Finite Group Databasebeta

← C2×#11737278 #14221997

Subgroups — C2×#11737278 #14221997

Order 1792.

2118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90269C211yesmaximal, characteristic
2C2×C4×Q8×D7C211yesmaximal, characteristic
3C2×C7×#441C211yesmaximal, characteristic, complemented
4C2×#89958C211yesmaximal, characteristic
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89802C211yesmaximal, characteristic, complemented
7C2×#89802C211yesmaximal, characteristic, complemented
8#11737278C2116yesmaximal, direct product factor
9C2×#89626C211yesmaximal, characteristic, complemented
10C2×#89634C211yesmaximal, characteristic
11C2×#89565C211yesmaximal, characteristic, complemented
12C2×#89577C211yesmaximal, characteristic
13C2×#89580C211yesmaximal, characteristic
14C2×#89563C211yesmaximal, characteristic, complemented
15C2×#89488C211yesmaximal, characteristic, complemented
16C2×#89477C211yesmaximal, characteristic
17C22×Q8×D7C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6507C2211yescharacteristic
24C22×#1144C2211yescharacteristic
25C22×#1144C2211yescharacteristic
26C22×Dic28C2211yescharacteristic
27#90269—24no—
28#90269C2218yes—
29C4×Q8×D7—24no—
30C4×Q8×D7C2218yes—
31C2×#6460C2211yescharacteristic
32C2×#6459—21no—
33C2×D7×C4⋊C4—21no—
34C2×D7×C4⋊C4C2211yescharacteristic
35C2×#6452—21no—
36C2×#6451C2211yescharacteristic
37C2×#6450—21no—
38C2×#6450C2211yescharacteristic
39C2×#6435—21no—
40C2×C42×D7—21no—
41C2×C42×D7C2211yescharacteristic
42C2×C4×Dic14—21no—
43C2×C4×Dic14—21no—
44C2×C4×Dic14C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C7×#441C2218yescomplemented
47C2×C7×#106C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53#89958C2218yes—
54#89954C2218yescomplemented
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×#6391C2211yescharacteristic
58C2×#6390C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62#89802C2218yescomplemented
63#89802C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6377C2211yescharacteristic
69#89634C2218yes—
70#89626C2218yescomplemented
71#89580C2218yes—
72#89577C2218yes—
73#89565C2218yescomplemented
74#89563C2218yescomplemented
75#89488C2218yescomplemented
76#89477C2218yes—
77C2×#3113—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C2×Q8×D7—24no—
81C2×Q8×D7—22no—
82C2×Q8×D7—24no—
83C2×Q8×D7C2314yes—
84C22×C4×D7—21no—
85C22×C4×D7—21no—
86C22×C4×D7D411yescharacteristic
87C22×C4×D7D411yescharacteristic
88C22×C4×D7C2311yescharacteristic
89C22×Dic14—21no—
90C22×Dic14—21no—
91C22×Dic14C2311yescharacteristic
92C22×Dic14C2311yescharacteristic
93C2×C7×Q16—24no—
94C2×C7×Q16C2314yes—
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C4×C7×Q8—22no—
98C4×C7×Q8—22no—
99C4×C7×Q8C2314yes—
100C4×C7×Q8C2314yes—
101C2×C7×C4⋊C4—21no—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4C2311yescharacteristic
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C42×C7—21no—
106C2×C42×C7—21no—
107C2×C42×C7C2311yescharacteristic
108#6509—22no—
109#6509C2314yes—
110Q8×Dic7—22no—
111Q8×Dic7C2314yes—
112#6507—22no—
113#6507C2314yes—
114C2×#1144—24no—
115C2×#1144—24no—
116C2×#1144C2314yes—
117C2×#1144C2314yes—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×C4⋊Dic7—21no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7C2311yescharacteristic
123C2×C4⋊Dic7C2311yescharacteristic
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×C4×Dic7—21no—
133C2×C4×Dic7—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—
143#6460—22no—
144#6460C2314yes—
145#6459—28no—
146D7×C4⋊C4—28no—
147D7×C4⋊C4—22no—
148D7×C4⋊C4C2314yes—
149#6452—28no—
150#6451—22no—
