Finite Group Databasebeta

← C2×#11738962 #14221601

Subgroups — C2×#11738962 #14221601

Order 1792.

2326 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C22⋊Q8C211yesmaximal, characteristic
2C2×D7×#117C211yesmaximal, characteristic
3C2×C7×#485C211yesmaximal, characteristic, complemented
4C2×#89817C211yesmaximal, characteristic, complemented
5C2×#89768C211yesmaximal, characteristic, complemented
6#11738962C2116yesmaximal, direct product factor
7C2×#89656C211yesmaximal, characteristic, complemented
8C2×#89653C211yesmaximal, characteristic, complemented
9C2×#89634C211yesmaximal, characteristic, complemented
10C2×#89633C211yesmaximal, characteristic, complemented
11C2×#89581C211yesmaximal, characteristic, complemented
12C2×#89577C211yesmaximal, characteristic, complemented
13C2×#89574C211yesmaximal, characteristic, complemented
14C2×#89574C211yesmaximal, characteristic, complemented
15C2×#89498C211yesmaximal, characteristic
16C2×#89495C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×#6489C2211yescharacteristic
23C2×#6487C2211yescharacteristic
24C22×#1131C2211yescharacteristic
25C22×#1131C2211yescharacteristic
26D7×C22⋊Q8—24no—
27D7×C22⋊Q8C2218yes—
28D7×#117—24no—
29D7×#117C2218yes—
30C2×#6460C2211yescharacteristic
31C2×#6459—21no—
32C2×#6455C2211yescharacteristic
33C2×#6455C2211yescharacteristic
34C2×D7×C4⋊C4—21no—
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×D7×C22⋊C4—21no—
39C2×D7×C22⋊C4—21no—
40C2×#6441—21no—
41C2×#6440—21no—
42C2×#6435—21no—
43C2×C42×D7—21no—
44C7×#485C2218yescomplemented
45C2×C7×#107C2211yescharacteristic, complemented
46C2×C7×#106C2211yescharacteristic, complemented
47C2×C7×#103C2211yescharacteristic, complemented
48C2×C7×#103C2211yescharacteristic, complemented
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×#6409C2211yescharacteristic, complemented
51C2×#6409C2211yescharacteristic, complemented
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6392C2211yescharacteristic, complemented
56C2×#6391C2211yescharacteristic, complemented
57C2×#6390C2211yescharacteristic, complemented
58C2×#6390C2211yescharacteristic, complemented
59#89817C2218yescomplemented
60#89768C2218yescomplemented
61C2×#6384C2211yescharacteristic, complemented
62C2×#6384C2211yescharacteristic, complemented
63C2×#6382C2211yescharacteristic, complemented
64C2×#6382C2211yescharacteristic, complemented
65C2×#6381C2211yescharacteristic, complemented
66C2×#6381C2211yescharacteristic, complemented
67#89656C2218yescomplemented
68#89653C2218yescomplemented
69#89634C2218yescomplemented
70#89633C2218yescomplemented
71#89581C2218yescomplemented
72#89577C2218yescomplemented
73#89574C2218yescomplemented
74#89574C2218yescomplemented
75#89498C2218yes—
76#89495C2218yescomplemented
77C2×#3095—71nomaximal, Sylow
78C24×D7D411yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×Dic7D411yescharacteristic
82C2×Q8×D7—22no—
83C2×Q8×D7—24no—
84C2×Q8×D7—24no—
85C2×Q8×D7C2314yes—
86C22×C4×D7—24no—
87C22×C4×D7—24no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×C4×D7—21no—
91C22×C4×D7—21no—
92C22×C4×D7D411yescharacteristic
93C22×C4×D7D411yescharacteristic
94C22×C4×D7D414yes—
95C22×C4×D7C2311yescharacteristic
96C22×C4×D7C2314yes—
97C22×C4×D7C2311yescharacteristic
98C22×Dic14—21no—
99C22×Dic14C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C22×C7×C8C2311yescharacteristic
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8C2314yes—
104C7×#117—22no—
