51#89907C2218yescomplemented
52#89899C2218yescomplemented
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×#6391C2211yescharacteristic
57C2×#6389C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59#89775C2218yescomplemented
60#89739C2218yescomplemented
61C2×#6383C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89662C2218yescomplemented
70#89657C2218yescomplemented
71#89655C2218yescomplemented
72#89648C2218yescomplemented
73#89643C2218yescomplemented
74#89641C2218yescomplemented
75#89638C2218yescomplemented
76#89632C2218yescomplemented
77C2×#3347—71nomaximal, Sylow
78C23×C4×C7—21no—
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C22×D28—21no—
84C22×D28—21no—
85C22×D28C2311yescharacteristic
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7C2311yescharacteristic
90C22×Dic14—21no—
91C2×C7×M16—24no—
92C2×C7×M16C2314yes—
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×#117—22no—
96C7×#117C2314yes—
97C2×C7×C4⋊C4—21no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C4⋊C4C2314yes—
104C2×C7×C22⋊C4—21no—
105C2×C42×C7—21no—
106C2×C22⋊Dic7D411yescharacteristic
107#6493—22no—
108#6493—22no—
109#6493—28no—
110#6493C2314yes—
111#6493C2314yes—
112C4×C22⋊D7—28no—
113C4×C22⋊D7D414yes—
114C4×C22⋊D7C2314yes—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4D411yescharacteristic
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4D411yescharacteristic
130C2×C4×Dic7—21no—
131C2×C4×Dic7—21no—
132C2×C4×Dic7C2311yescharacteristic
133C22×C7⋊C8C2311yescharacteristic
134C22×C7⋊C8C2311yescharacteristic
135C2×D56—24no—
136C2×D56C2314yes—
137C2×C8×D7—24no—
138C2×C8×D7C2314yes—
139#6461—28no—
140#6458—22no—
141#6458—22no—
142#6458C2314yes—
143#6458C2314yes—
144#6457—28no—
145#6456—22no—
146#6456—22no—
147#6456C2314yes—
148#6456C2314yes—
149#6455—22no—
150#6455—22no—
151#6455C2314yes—
152#6455C2314yes—
153#6453—22no—
154#6453C2314yes—
155#6451—22no—
156#6451C2314yes—
157#6448—28no—
158#6447—28no—
159#6438—28no—
160#6435—28no—
161C7×#107C2314yes—
162C7×#107C2314yes—
163C7×#106C2314yes—
164C7×#106C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6395C2314yes—
167#6395C2314yes—
168(C2×D7)⋊C8C2314yes—
169#6391C2314yes—
170#6389C2314yes—
171Dic7⋊C8C2314yes—
172#6383C2314yes—
173#6383C2314yes—
174#6383C2314yes—
175#6383C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#555—71no—
181C2×#553—71no—
182#3347—716no—
183C2×#501—71no—
184C2×#482—71no—
185C2×#482—71no—
186C2×#482—71no—
187C2×#480—71no—
188C2×#478—71no—
189C2×#474—71no—
190C2×#469—71no—
191C2×#466—71no—
192C2×#442—71no—
193C2×#435—71no—
194C2×#428D711yescharacteristic, complemented
195C2×#427—71no—
196C24×C7C2×D411yescharacteristic
197C23×D7—21no—
198C23×D7—21no—
199C23×D7C2×D411yescharacteristic
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—24no—
207C22×C4×C7—82no—
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2411yescharacteristic
212C2×C22⋊D7—24no—
213C2×C22⋊D7—24no—
214C2×C22⋊D7—42no—
215C2×C22⋊D7—44no—
216C2×C22⋊D7—82no—
217C2×C22⋊D7C2×D414yes—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7C2×D411yescharacteristic
221C22×Dic7C2×D411yescharacteristic
222C22×Dic7C2×D411yescharacteristic
223C2×D28—22no—
224C2×D28—22no—
225C2×D28—22no—
226C2×D28—22no—
227C2×D28—21no—
228C2×D28—21no—
229C2×D28—24no—
230C2×D28—24no—
231C2×D28—82no—