151#6451C2314yes—
152#6450—28no—
153#6450—22no—
154#6450C2314yes—
155#6435—28no—
156C42×D7—28no—
157C42×D7D414yes—
158C42×D7C2314yes—
159C4×Dic14—22no—
160C4×Dic14—22no—
161C4×Dic14—28no—
162C4×Dic14—28no—
163C4×Dic14C2314yes—
164C4×Dic14C2314yes—
165C7×#106C2314yes—
166C7×#103C2314yes—
167C7×#103C2314yes—
168C7×#97C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171(C2×D7)⋊C8C2314yes—
172(C2×D7)⋊C8C2314yes—
173#6391C2314yes—
174#6390C2314yes—
175#6390C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178#6384C2314yes—
179#6384C2314yes—
180#6382C2314yes—
181#6382C2314yes—
182#6377C2314yes—
183C2×#533—71no—
184C22×C4×Q8—71no—
185#3113—716no—
186C2×#483—71no—
187C2×#483—71no—
188C2×#475—71no—
189C2×#475—71no—
190C2×#462—71no—
191C2×#462—71no—
192C2×#451—71no—
193C2×#451—71no—
194C2×#441—71no—
195C2×#441—71no—
196C2×#441—71no—
197C2×#441D711yescharacteristic, complemented
198C2×#432—71no—
199C23×D7C2×D411yescharacteristic
200C2×C7×Q8—21no—
201C2×C7×Q8—21no—
202C2×C7×Q8—22no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8#4114yes—
206C2×C7×Q8C2412yes—
207C2×C7×Q8C2412yes—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2411yescharacteristic
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C22×Dic7C2×D411yescharacteristic
222Q8×D7—216no—
223Q8×D7—28no—
224Q8×D7—28no—
225C2×C4×D7—28no—
226C2×C4×D7—24no—
227C2×C4×D7—24no—
228C2×C4×D7—22no—
229C2×C4×D7—22no—
230C2×C4×D7—24no—
231C2×C4×D7—24no—
232C2×C4×D7—44no—
233C2×C4×D7C2×D414yes—
234C2×C4×D7C2×D412yes—
235C2×C4×D7C2×D414yes—
236C2×C4×D7C2412yes—
237C2×Dic14—28no—
238C2×Dic14—21no—
239C2×Dic14—22no—
240C2×Dic14—24no—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14—24no—
245C2×Dic14—44no—
246C2×Dic14#4114yes—
247C2×Dic14C2412yes—
248C2×Dic14C2412yes—
249C7×Q16—28no—
250C2×C7×C8—22no—
251C2×C7×C8—22no—
252C2×C7×C8C2412yes—
253C2×C7×C8C2412yes—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—24no—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C42×C7—24no—
261C42×C7—24no—
262C42×C7C2×D412yes—
263C42×C7C2412yes—
264#1144—28no—
265#1144—28no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2412yes—
273C4⋊Dic7C2412yes—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282C4×Dic7—24no—
283C4×Dic7—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7C2×D414yes—
287C4×Dic7C2×D414yes—
288C4×Dic7C2×D412yes—
289C4×Dic7C2412yes—
290C2×C7⋊C8—22no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8C2412yes—
293C2×C7⋊C8C2412yes—
294Dic28—28no—
295C23×Q8—71no—
296C22×Q16—71no—
297C22×Q16—71no—
298C22×Q16—71no—
299C22×Q16C2×D711yescharacteristic
300#533—78no—
301#533—144no—
302C2×C4⋊Q8—71no—
303C2×C4⋊Q8—71no—
304C2×#125—141no—
305C2×C22⋊Q8—71no—
306C2×C22⋊Q8—71no—
307C2×C22⋊Q8—141no—
308C2×C4×Q8—71no—
309C2×C4×Q8—78no—
310C2×C4×Q8—71no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8—141no—
314C2×C4×Q8—141no—
315C2×C4×Q8—141no—
316C2×C4×Q8—144no—
317C2×C4×Q8C2×D711yescharacteristic
318C2×C4×Q8C2×D711yescharacteristic
319C2×#117—141no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—141no—
322C22×C42—71no—
323C22×C42—141no—
324#483—78no—
325#483—78no—
326#475—78no—
327#475—78no—
328#462—78no—
329#462—78no—
330#451—78no—
331#451—78no—
332#441—78no—
333#441—78no—
334#441—78no—
335#441C2×D718yescomplemented
336#432—78no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×#106C2×D711yescharacteristic
341C2×C4⋊C8—71no—
342C2×C4⋊C8—71no—
343C2×#103—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#103C2×D711yescharacteristic
350C2×#103C2×D711yescharacteristic
351C2×C22⋊C8—71no—
352C2×C22⋊C8—71no—
353C2×#97—71no—