105C7×#117C2314yes—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C42×C7—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115#6509—22no—
116#6509C2314yes—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121#6489—22no—
122#6489C2314yes—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127#6487—22no—
128#6487C2314yes—
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×Dic7—21no—
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C2×#1131—24no—
140C2×#1131—24no—
141C2×#1131C2314yes—
142C2×#1131C2314yes—
143#6460—22no—
144#6460C2314yes—
145#6459—28no—
146#6455—22no—
147#6455—22no—
148#6455C2314yes—
149#6455C2314yes—
150D7×C4⋊C4—28no—
151D7×C4⋊C4—22no—
152D7×C4⋊C4—22no—
153D7×C4⋊C4—22no—
154D7×C4⋊C4C2314yes—
155D7×C4⋊C4C2314yes—
156D7×C4⋊C4C2314yes—
157D7×C22⋊C4—28no—
158D7×C22⋊C4—28no—
159#6441—28no—
160#6440—28no—
161#6435—28no—
162C42×D7—28no—
163C7×#107C2314yescomplemented
164C7×#106C2314yescomplemented
165C7×#103C2314yescomplemented
166C7×#103C2314yescomplemented
167C7×C22⋊C8C2314yes—
168#6409C2314yescomplemented
169#6409C2314yescomplemented
170C22⋊(C7⋊C8)C2314yes—
171(C2×D7)⋊C8C2314yes—
172(C2×D7)⋊C8C2314yes—
173#6392C2314yescomplemented
174#6391C2314yescomplemented
175#6390C2314yescomplemented
176#6390C2314yescomplemented
177#6384C2314yescomplemented
178#6384C2314yescomplemented
179#6382C2314yescomplemented
180#6382C2314yescomplemented
181#6381C2314yescomplemented
182#6381C2314yescomplemented
183C22×C22⋊Q8—71no—
184C22×#117—71no—
185#3095—716no—
186C2×#484—71no—
187C2×#484—71no—
188C2×#485—71no—
189C2×#485—71no—
190C2×#485—71no—
191C2×#485D711yescharacteristic, complemented
192C2×#483—71no—
193C2×#483—71no—
194C2×#428—71no—
195C2×#428—71no—
196C2×#419—71no—
197C2×#419—71no—
198C2×#407—71no—
199C24×C7C2×D411yescharacteristic
200C23×D7—24no—
201C23×D7—24no—
202C23×D7—42no—
203C23×D7C2×D414yes—
204C23×D7C2×D411yescharacteristic
205C23×D7C2×D411yescharacteristic
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8C2412yes—
210C22×C4×C7—22no—
211C22×C4×C7—22no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2411yescharacteristic
220C22×Dic7—24no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7C2×D414yes—
226C22×Dic7C2×D411yescharacteristic
227C22×Dic7C2×D411yescharacteristic
228Q8×D7—28no—
229Q8×D7—28no—
230Q8×D7—48no—
231C2×C4×D7—24no—
232C2×C4×D7—22no—
233C2×C4×D7—22no—
234C2×C4×D7—24no—
235C2×C4×D7—216no—
236C2×C4×D7—28no—
237C2×C4×D7—28no—
238C2×C4×D7—24no—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—24no—
242C2×C4×D7—44no—
243C2×C4×D7—44no—
244C2×C4×D7—44no—
245C2×C4×D7—44no—
246C2×C4×D7C2×D414yes—
247C2×C4×D7C2×D414yes—
248C2×C4×D7C2×D412yes—
249C2×C4×D7C2×D412yes—
250C2×C4×D7#4114yes—
251C2×C4×D7#4114yes—
252C2×C4×D7C2412yes—
253C2×C4×D7C2412yes—
254C2×Dic14—22no—
255C2×Dic14—22no—
256C2×Dic14—21no—
257C2×Dic14—24no—
258C2×Dic14—44no—
259C2×Dic14C2412yes—
260C2×C7×C8—22no—
261C2×C7×C8—22no—
262C2×C7×C8C2412yes—
263C2×C7×C8C2412yes—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—24no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4C2412yes—
269C7×C4⋊C4C2412yes—
270C7×C4⋊C4C2412yes—
271C7×C22⋊C4—24no—
272C7×C22⋊C4—24no—
273C42×C7—24no—
274C22⋊Dic7—24no—
275C22⋊Dic7—24no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—21no—
283C4⋊Dic7—24no—
284C4⋊Dic7C2412yes—
285C4⋊Dic7C2412yes—
286C4⋊Dic7C2412yes—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292C4×Dic7—24no—
293C4×Dic7—24no—
294C4×Dic7—24no—
295C2×C7⋊C8—22no—
296C2×C7⋊C8—22no—
