Finite Group Databasebeta

← C2×#11737236 #14223715

Subgroups — C2×#11737236 #14223715

Order 1792.

1998 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×#90269C211yesmaximal, characteristic, complemented
2C2×#90248C211yesmaximal, characteristic
3C2×C7×#440C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic
5C2×#89939C211yesmaximal, characteristic, complemented
6C2×#89802C211yesmaximal, characteristic, complemented
7C2×#89790C211yesmaximal, characteristic, complemented
8#11737236C2116yesmaximal, direct product factor
9C2×#89659C211yesmaximal, characteristic, complemented
10C2×#89648C211yesmaximal, characteristic, complemented
11C2×#89585C211yesmaximal, characteristic, complemented
12C2×#89569C211yesmaximal, characteristic, complemented
13C2×#89550C211yesmaximal, characteristic
14C2×#89537C211yesmaximal, characteristic, complemented
15C2×#89488C211yesmaximal, characteristic, complemented
16C2×D7×#97C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×C4×C7×D4C2211yescharacteristic
20C2×#6509C2211yescharacteristic
21C2×#6507C2211yescharacteristic
22C22×#1144C2211yescharacteristic
23C2×#6501C2211yescharacteristic
24C2×#6499C2211yescharacteristic
25C22×#1142C2211yescharacteristic
26C2×C4×C22⋊D7—21no—
27C2×#6489—21no—
28C22×Dic28C2211yescharacteristic
29C22×C8×D7C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90269—24no—
32#90269C2218yescomplemented
33#90248—24no—
34#90248C2218yes—
35C2×#6460C2211yescharacteristic
36C2×#6460C2211yescharacteristic
37C2×#6459—21no—
38C2×#6453C2211yescharacteristic
39C2×#6452—21no—
40C2×#6451C2211yescharacteristic
41C2×#6446—21no—
42C2×#6442—21no—
43C2×#6435—21no—
44C2×C42×D7C2211yescharacteristic
45C2×C4×Dic14—21no—
46C2×C4×Dic14C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C7×#440C2218yescomplemented
49C2×C7×#107C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×C7×#97C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55#89943C2218yes—
56#89939C2218yescomplemented
57C2×#6391C2211yescharacteristic
58C2×#6390C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×#6389C2211yescharacteristic
61C2×#6389C2211yescharacteristic
62#89802C2218yescomplemented
63#89790C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6377C2211yescharacteristic
69#89659C2218yescomplemented
70#89648C2218yescomplemented
71#89585C2218yescomplemented
72#89569C2218yescomplemented
73#89550C2218yes—
74#89537C2218yescomplemented
75#89488C2218yescomplemented
76D7×#97C2218yescomplemented
77C2×#3181—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C22×C4×D7D411yescharacteristic
83C22×C4×D7D411yescharacteristic
84C22×C4×D7C2311yescharacteristic
85C22×Dic14—21no—
86C22×Dic14C2311yescharacteristic
87C22×Dic14C2311yescharacteristic
88C2×C7×SD16—24no—
89C2×C7×SD16C2314yes—
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C4×C7×Q8—22no—
93C4×C7×Q8C2314yes—
94C4×C7×D4—22no—
95C4×C7×D4C2314yes—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C42×C7—21no—
101C2×C42×C7C2311yescharacteristic
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7—21no—
104C2×C22⋊Dic7—21no—
105#6509—22no—
106#6509C2314yes—
107#6507—22no—
108#6507C2314yes—
109C2×#1144—24no—
110C2×#1144C2314yes—
111#6501—22no—
112#6501C2314yes—
113#6499—22no—
114#6499C2314yes—
115C2×#1142—24no—
116C2×#1142C2314yes—
117C4×C22⋊D7—28no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121#6489—28no—
122C2×C4⋊Dic7—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7D411yescharacteristic
