Finite Group Databasebeta

← #13354541

Subgroups — #13354541

Order 1792.

1630 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×#117C211yesmaximal, characteristic
2C2×#89653C211yesmaximal, characteristic, complemented
3C2×#89633C211yesmaximal, characteristic, complemented
4C2×#89498C211yesmaximal, characteristic
5D7×#380C211yesmaximal, characteristic
6C7×#1854C211yesmaximal, characteristic, complemented
7#11729330C211yesmaximal, characteristic, complemented
8#11728386C211yesmaximal, characteristic, complemented
9#11728333C211yesmaximal, characteristic, complemented
10#11727683C211yesmaximal, characteristic, complemented
11#11727260C211yesmaximal, characteristic, complemented
12#11726629C211yesmaximal, characteristic, complemented
13#11726628C211yesmaximal, characteristic, complemented
14#11726621C211yesmaximal, characteristic, complemented
15#11726621C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C2×#6489C2211yescharacteristic
19C22×#1131C2211yescharacteristic
20C22×#1131C2211yescharacteristic
21D7×#117—24no—
22D7×#117—24no—
23C2×#6455C2211yescharacteristic
24C2×#6455C2211yescharacteristic
25C2×D7×C4⋊C4C2211yescharacteristic
26C2×D7×C4⋊C4C2211yescharacteristic
27C2×D7×C4⋊C4C2211yescharacteristic
28C2×D7×C4⋊C4C2211yescharacteristic
29C2×D7×C22⋊C4—21no—
30C2×D7×C22⋊C4—21no—
31C2×#6440—21no—
32C2×#6435—21no—
33C2×C42×D7—21no—
34C2×C7×#107C2211yescharacteristic, complemented
35C2×C7×#106C2211yescharacteristic, complemented
36C2×C7×C22⋊C8C2211yescharacteristic
37C7×#380C2211yescharacteristic
38#89984C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×(C2×D7)⋊C8C2211yescharacteristic
41C2×(C2×D7)⋊C8C2211yescharacteristic
42C2×#6392C2211yescharacteristic, complemented
43C2×#6391C2211yescharacteristic, complemented
44#89759C2211yescharacteristic
45#89759C2211yescharacteristic
46C2×#6382C2211yescharacteristic, complemented
47C2×#6382C2211yescharacteristic, complemented
48C2×#6381C2211yescharacteristic, complemented
49C2×#6381C2211yescharacteristic, complemented
50#89714—21no—
51#89653—24no—
52#89633—24no—
53#89498C418yescomplemented
54#89439—21no—
55D7×#95—21no—
56C7×#340C2211yescharacteristic, complemented
57C7×#340C2211yescharacteristic, complemented
58#89346C2211yescharacteristic, complemented
59#89346C2211yescharacteristic, complemented
60#89324C2211yescharacteristic, complemented
61#89324C2211yescharacteristic, complemented
62#89324C2211yescharacteristic, complemented
63#89324C2211yescharacteristic, complemented
64#20846—71nomaximal, Sylow
65C24×D7D411yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7D411yescharacteristic
68C22×C4×D7—22no—
69C22×C4×D7—22no—
70C22×C4×D7—22no—
71C22×C4×D7—22no—
72C22×C4×D7—21no—
73C22×C4×D7—21no—
74C22×C4×D7—21no—
75C22×C4×D7—21no—
76C22×C4×D7C2×C414yes—
77C22×C4×D7D411yescharacteristic
78C22×C4×D7D411yescharacteristic
79C22×C4×D7Q814yes—
80C22×C4×D7C2311yescharacteristic
81C22×C4×D7C2311yescharacteristic
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C7×#117—22no—
85C7×#117—22no—
86C2×C7×C4⋊C4C2311yescharacteristic
87C2×C7×C4⋊C4C2311yescharacteristic
88C2×C7×C4⋊C4C2311yescharacteristic
89C2×C7×C4⋊C4C2311yescharacteristic
90C2×C7×C22⋊C4—21no—
91C2×C7×C22⋊C4—21no—
92C2×C42×C7—21no—
93C2×C22⋊Dic7—21no—
94C2×C22⋊Dic7—21no—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×(C2×D7)⋊C4—21no—
98C2×(C2×D7)⋊C4—21no—
99#6489—22no—
100#6489—22no—
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4⋊Dic7C2311yescharacteristic
104C2×C4⋊Dic7C2311yescharacteristic