297C2×C7⋊C8C2412yes—
298C2×C7⋊C8C2412yes—
299#1131—28no—
300#1131—28no—
301C23×Q8—71no—
302C24×C4—71no—
303C22×M16—71no—
304C22×M16—71no—
305C2×C22⋊Q8—71no—
306C2×C22⋊Q8—71no—
307C2×C22⋊Q8—78no—
308C2×C22⋊Q8—71no—
309C2×C22⋊Q8—141no—
310C2×C22⋊Q8—141no—
311C2×C22⋊Q8—144no—
312C2×C22⋊Q8C2×D711yescharacteristic
313C2×#117—71no—
314C2×#117—78no—
315C2×#117—71no—
316C2×#117—71no—
317C2×#117—141no—
318C2×#117—141no—
319C2×#117—144no—
320C2×#117C2×D711yescharacteristic
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—141no—
325C22×C22⋊C4—141no—
326C22×C22⋊C4—141no—
327C22×C42—141no—
328#485—78no—
329#485—78no—
330#485—78no—
331#485C2×D718yescomplemented
332#484—78no—
333#484—78no—
334#483—78no—
335#483—78no—
336#428—78no—
337#428—78no—
338C2×#107—71no—
339C2×#107—71no—
340C2×#107—71no—
341C2×#107C2×D711yescharacteristic, complemented
342C2×#106—71no—
343C2×#106—71no—
344C2×#106—71no—
345C2×#106C2×D711yescharacteristic, complemented
346#419—78no—
347#419—78no—
348C2×#103—71no—
349C2×#103—71no—
350C2×#103—71no—
351C2×#103—71no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103C2×D711yescharacteristic, complemented
355C2×#103C2×D711yescharacteristic, complemented
356#407—78no—
357C2×C22⋊C8—71no—
358C2×C22⋊C8—71no—
359C2×C22⋊C8—71no—
360C2×C22⋊C8C2×D711yescharacteristic
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7C22×D412yes—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—28no—
371C22×D7—28no—
372C22×D7—44no—
373C22×D7—416no—
374C22×D7#12314yes—
375C22×D7#13714yes—
376C22×D7C22×D412yes—
377C22×D7C22×D412yes—
378C7×Q8—22no—
379C7×Q8—22no—
380C7×Q8—42no—
381C2×C4×C7—22no—
382C2×C4×C7—24no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D411yescharacteristic
395C2×C4×C7C2×#4112yes—
396C2×C4×C7C2×#4112yes—
397C2×C4×C7C2511yescharacteristic
398C2×Dic7—22no—
399C2×Dic7—28no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407C2×Dic7—42no—
408C2×Dic7#12314yes—
409C2×Dic7C22×D412yes—
410C2×Dic7C22×D412yes—
411C4×D7—28no—
412C4×D7—24no—
413C4×D7—22no—
414C4×D7—22no—
415C4×D7—28no—
416C4×D7—48no—
417C4×D7—48no—
418C4×D7—48no—
419C4×D7—48no—
420C4×D7#12318yes—
421C4×D7C2×#4114yes—
422C4×D7C2×#4114yes—
423Dic14—22no—
424Dic14—22no—
425Dic14—42no—
426Dic14—48no—
427C7×C8—22no—
428C7×C8—22no—
429C7⋊C8—22no—
430C7⋊C8—22no—
431C25—71no—
432C22×Q8—74no—
433C22×Q8—71no—
434C22×Q8—141no—
435C22×Q8—142no—
436C22×Q8—144no—
437C22×Q8—144no—
438C22×Q8C22×D711yescharacteristic
439C23×C4—71no—
440C23×C4—71no—
441C23×C4—71no—
442C23×C4—74no—
443C23×C4—71no—
444C23×C4—71no—
445C23×C4—74no—
446C23×C4—144no—
447C23×C4—144no—
448C23×C4—141no—
449C23×C4—141no—
450C23×C4—141no—
451C23×C4—141no—
452C23×C4C22×D711yescharacteristic
453C2×M16—74no—
454C2×M16—74no—
455C2×M16—144no—
456C2×M16—144no—
457C22×C8—71no—
458C22×C8—71no—
459C22×C8C22×D711yescharacteristic
460C22×C8C22×D711yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8—74no—
463C22⋊Q8—74no—
464C22⋊Q8—74no—
465C22⋊Q8—148no—
466C22⋊Q8—148no—
467C22⋊Q8—142no—
468C22⋊Q8—142no—
469C22⋊Q8—142no—
470C22⋊Q8C22×D714yes—
471#117—22no—
472#117—74no—
473#117—74no—
474#117—74no—
475#117—148no—
476#117—148no—
477#117—142no—
478#117—142no—
479#117—142no—
480#117C22×D714yes—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—74no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—142no—
490C2×C4⋊C4—142no—
491C2×C4⋊C4—148no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4—141no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4C22×D711yescharacteristic