232C2×D28—82no—
233C2×D28C2412yes—
234C2×D28C2412yes—
235C2×C4×D7—22no—
236C2×C4×D7—22no—
237C2×C4×D7—24no—
238C2×C4×D7—24no—
239C2×C4×D7—44no—
240C2×C4×D7—82no—
241C2×C4×D7C2×D412yes—
242C2×C4×D7C2412yes—
243C2×Dic14—24no—
244C2×Dic14—82no—
245C7×M16—28no—
246C2×C7×C8—22no—
247C2×C7×C8#4114yes—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4C2412yes—
256C7×C4⋊C4C2412yes—
257C7×C4⋊C4C2412yes—
258C7×C4⋊C4C2412yes—
259C7×C22⋊C4—24no—
260C42×C7—24no—
261C22⋊Dic7C2×D414yes—
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—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4C2×D414yes—
271C4⋊Dic7—21no—
272C4⋊Dic7—21no—
273C4⋊Dic7—24no—
274C4⋊Dic7C2412yes—
275C4⋊Dic7C2412yes—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4C2×D414yes—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7C2×D412yes—
282C4×Dic7C2412yes—
283C2×C7⋊C8—22no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8C2412yes—
286C2×C7⋊C8C2412yes—
287D56—28no—
288C8×D7—28no—
289C22×D8—71no—
290C22×M16C2×D711yescharacteristic
291C23×C8—71no—
292#555—78no—
293#555—144no—
294#553—78no—
295#553—144no—
296C2×C4⋊Q8—71no—
297C2×#126—141no—
298C2×#125—71no—
299C2×#124—141no—
300C2×#124—141no—
301C2×#123—141no—
302C2×#121—71no—
303C2×#121—71no—
304C2×#121—71no—
305C2×#121—71no—
306C2×#121—141no—
307C2×#121—141no—
308C2×C4×D4—71no—
309C2×C4×D4—71no—
310C2×C4×D4—71no—
311C2×C4×D4—141no—
312C2×#117—71no—
313C2×#117—71no—
314C2×#117—141no—
315C2×#117C2×D711yescharacteristic
316C22×C4⋊C4C2×D711yescharacteristic
317#501—78no—
318#482—78no—
319#482—78no—
320#482—78no—
321#480—78no—
322#478—78no—
323#474—78no—
324#469—78no—
325#466—78no—
326#442—78no—
327#435—78no—
328#428C2×D718yescomplemented
329#427—78no—
330C2×#107—71no—
331C2×#107—71no—
332C2×#107—71no—
333C2×#107C2×D711yescharacteristic
334C2×#107C2×D711yescharacteristic
335C2×#106—71no—
336C2×#106—71no—
337C2×#106C2×D711yescharacteristic
338C2×#106C2×D711yescharacteristic
339C2×C4⋊C8—71no—
340C2×#102—71no—
341C2×#102—71no—
342C2×#102—71no—
343C2×#102—71no—
344C2×#102—71no—
345C2×#102—71no—
346C2×C22⋊C8—71no—
347C2×C22⋊C8—71no—
348C2×#97—71no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7C22×D412yes—
353C23×C7C22×D411yescharacteristic
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—42no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7—42no—
364C22×D7—42no—
365C22×D7C22×D412yes—
366C2×C4×C7—22no—
367C2×C4×C7—24no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—84no—
379C2×C4×C7C22×D412yes—
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C2×#4112yes—
382C2×C4×C72−1+412yes—
383C2×C4×C7C2511yescharacteristic
384C22⋊D7—44no—
385C22⋊D7—48no—
386C22⋊D7—84no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7C22×D412yes—
395C2×Dic7C22×D412yes—
396C2×Dic7C22×D412yes—
397D28—22no—
398D28—22no—
399D28—22no—
400D28—22no—
401D28—42no—
402D28—42no—
403D28—84no—
404D28—84no—
405C4×D7—24no—
406C4×D7—22no—
407C4×D7—22no—
408C4×D7—48no—
409C4×D7—84no—
410Dic14—84no—
411C7×C8—22no—
412C7×C8C2×#4114yes—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C22×Q8—141no—
416C22×D4—71no—
417C22×D4—71no—
418C22×D4—71no—
419C22×D4—141no—
420C22×D4—141no—
421C22×D4—141no—
422C22×D4—141no—
423C23×C4—21no—
424C23×C4—71no—
425C23×C4—141no—
426C23×C4—141no—
427C23×C4C22×D711yescharacteristic
428C2×D8—74no—