354C2×#97C2×D711yescharacteristic
355C23×C7C22×D411yescharacteristic
356C22×D7—22no—
357C22×D7—22no—
358C22×D7#13714yes—
359C22×D7C22×D412yes—
360C7×Q8—24no—
361C7×Q8—22no—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—42no—
365C7×Q8C2×#4114yes—
366C2×C4×C7—24no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D411yescharacteristic
379C2×C4×C7C2×#4112yes—
380C2×C4×C7C2×#4112yes—
381C2×C4×C7C2511yescharacteristic
382C2×Dic7—22no—
383C2×Dic7—24no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—22no—
388C2×Dic7—22no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392C2×Dic7#13714yes—
393C2×Dic7C22×D412yes—
394C2×Dic7C22×D412yes—
395C2×Dic7C22×D412yes—
396C4×D7—216no—
397C4×D7—28no—
398C4×D7—24no—
399C4×D7—22no—
400C4×D7—22no—
401C4×D7—28no—
402C4×D7—48no—
403Dic14—216no—
404Dic14—24no—
405Dic14—22no—
406Dic14—22no—
407Dic14—22no—
408Dic14—42no—
409Dic14—48no—
410Dic14C2×#4114yes—
411C7×C8—22no—
412C7×C8—22no—
413C7⋊C8—22no—
414C7⋊C8—22no—
415C22×Q8—74no—
416C22×Q8—71no—
417C22×Q8—71no—
418C22×Q8—141no—
419C22×Q8—141no—
420C22×Q8—142no—
421C22×Q8—144no—
422C22×Q8—144no—
423C22×Q8C22×D711yescharacteristic
424C22×Q8C22×D711yescharacteristic
425C23×C4—71no—
426C23×C4—71no—
427C23×C4—71no—
428C23×C4—141no—
429C23×C4—141no—
430C2×Q16—24no—
431C2×Q16—74no—
432C2×Q16—74no—
433C2×Q16—74no—
434C2×Q16—144no—
435C2×Q16—144no—
436C2×Q16—144no—
437C2×Q16C22×D714yes—
438C22×C8—71no—
439C22×C8—71no—
440C22×C8C22×D711yescharacteristic
441C22×C8C22×D711yescharacteristic
442C4⋊Q8—74no—
443C4⋊Q8—74no—
444C4⋊Q8—142no—
445C4⋊Q8—142no—
446#125—148no—
447C22⋊Q8—74no—
448C22⋊Q8—74no—
449C22⋊Q8—142no—
450C22⋊Q8—148no—
451C22⋊Q8—142no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—74no—
455C4×Q8—74no—
456C4×Q8—74no—
457C4×Q8—74no—
458C4×Q8—148no—
459C4×Q8—148no—
460C4×Q8—148no—
461C4×Q8—142no—
462C4×Q8—142no—
463C4×Q8—142no—
464C4×Q8—142no—
465C4×Q8C22×D714yes—
466C4×Q8C22×D714yes—
467#117—148no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—71no—
471C2×C4⋊C4—71no—
472C2×C4⋊C4—74no—
473C2×C4⋊C4—142no—
474C2×C4⋊C4—148no—
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—141no—
488C2×C22⋊C4—141no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—71no—
492C2×C42—71no—
493C2×C42—71no—
494C2×C42—74no—
495C2×C42—74no—
496C2×C42—148no—
497C2×C42—141no—
498C2×C42—141no—
499C2×C42—141no—
500C2×C42—141no—
501C2×C42C22×D711yescharacteristic
502#106—74no—
503#106—74no—
504#106—74no—
505#106C22×D714yes—
506C4⋊C8—74no—
507C4⋊C8—74no—
508#103—74no—
509#103—74no—
510#103—74no—
511#103—74no—
512#103—74no—
513#103—74no—
514#103C22×D714yes—
515#103C22×D714yes—
516C22⋊C8—74no—
517C22⋊C8—74no—
518#97—74no—
519#97C22×D714yes—
520C22×C7#52512yes—
521C22×C7C2×#13712yes—
522C22×C7C2×#13712yes—
523C22×C7C23×D411yescharacteristic
524C2×D7—28no—
525C2×D7—22no—
526C2×D7—22no—
527C2×D7C2×#13714yes—
528C4×C7—24no—
529C4×C7—22no—
530C4×C7—22no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7#52512yes—
535C4×C7C22×#4111yescharacteristic
536C4×C7C22×#4111yescharacteristic
537Dic7—22no—
538Dic7—24no—
539Dic7—22no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543Dic7C2×#13714yes—
544C24—71no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—74no—
551C2×Q8—72no—
552C2×Q8—72no—
553C2×Q8—144no—
554C2×Q8—144no—
555C2×Q8—148no—
556C2×Q8—148no—
557C2×Q8—1416no—
558C2×Q8—148no—
559C2×Q8—142no—
560C2×Q8—141no—
561C2×Q8—141no—
562C2×Q8—142no—
563C2×Q8—142no—
564C2×Q8—284no—
565C2×Q8#115714yes—
566C2×Q8C23×D712yes—
567C2×Q8C23×D712yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—71no—
573C22×C4—71no—