499C2×C4⋊C4C22×D711yescharacteristic
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—148no—
504C2×C22⋊C4—148no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C42—21no—
512C2×C42—148no—
513C2×C42—141no—
514C2×C42—141no—
515C2×C42—141no—
516#107—74no—
517#107—74no—
518#107—74no—
519#107C22×D714yescomplemented
520#106—74no—
521#106—74no—
522#106—74no—
523#106C22×D714yescomplemented
524#103—74no—
525#103—74no—
526#103—74no—
527#103—74no—
528#103—74no—
529#103—74no—
530#103C22×D714yescomplemented
531#103C22×D714yescomplemented
532C22⋊C8—74no—
533C22⋊C8—74no—
534C22⋊C8—74no—
535C22⋊C8C22×D714yes—
536C22×C7—22no—
537C22×C7—22no—
538C22×C7—22no—
539C22×C7—44no—
540C22×C7C2×#12312yes—
541C22×C7C2×#13712yes—
542C22×C7#57512yes—
543C22×C7C23×D411yescharacteristic
544C2×D7—28no—
545C2×D7—28no—
546C2×D7—22no—
547C2×D7—22no—
548C2×D7—22no—
549C2×D7—22no—
550C2×D7—416no—
551C2×D7C2×#12314yes—
552C2×D7C2×#13714yes—
553C4×C7—22no—
554C4×C7—42no—
555C4×C7—42no—
556C4×C7—42no—
557C4×C7—42no—
558C4×C7C2×#12312yes—
559C4×C7C22×#4111yescharacteristic
560C4×C7C22×#4111yescharacteristic
561Dic7—22no—
562Dic7—42no—
563Dic7—42no—
564Dic7—42no—
565Dic7—42no—
566Dic7C2×#12314yes—
567C24—71no—
568C24—71no—
569C24—74no—
570C24—144no—
571C24—144no—
572C24—282no—
573C24D4×D711yescharacteristic
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—72no—
578C2×Q8—144no—
579C2×Q8—148no—
580C2×Q8—148no—
581C2×Q8—141no—
582C2×Q8—142no—
583C2×Q8—142no—
584C2×Q8—284no—
585C2×Q8—288no—
586C2×Q8C23×D712yes—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—71no—
594C22×C4—72no—
595C22×C4—74no—
596C22×C4—74no—
597C22×C4—72no—
598C22×C4—74no—
599C22×C4—71no—
600C22×C4—74no—
601C22×C4—74no—
602C22×C4—72no—
603C22×C4—72no—
604C22×C4—144no—
605C22×C4—1416no—
606C22×C4—148no—
607C22×C4—148no—
608C22×C4—144no—
609C22×C4—144no—
610C22×C4—144no—
611C22×C4—144no—
612C22×C4—144no—
613C22×C4—144no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—141no—
617C22×C4—141no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4—284no—
621C22×C4—284no—
622C22×C4—284no—
623C22×C4—284no—
624C22×C4D4×D712yes—
625C22×C4D4×D711yescharacteristic
626C22×C4C23×D712yes—
627C22×C4C23×D711yescharacteristic
628M16—148no—
629M16—148no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—72no—
633C2×C8—72no—
634C2×C8—142no—
635C2×C8—142no—
636C2×C8C23×D712yes—
637C2×C8C23×D712yes—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—72no—
643C4⋊C4—72no—
644C4⋊C4—72no—
645C4⋊C4—144no—
646C4⋊C4—144no—
647C4⋊C4—144no—
648C4⋊C4—144no—
649C4⋊C4—144no—
650C4⋊C4—144no—
651C4⋊C4—141no—
652C4⋊C4—141no—
653C4⋊C4—141no—
654C4⋊C4C23×D712yes—
655C4⋊C4C23×D712yes—
656C4⋊C4C23×D712yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—144no—
660C22⋊C4—144no—
661C22⋊C4—144no—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C22⋊C4—144no—
665C42—24no—
666C42—144no—
667C42—144no—
668C42—144no—
669C2×C7—42no—
670C2×C7#309514yescomplemented
671C2×C7C22×#12311yescharacteristic
672C2×C7C22×#13711yescharacteristic
673C2×C7C2×#57511yescharacteristic
674D7—24no—
675D7—24no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—74no—
680C23—74no—
681C23—72no—
682C23—72no—
683C23—148no—
684C23—148no—
685C23—142no—
686C23—142no—
687C23—142no—
688C23—142no—
689C23—284no—
690C23—2816no—
691C23C2×D4×D712yes—
692C23C2×D4×D711yescharacteristic
693Q8—22no—
694Q8—22no—
695Q8—42no—
696Q8—142no—
697Q8—142no—
698Q8—288no—