429C2×D8—144no—
430C2×M16—24no—
431C2×M16C22×D714yes—
432C22×C8—71no—
433C22×C8—71no—
434C22×C8—74no—
435C22×C8—144no—
436C22×C8C22×D711yescharacteristic
437C22×C8C22×D711yescharacteristic
438C4⋊Q8—74no—
439C4⋊Q8—142no—
440#126—148no—
441#125—74no—
442#125—142no—
443#124—148no—
444#124—148no—
445#123—148no—
446#121—74no—
447#121—74no—
448#121—74no—
449#121—74no—
450#121—148no—
451#121—142no—
452#121—142no—
453#121—148no—
454#121—142no—
455#121—142no—
456C4×D4—74no—
457C4×D4—74no—
458C4×D4—74no—
459C4×D4—74no—
460C4×D4—142no—
461C4×D4—142no—
462C4×D4—148no—
463#117—22no—
464#117—74no—
465#117—74no—
466#117—148no—
467#117—142no—
468#117—142no—
469#117C22×D714yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—71no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—141no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4C22×D711yescharacteristic
479C2×C4⋊C4C22×D711yescharacteristic
480C2×C4⋊C4C22×D714yes—
481C2×C4⋊C4C22×D711yescharacteristic
482C2×C4⋊C4C22×D711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—71no—
485C2×C22⋊C4—71no—
486C2×C22⋊C4—141no—
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
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—141no—
497C2×C42—141no—
498#107—74no—
499#107—74no—
500#107—74no—
501#107C22×D714yes—
502#107C22×D714yes—
503#106—74no—
504#106—74no—
505#106C22×D714yes—
506#106C22×D714yes—
507C4⋊C8—74no—
508#102—74no—
509#102—74no—
510#102—74no—
511#102—74no—
512#102—74no—
513#102—74no—
514C22⋊C8—74no—
515C22⋊C8—74no—
516#97—74no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—44no—
521C22×C7#54712yes—
522C22×C7#57512yes—
523C22×C7#57612yes—
524C22×C7C23×D411yescharacteristic
525C2×D7—22no—
526C2×D7—22no—
527C2×D7—22no—
528C2×D7—44no—
529C2×D7—42no—
530C2×D7—42no—
531C2×D7—42no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—42no—
535C2×D7—84no—
536C2×D7—84no—
537C4×C7—22no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7#54712yes—
543C4×C7C22×#4111yescharacteristic
544C4×C7C2×2−1+411yescharacteristic
545Dic7—22no—
546Dic7—22no—
547Dic7—22no—
548Dic7—42no—
549Dic7—42no—
550C24—71no—
551C24—141no—
552C24—141no—
553C24D4×D711yescharacteristic
554C2×Q8—144no—
555C2×Q8—562no—
556C2×D4—74no—
557C2×D4—72no—
558C2×D4—72no—
559C2×D4—144no—
560C2×D4—144no—
561C2×D4—144no—
562C2×D4—144no—
563C2×D4—142no—
564C2×D4—142no—
565C2×D4—141no—
566C2×D4—141no—
567C2×D4—142no—
568C2×D4—142no—
569C2×D4—282no—
570C2×D4—284no—
571C2×D4—562no—
572C2×D4—562no—
573C2×D4—562no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—71no—
582C22×C4—71no—
583C22×C4—71no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—82no—
587C22×C4—144no—
588C22×C4—144no—
589C22×C4—142no—
590C22×C4—142no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—284no—
594C22×C4—562no—
595C22×C4D4×D712yes—
596C22×C4D4×D711yescharacteristic
597C22×C4C23×D712yes—
598C22×C4C23×D711yescharacteristic
599D8—148no—
600M16—28no—
601C2×C8—22no—
602C2×C8—72no—
603C2×C8—72no—
604C2×C8—142no—
605C2×C8—142no—
606C2×C8—148no—
607C2×C8#115714yes—
608C2×C8C23×D712yes—
609C2×C8C23×D712yes—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—74no—
616C4⋊C4—72no—
617C4⋊C4—72no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—144no—
621C4⋊C4—141no—
622C4⋊C4—141no—
623C4⋊C4C23×D712yes—
624C4⋊C4C23×D712yes—
625C4⋊C4C23×D712yes—