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C2×Dic7⋊C4—21no—
109C2×C4×Dic7—21no—
110C2×C4×Dic7—21no—
111C2×C4×Dic7—21no—
112C22×C7⋊C8C2311yescharacteristic
113C22×C7⋊C8C2311yescharacteristic
114C2×#1131—22no—
115C2×#1131—22no—
116C2×#1131—22no—
117C2×#1131—22no—
118C2×#1131C2×C414yescomplemented
119C2×#1131C2×C414yescomplemented
120#6455—22no—
121#6455—22no—
122#6455D414yes—
123#6455D414yes—
124D7×C4⋊C4—22no—
125D7×C4⋊C4—22no—
126D7×C4⋊C4—22no—
127D7×C4⋊C4—22no—
128D7×C4⋊C4—22no—
129D7×C4⋊C4—22no—
130D7×C4⋊C4—22no—
131D7×C4⋊C4—22no—
132D7×C22⋊C4—28no—
133D7×C22⋊C4—44no—
134#6440—28no—
135#6435—28no—
136C42×D7—28no—
137C7×#107—22no—
138C7×#106—22no—
139C7×C22⋊C8C2×C414yescomplemented
140C7×#95—21no—
141C7⋊#95—21no—
142C7⋊#95—21no—
143C7⋊#95—21no—
144C22⋊(C7⋊C8)C2×C414yescomplemented
145(C2×D7)⋊C8C2×C414yescomplemented
146(C2×D7)⋊C8C2×C414yescomplemented
147#6392—22no—
148#6391—22no—
149#6382—22no—
150#6382—22no—
151#6381—22no—
152#6381—22no—
153C22×#117—71no—
154C2×#428—71no—
155C2×#428—71no—
156C2×#407—71no—
157C2×#380—71no—
158#1854—71no—
159#1854—71no—
160#1854—71no—
161#1854D711yescharacteristic, complemented
162#1853—71no—
163#1853—71no—
164#1852—71no—
165#1852—71no—
166#1736—71no—
167#1736—71no—
168C24×C7C2×D411yescharacteristic
169C23×D7—22no—
170C23×D7—22no—
171C23×D7—22no—
172C23×D7—22no—
173C23×D7—41no—
174C23×D7—41no—
175C23×D7C4⋊C414yes—
176C23×D7C2×D411yescharacteristic
177C23×D7C2×D411yescharacteristic
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7C22×C412yes—
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×Q812yes—
189C22×C4×C7C2411yescharacteristic
190C22×Dic7—22no—
191C22×Dic7—22no—
192C22×Dic7—21no—
193C22×Dic7—21no—
194C22×Dic7—21no—
195C22×Dic7—21no—
196C22×Dic7C4⋊C414yes—
197C22×Dic7C2×D411yescharacteristic
198C22×Dic7C2×D411yescharacteristic
199C2×C4×D7—22no—
200C2×C4×D7—22no—
201C2×C4×D7—21no—
202C2×C4×D7—21no—
203C2×C4×D7—21no—
204C2×C4×D7—21no—
205C2×C4×D7—22no—
206C2×C4×D7—22no—
207C2×C4×D7—28no—
208C2×C4×D7—28no—
209C2×C4×D7—28no—
210C2×C4×D7—28no—
211C2×C4×D7—24no—
212C2×C4×D7—24no—
213C2×C4×D7—42no—
214C2×C4×D7—42no—
215C2×C4×D7—42no—
216C2×C4×D7—42no—
217C2×C4×D7—42no—
218C2×C4×D7—42no—
219C2×C4×D7—42no—
220C2×C4×D7—42no—
221C2×C4×D7—42no—
222C2×C4×D7—42no—
223C2×C4×D7C4⋊C414yes—
224C2×C4×D7C4⋊C414yes—
225C2×C4×D7C22×C412yes—
226C2×C4×D7C22×C412yes—
227C2×C4×D7C2×D412yes—
228C2×C4×D7C2×D412yes—
229C2×C4×D7C2×Q812yes—
230C2×C4×D7C2×Q812yes—
231C2×C4×D7#4112yes—
232C2×C4×D7#4112yes—
233C2×C7×C8—21no—
234C2×C7×C8—21no—
235C2×C7×C8—21no—
236C2×C7×C8—21no—
237C2×C7×C8C22×C412yes—
238C2×C7×C8C22×C412yes—
239C7×C4⋊C4—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4—21no—
242C7×C4⋊C4—21no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4C2×D412yes—
246C7×C4⋊C4C2×D412yes—
247C7×C22⋊C4—24no—
248C7×C22⋊C4—42no—
249C42×C7—24no—
250C22⋊Dic7—24no—
251C22⋊Dic7—42no—
252(C2×D7)⋊C4—24no—
253(C2×D7)⋊C4—24no—
254(C2×D7)⋊C4—42no—
255(C2×D7)⋊C4—42no—
256C4⋊Dic7—21no—
257C4⋊Dic7—21no—
258C4⋊Dic7—21no—
259C4⋊Dic7—21no—
260C4⋊Dic7—21no—
261C4⋊Dic7—21no—
262C4⋊Dic7C2×D412yes—
263C4⋊Dic7C2×D412yes—
264Dic7⋊C4—24no—
265Dic7⋊C4—24no—
266Dic7⋊C4—42no—
267Dic7⋊C4—42no—
268C4×Dic7—24no—
269C4×Dic7—24no—
270C4×Dic7—24no—
271C2×C7⋊C8—21no—
272C2×C7⋊C8—21no—
273C2×C7⋊C8—21no—
274C2×C7⋊C8—21no—
275C2×C7⋊C8C22×C412yes—
276C2×C7⋊C8C22×C412yes—
277#1131—28no—
278#1131—28no—
279C24×C4—71no—
280C22×M16—71no—
281C22×M16—71no—
282C2×#117—71no—
283C2×#117—71no—
284C2×#117—71no—
285C2×#117—141no—
286C2×#117—141no—
287C2×#117—144no—
288C2×#117—144no—