699Q8—282no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—74no—
713C2×C4—72no—
714C2×C4—78no—
715C2×C4—74no—
716C2×C4—74no—
717C2×C4—72no—
718C2×C4—148no—
719C2×C4—148no—
720C2×C4—148no—
721C2×C4—142no—
722C2×C4—144no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—288no—
730C2×C4—288no—
731C2×C4—288no—
732C2×C4—288no—
733C2×C4—282no—
734C2×C4—282no—
735C2×C4—282no—
736C2×C4—282no—
737C2×C4C2×D4×D712yes—
738C2×C4C2×D4×D711yescharacteristic
739C2×C4D7×#4112yes—
740C2×C4D7×#4112yes—
741C2×C4C24×D711yescharacteristic
742C8—22no—
743C8—22no—
744C8—142no—
745C8—142no—
746C7C2×#309511yescharacteristic, complemented, Sylow
747C22—22no—
748C22—22no—
749C22—22no—
750C22—44no—
751C22—74no—
752C22—74no—
753C22—142no—
754C22—148no—
755C22—148no—
756C22—142no—
757C22—142no—
758C22—142no—
759C22—2816no—
760C22D7×#12312yes—
761C22#9045912yes—
762C22D7×#13712yes—
763C22C22×D4×D711yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—74no—
770C4—142no—
771C4—282no—
772C4—282no—
773C4—282no—
774C4—282no—
775C4D7×#12312yes—
776C4C2×D7×#4111yescharacteristic
777C4C2×D7×#4111yescharacteristic
778C2—42no—
779C2—144no—
780C2—144no—
781C2#1173896214yesdirect product factor
782C2C2×D7×#12311yescharacteristic
783C2C2×#9045911yescharacteristic
784C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#485C2
socleC23×C7C22×D4
prime radicalC24×D7D4
hypercenterC2×#485D7
hypocenterC7C2×#3095
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. C2×C7×#485C2semidirect
4. C2×#89817C2semidirect
5. C2×#89768C2semidirect
6. #11738962C2direct (N × H)
7. C2×#89656C2semidirect
8. C2×#89653C2semidirect
9. C2×#89634C2semidirect
10. C2×#89633C2semidirect
11. C2×#89581C2semidirect
12. C2×#89577C2semidirect
13. C2×#89574C2semidirect
14. C2×#89574C2semidirect
16. C2×#89495C2semidirect
44. C7×#485C22semidirect
45. C2×C7×#107C22semidirect
46. C2×C7×#106C22semidirect
47. C2×C7×#103C22semidirect
48. C2×C7×#103C22semidirect
50. C2×#6409C22semidirect
51. C2×#6409C22semidirect
55. C2×#6392C22semidirect
56. C2×#6391C22semidirect
57. C2×#6390C22semidirect
58. C2×#6390C22semidirect
59. #89817C22semidirect
60. #89768C22semidirect
61. C2×#6384C22semidirect
62. C2×#6384C22semidirect
63. C2×#6382C22semidirect
64. C2×#6382C22semidirect
65. C2×#6381C22semidirect
66. C2×#6381C22semidirect
67. #89656C22semidirect
68. #89653C22semidirect
69. #89634C22semidirect
70. #89633C22semidirect
71. #89581C22semidirect
72. #89577C22semidirect
73. #89574C22semidirect
74. #89574C22semidirect
76. #89495C22semidirect
163. C7×#107C23semidirect
164. C7×#106C23semidirect
165. C7×#103C23semidirect
166. C7×#103C23semidirect
168. #6409C23semidirect
169. #6409C23semidirect
173. #6392C23semidirect
174. #6391C23semidirect
175. #6390C23semidirect
176. #6390C23semidirect
177. #6384C23semidirect
178. #6384C23semidirect
179. #6382C23semidirect
180. #6382C23semidirect
181. #6381C23semidirect
182. #6381C23semidirect
191. C2×#485D7semidirect
331. #485C2×D7semidirect
341. C2×#107C2×D7semidirect
345. C2×#106C2×D7semidirect
354. C2×#103C2×D7semidirect
355. C2×#103C2×D7semidirect
519. #107C22×D7semidirect
523. #106C22×D7semidirect
530. #103C22×D7semidirect
531. #103C22×D7semidirect
670. C2×C7#3095semidirect
746. C7C2×#3095semidirect
781. C2#11738962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C22⋊Q82
C2×D7×#1172
C2×C7×#4852
C2×#898172
C2×#897682
#117389622
C2×#896562
C2×#896532
C2×#896342
C2×#896332
C2×#895812
C2×#895772
C2×#895742
C2×#894982
C2×#894952
C2×#30957