626C4⋊C4C23×D712yes—
627C22⋊C4—24no—
628C22⋊C4—74no—
629C22⋊C4—74no—
630C22⋊C4—144no—
631C22⋊C4—144no—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C42—24no—
639C42—72no—
640C42—72no—
641C42—144no—
642C42—144no—
643C2×C7—42no—
644C2×C7#334714yescomplemented
645C2×C7C2×#54711yescharacteristic
646C2×C7C2×#57511yescharacteristic
647C2×C7C2×#57611yescharacteristic
648D7—42no—
649D7—82no—
650D7—82no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—72no—
655C23—142no—
656C23—142no—
657C23—142no—
658C23—142no—
659C23—142no—
660C23—282no—
661C23—282no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23—282no—
666C23C2×D4×D712yes—
667C23C2×D4×D711yescharacteristic
668Q8—564no—
669D4—142no—
670D4—142no—
671D4—142no—
672D4—142no—
673D4—284no—
674D4—288no—
675D4—282no—
676D4—282no—
677D4—564no—
678D4—564no—
679D4—564no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—72no—
693C2×C4—72no—
694C2×C4—72no—
695C2×C4—84no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—144no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—288no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4—564no—
708C2×C4C2×#115712yes—
709C2×C4C2×D4×D712yes—
710C2×C4C2×D4×D711yescharacteristic
711C2×C4#655112yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—142no—
715C8—142no—
716C8C2×#115714yes—
717C7C2×#334711yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—142no—
723C22—142no—
724C22—142no—
725C22—284no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—282no—
730C22—282no—
731C22—282no—
732C22—564no—
733C22—564no—
734C22#9019812yes—
735C22#9046512yes—
736C22#9046812yes—
737C22C22×D4×D711yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—142no—
744C4—142no—
745C4—142no—
746C4—282no—
747C4—282no—
748C4#9019812yes—
749C4C22×#115711yescharacteristic
750C4C2×#655111yescharacteristic
751C2—42no—
752C2—282no—
753C2—562no—
754C2—562no—
755C2#1173667214yesdirect product factor
756C2C2×#9019811yescharacteristic
757C2C2×#9046511yescharacteristic
758C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#428C2
socleC23×C7C22×D4
hypercenterC2×#428D7
hypocenterC7C2×#3347
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#90223C2semidirect
2. C2×#90205C2semidirect
3. C2×C7×#428C2semidirect
4. C2×#89907C2semidirect
5. C2×#89899C2semidirect
6. C2×#89775C2semidirect
7. C2×#89739C2semidirect
8. #11736672C2direct (N × H)
9. C2×#89662C2semidirect
10. C2×#89655C2semidirect
11. C2×#89657C2semidirect
12. C2×#89648C2semidirect
13. C2×#89643C2semidirect
14. C2×#89638C2semidirect
15. C2×#89632C2semidirect
16. C2×#89641C2semidirect
28. #90223C22semidirect
30. #90205C22semidirect
45. C7×#428C22semidirect
51. #89907C22semidirect
52. #89899C22semidirect
59. #89775C22semidirect
60. #89739C22semidirect
69. #89662C22semidirect
70. #89657C22semidirect
71. #89655C22semidirect
72. #89648C22semidirect
73. #89643C22semidirect
74. #89641C22semidirect
75. #89638C22semidirect
76. #89632C22semidirect
194. C2×#428D7semidirect
328. #428C2×D7semidirect
644. C2×C7#3347semidirect
717. C7C2×#3347semidirect
755. C2#11736672direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902232
C2×#902052
C2×C7×#4282
C2×#899072
C2×#898992
C2×#897752
C2×#897392
#117366722
C2×#896622
C2×#896552
C2×#896572
C2×#896482
C2×#896432
C2×#896382
C2×#896322
C2×#896412
C2×#33477