137C2×C4×Dic7D411yescharacteristic
138C2×C4×Dic7C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C2×Dic28—24no—
142C2×Dic28C2314yes—
143C2×C8×D7—24no—
144C2×C8×D7—24no—
145C2×C8×D7C2314yes—
146C2×C8×D7C2314yes—
147#6460—22no—
148#6460—22no—
149#6460C2314yes—
150#6460C2314yes—
151#6459—28no—
152#6453—22no—
153#6453C2314yes—
154#6452—28no—
155#6451—22no—
156#6451C2314yes—
157#6446—28no—
158#6442—28no—
159#6435—28no—
160C42×D7D414yes—
161C42×D7C2314yes—
162C4×Dic14—22no—
163C4×Dic14—22no—
164C4×Dic14—28no—
165C4×Dic14C2314yes—
166C4×Dic14C2314yes—
167C7×#107C2314yes—
168C7×#103C2314yes—
169C7×#102C2314yes—
170C7×#97C2314yes—
171#6409C2314yes—
172#6406C2314yes—
173#6391C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176#6389C2314yes—
177#6389C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182#6377C2314yes—
183C2×#533—71no—
184C2×#529—71no—
185#3181—716no—
186C2×#501—71no—
187C2×#497—71no—
188C2×#491—71no—
189C2×#489—71no—
190C2×#467—71no—
191C2×#467—71no—
192C2×#465—71no—
193C2×#465—71no—
194C2×#441—71no—
195C2×#441—71no—
196C2×#440—71no—
197C2×#440D711yescharacteristic, complemented
198C22×#97—71no—
199C24×C7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—22no—
203C2×C7×Q8—22no—
204C2×C7×Q8C2412yes—
205C2×C7×D4—21no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4C2412yes—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—24no—
213C22×C4×C7—44no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2411yescharacteristic
217C2×C22⋊D7—24no—
218C2×C22⋊D7—44no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7C2×D411yescharacteristic
224C22×Dic7C2×D411yescharacteristic
225C22×Dic7C2×D411yescharacteristic
226C2×C4×D7—24no—
227C2×C4×D7—22no—
228C2×C4×D7—22no—
229C2×C4×D7—42no—
230C2×C4×D7C2×D412yes—
231C2×C4×D7C2×D414yes—
232C2×C4×D7C2×D414yes—
233C2×C4×D7C2412yes—
234C2×Dic14—22no—
235C2×Dic14—22no—
236C2×Dic14—22no—
237C2×Dic14—22no—
238C2×Dic14—21no—
239C2×Dic14—21no—
240C2×Dic14—24no—
241C2×Dic14—44no—
242C2×Dic14C2412yes—
243C2×Dic14C2412yes—
244C7×SD16—28no—
245C2×C7×C8—22no—
246C2×C7×C8#4114yes—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C22⋊C4—24no—
255C42×C7—24no—
256C42×C7C2×D412yes—
257C42×C7C2412yes—
258C22⋊Dic7—24no—
259C22⋊Dic7—24no—
260C22⋊Dic7—24no—
261#1144—28no—
262#1142—28no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7—24no—
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—
280C4×Dic7—24no—
281C4×Dic7—24no—
282C4×Dic7C2×D414yes—
283C4×Dic7C2×D412yes—
284C4×Dic7C2×D414yes—
285C4×Dic7C2412yes—
286C2×C7⋊C8—22no—
287C2×C7⋊C8#4114yes—
288C2×C7⋊C8C2412yes—
289C2×C7⋊C8C2412yes—
290Dic28—28no—
291C8×D7—28no—
292C8×D7—28no—
293C22×Q16—71no—
294C22×Q16—71no—
295C22×SD16—71no—
296C22×SD16C2×D711yescharacteristic
297C23×C8—71no—
298C23×C8—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×#124—71no—
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—141no—
320C2×C4×D4C2×D711yescharacteristic
321C2×#117—141no—
322C2×#117—141no—
323C22×C42—71no—
324#501—78no—
325#497—78no—
326#491—78no—
327#489—78no—
328#467—78no—
329#467—78no—
330#465—78no—
331#465—78no—
332#441—78no—
333#441—78no—
334#440—78no—
335#440C2×D718yescomplemented
336C2×#107—71no—
337C2×#107C2×D711yescharacteristic
338C2×#106—71no—
339C2×#106—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×#103—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103C2×D711yescharacteristic
346C2×#102—71no—