574C22×C4—71no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—144no—
580C22×C4—144no—
581C22×C4—144no—
582C22×C4—148no—
583C22×C4—144no—
584C22×C4—141no—
585C22×C4—142no—
586C22×C4—142no—
587C22×C4—141no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—284no—
591C22×C4D4×D711yescharacteristic
592C22×C4D4×D711yescharacteristic
593C22×C4C23×D711yescharacteristic
594Q16—28no—
595Q16—148no—
596Q16—148no—
597Q16—148no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—72no—
601C2×C8—72no—
602C2×C8—142no—
603C2×C8—142no—
604C2×C8C23×D712yes—
605C2×C8C23×D712yes—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—72no—
611C4⋊C4—72no—
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—144no—
621C4⋊C4—144no—
622C4⋊C4—141no—
623C4⋊C4—141no—
624C4⋊C4C23×D712yes—
625C4⋊C4C23×D712yes—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C42—24no—
629C42—24no—
630C42—74no—
631C42—74no—
632C42—72no—
633C42—72no—
634C42—144no—
635C42—144no—
636C42—144no—
637C42—144no—
638C42D4×D712yes—
639C42C23×D712yes—
640C2×C7#311314yescomplemented
641C2×C7C2×#52511yescharacteristic
642C2×C7C22×#13711yescharacteristic
643C2×C7C22×#13711yescharacteristic
644D7—24no—
645C23—74no—
646C23—72no—
647C23—142no—
648C23—142no—
649C23C2×D4×D711yescharacteristic
650Q8—24no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—74no—
656Q8—1416no—
657Q8—144no—
658Q8—142no—
659Q8—142no—
660Q8—142no—
661Q8—288no—
662Q8—282no—
663Q8C2×#115714yes—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—74no—
675C2×C4—72no—
676C2×C4—72no—
677C2×C4—72no—
678C2×C4—148no—
679C2×C4—148no—
680C2×C4—1416no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—144no—
684C2×C4—142no—
685C2×C4—144no—
686C2×C4—142no—
687C2×C4—142no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—288no—
692C2×C4—282no—
693C2×C4—282no—
694C2×C4—282no—
695C2×C4C2×#115712yes—
696C2×C4C2×D4×D712yes—
697C2×C4C2×D4×D712yes—
698C2×C4C2×D4×D711yescharacteristic
699C2×C4D7×#4112yes—
700C2×C4C24×D711yescharacteristic
701C8—22no—
702C8—22no—
703C8—142no—
704C8—142no—
705C7C2×#311311yescharacteristic, complemented, Sylow
706C22—74no—
707C22—142no—
708C22—142no—
709C22—148no—
710C22#9023812yes—
711C22D7×#13712yes—
712C22D7×#13712yes—
713C22C22×D4×D711yescharacteristic
714C4—22no—
715C4—22no—
716C4—24no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—74no—
721C4—142no—
722C4—142no—
723C4—144no—
724C4—282no—
725C4—282no—
726C4—282no—
727C4#9023812yes—
728C4C22×#115711yescharacteristic
729C4C2×D7×#4111yescharacteristic
730C2—144no—
731C2#1173727814yesdirect product factor
732C2C2×#9023811yescharacteristic
733C2C2×D7×#13711yescharacteristic
734C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#441C2
socleC23×C7C22×D4
prime radicalC23×D7C2×D4
hypercenterC2×#441D7
hypocenterC7C2×#3113
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×C7×#441C2semidirect
5. C2×#89954C2semidirect
6. C2×#89802C2semidirect
7. C2×#89802C2semidirect
8. #11737278C2direct (N × H)
9. C2×#89626C2semidirect
11. C2×#89565C2semidirect
14. C2×#89563C2semidirect
15. C2×#89488C2semidirect
46. C7×#441C22semidirect
54. #89954C22semidirect
62. #89802C22semidirect
63. #89802C22semidirect
70. #89626C22semidirect
73. #89565C22semidirect
74. #89563C22semidirect
75. #89488C22semidirect
197. C2×#441D7semidirect
335. #441C2×D7semidirect
640. C2×C7#3113semidirect
705. C7C2×#3113semidirect
731. C2#11737278direct (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×C4×Q8×D72
C2×C7×#4412
C2×#899582
C2×#899542
C2×#898022
#117372782
C2×#896262
C2×#896342
C2×#895652
C2×#895772
C2×#895802
C2×#895632
C2×#894882
C2×#894772
C2×#31137