347C2×#102C2×D711yescharacteristic
348C2×#97—71no—
349C2×#97—71no—
350C2×#97—71no—
351C2×#97—78no—
352C2×#97C2×D711yescharacteristic
353C23×C7—22no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—22no—
360C22×D7#13714yes—
361C22×D7C22×D412yes—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—42no—
365C7×D4—22no—
366C7×D4—22no—
367C7×D4—42no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—48no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D411yescharacteristic
380C2×C4×C7C2×#4112yes—
381C2×C4×C7C2×#4112yes—
382C2×C4×C7C2511yescharacteristic
383C22⋊D7—48no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—42no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7C22×D412yes—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398C4×D7—28no—
399C4×D7—24no—
400C4×D7—22no—
401C4×D7—22no—
402C4×D7—44no—
403Dic14—22no—
404Dic14—22no—
405Dic14—22no—
406Dic14—22no—
407Dic14—48no—
408Dic14—42no—
409Dic14—42no—
410C7×C8—22no—
411C7×C8C2×#4114yes—
412C7⋊C8—22no—
413C7⋊C8C2×#4114yes—
414C22×Q8—71no—
415C22×Q8—71no—
416C22×Q8—141no—
417C22×Q8C22×D711yescharacteristic
418C22×D4—141no—
419C22×D4C22×D711yescharacteristic
420C23×C4—21no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—71no—
424C2×Q16—74no—
425C2×Q16—74no—
426C2×Q16—144no—
427C2×Q16—144no—
428C2×SD16—24no—
429C2×SD16—74no—
430C2×SD16—144no—
431C2×SD16C22×D714yes—
432C22×C8—71no—
433C22×C8—71no—
434C22×C8—74no—
435C22×C8—74no—
436C22×C8—144no—
437C22×C8—144no—
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—142no—
447#125—148no—
448#124—74no—
449#124—142no—
450#123—148no—
451C22⋊Q8—74no—
452C22⋊Q8—74no—
453C22⋊Q8—74no—
454C22⋊Q8—142no—
455C22⋊Q8—142no—
456C22⋊Q8—148no—
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—22no—
468C4×D4—148no—
469C4×D4C22×D714yes—
470#117—148no—
471#117—148no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—71no—
474C2×C4⋊C4—71no—
475C2×C4⋊C4—141no—
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⋊C4C22×D711yescharacteristic
486C2×C4⋊C4C22×D711yescharacteristic
487C2×C22⋊C4—21no—
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—71no—
497C2×C42—71no—
498C2×C42—74no—
499C2×C42—74no—
500C2×C42—141no—
501C2×C42—141no—
502C2×C42C22×D711yescharacteristic
503#107—74no—
504#107C22×D714yes—
505#106—74no—
506#106—74no—
507#103—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103C22×D714yes—
513#102—74no—
514#102C22×D714yes—
515#97—74no—
516#97—74no—
517#97—74no—
518#97C22×D714yes—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—84no—
523C22×C7#53212yes—
524C22×C7C2×#13712yes—
525C22×C7#57512yes—
526C22×C7C23×D411yescharacteristic
527C2×D7—28no—
528C2×D7—22no—
529C2×D7—22no—
530C2×D7C2×#13714yes—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#53212yes—
537C4×C7C22×#4111yescharacteristic
538C4×C7C22×#4111yescharacteristic
539Dic7—22no—
540Dic7—22no—
541Dic7—22no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7—42no—
546C24—21no—
547C24—71no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—72no—
552C2×Q8—72no—
553C2×Q8—144no—
554C2×Q8—141no—
555C2×Q8—141no—
556C2×Q8—142no—
557C2×Q8—142no—
558C2×Q8—142no—
559C2×Q8—142no—
560C2×Q8—284no—
561C2×Q8C23×D712yes—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—144no—
566C2×D4—284no—
567C2×D4C23×D712yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—71no—
574C22×C4—71no—
575C22×C4—71no—
576C22×C4—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—74no—
580C22×C4—144no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—282no—
588C22×C4D4×D711yescharacteristic
589C22×C4D4×D711yescharacteristic
590C22×C4C23×D711yescharacteristic
591Q16—148no—
592Q16—148no—
593SD16—28no—
594SD16—148no—
595C2×C8—22no—
596C2×C8—74no—
597C2×C8—72no—
598C2×C8—72no—
599C2×C8—148no—
600C2×C8—142no—
601C2×C8—148no—
602C2×C8#115714yes—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
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⋊C4C23×D712yes—
623C4⋊C4C23×D712yes—
624C22⋊C4—24no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—24no—
632C42—74no—
633C42—74no—
634C42—72no—
635C42—72no—
636C42—144no—
637C42—144no—
638C42D4×D712yes—
639C42C23×D712yes—
640C2×C7—82no—
641C2×C7#318114yescomplemented
642C2×C7C2×#53211yescharacteristic
643C2×C7C22×#13711yescharacteristic
644C2×C7C2×#57511yescharacteristic
645D7—24no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—74no—
651C23—72no—
652C23—142no—
653C23—142no—
654C23C2×D4×D711yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—142no—
659Q8—142no—
660Q8—142no—
661Q8—142no—
662Q8—288no—
663Q8—282no—
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—48no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—72no—
679C2×C4—72no—
680C2×C4—72no—
681C2×C4—148no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—142no—
685C2×C4—144no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—284no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4C2×#115712yes—
698C2×C4C2×D4×D712yes—
699C2×C4C2×D4×D712yes—
700C2×C4C2×D4×D711yescharacteristic
701C2×C4D7×#4112yes—
702C2×C4C24×D711yescharacteristic
703C8—22no—
704C8—74no—
705C8—142no—
706C8C2×#115714yes—
707C7C2×#318111yescharacteristic, complemented, Sylow
708C22—42no—
709C22—42no—
710C22—42no—
711C22—74no—
712C22—84no—
713C22—142no—
714C22—142no—
715C22—148no—
716C22#9023912yes—
717C22#9046412yes—
718C22D7×#13712yes—
719C22C22×D4×D711yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—142no—
726C4—142no—
727C4—142no—
728C4—282no—
729C4—282no—
730C4—282no—
731C4—282no—
732C4#9023912yes—
733C4C22×#115711yescharacteristic
734C4C2×D7×#4111yescharacteristic
735C2—82no—
736C2—144no—
737C2#1173723614yesdirect product factor
738C2C2×#9023911yescharacteristic
739C2C2×#9046411yescharacteristic
740C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#440C2
socleC23×C7C22×D4
prime radicalC2×#6501C22
hypercenterC2×#440D7
hypocenterC7C2×#3181
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#90269C2semidirect
3. C2×C7×#440C2semidirect
5. C2×#89939C2semidirect
6. C2×#89802C2semidirect
7. C2×#89790C2semidirect
8. #11737236C2direct (N × H)
9. C2×#89659C2semidirect
10. C2×#89648C2semidirect
11. C2×#89585C2semidirect
12. C2×#89569C2semidirect
14. C2×#89537C2semidirect
15. C2×#89488C2semidirect
16. C2×D7×#97C2semidirect
32. #90269C22semidirect
48. C7×#440C22semidirect
56. #89939C22semidirect
62. #89802C22semidirect
63. #89790C22semidirect
69. #89659C22semidirect
70. #89648C22semidirect
71. #89585C22semidirect
72. #89569C22semidirect
74. #89537C22semidirect
75. #89488C22semidirect
76. D7×#97C22semidirect
197. C2×#440D7semidirect
335. #440C2×D7semidirect
641. C2×C7#3181semidirect
707. C7C2×#3181semidirect
737. C2#11737236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902692
C2×#902482
C2×C7×#4402
C2×#899432
C2×#899392
C2×#898022
C2×#897902
#117372362
C2×#896592
C2×#896482
C2×#895852
C2×#895692
C2×#895502
C2×#895372
C2×#894882
C2×D7×#972
C2×#31817