289C2×#117C2×D711yescharacteristic
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4—71no—
294C22×C22⋊C4—141no—
295C22×C22⋊C4—141no—
296C22×C42—141no—
297#428—144no—
298#428—144no—
299C2×#107—71no—
300C2×#107—71no—
301C2×#107—71no—
302C2×#107C2×D711yescharacteristic, complemented
303C2×#106—71no—
304C2×#106—71no—
305C2×#106—71no—
306C2×#106C2×D711yescharacteristic, complemented
307#407—78no—
308C2×C22⋊C8—71no—
309C2×C22⋊C8—71no—
310C2×C22⋊C8—71no—
311C2×C22⋊C8C2×D711yescharacteristic
312#380—71no—
313#380—71no—
314#380—71no—
315#380—141no—
316#380—141no—
317#380C2×D711yescharacteristic
318C2×#95—141no—
319#340—71no—
320#340—71no—
321#340—71no—
322#340—71no—
323#340—71no—
324#340—71no—
325#340C2×D711yescharacteristic, complemented
326#340C2×D711yescharacteristic, complemented
327C23×C7—21no—
328C23×C7—21no—
329C23×C7—21no—
330C23×C7—21no—
331C23×C7—21no—
332C23×C7—21no—
333C23×C7C2×C4⋊C412yes—
334C23×C7C22×D411yescharacteristic
335C22×D7—21no—
336C22×D7—21no—
337C22×D7—21no—
338C22×D7—21no—
339C22×D7—21no—
340C22×D7—21no—
341C22×D7—21no—
342C22×D7—21no—
343C22×D7—28no—
344C22×D7—28no—
345C22×D7—44no—
346C22×D7—44no—
347C22×D7—44no—
348C22×D7—44no—
349C22×D7—44no—
350C22×D7C2×C4⋊C412yes—
351C22×D7C2×C4⋊C412yes—
352C22×D7#12012yes—
353C22×D7#12312yes—
354C22×D7AGL(1,ℤ/8)12yes—
355C22×D7#13712yes—
356C2×C4×C7—21no—
357C2×C4×C7—21no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—41no—
373C2×C4×C7—41no—
374C2×C4×C7C2×C4⋊C412yes—
375C2×C4×C7C23×C411yescharacteristic
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C22×Q811yescharacteristic
379C2×C4×C7C2×#4111yescharacteristic
380C2×C4×C7C2×#4111yescharacteristic
381C2×Dic7—21no—
382C2×Dic7—21no—
383C2×Dic7—28no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—41no—
387C2×Dic7—41no—
388C2×Dic7—41no—
389C2×Dic7—41no—
390C2×Dic7—41no—
391C2×Dic7—41no—
392C2×Dic7—41no—
393C2×Dic7—41no—
394C2×Dic7—41no—
395C2×Dic7—41no—
396C2×Dic7C2×C4⋊C412yes—
397C2×Dic7C2×C4⋊C412yes—
398C2×Dic7#12012yes—
399C2×Dic7#12312yes—
400C4×D7—28no—
401C4×D7—22no—
402C4×D7—22no—
403C4×D7—22no—
404C4×D7—22no—
405C4×D7—28no—
406C4×D7—48no—
407C4×D7—48no—
408C4×D7—84no—
409C4×D7—84no—
410C4×D7C4×D414yes—
411C4×D7C4×D414yes—
412C4×D7C22⋊Q814yes—
413C4×D7C22⋊Q814yes—
414C7×C8—22no—
415C7×C8—22no—
416C7⋊C8—22no—
417C7⋊C8—22no—
418C25—71no—
419C23×C4—71no—
420C23×C4—71no—
421C23×C4—74no—
422C23×C4—71no—
423C23×C4—71no—
424C23×C4—74no—
425C23×C4—71no—
426C23×C4—142no—
427C23×C4—142no—
428C23×C4—142no—
429C23×C4—142no—
430C23×C4—141no—
431C23×C4—141no—
432C23×C4—141no—
433C23×C4—141no—
434C23×C4C22×D711yescharacteristic
435C2×M16—74no—
436C2×M16—74no—
437C2×M16—142no—
438C2×M16—142no—
439C2×M16—142no—
440C2×M16—142no—
441C22×C8—71no—
442C22×C8—71no—
443C22×C8C22×D711yescharacteristic
444C22×C8C22×D711yescharacteristic
445#117—22no—
446#117—22no—
447#117—74no—
448#117—74no—
449#117—148no—
450#117—148no—
451#117—142no—
452#117—142no—
453#117—142no—
454#117—142no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—71no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—142no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—142no—
463C2×C4⋊C4—142no—
464C2×C4⋊C4—142no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—142no—
468C2×C4⋊C4—142no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4C22×D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—148no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C22⋊C4—141no—
483C2×C22⋊C4—141no—
484C2×C22⋊C4—284no—
485C2×C42—21no—
486C2×C42—148no—
487C2×C42—141no—
488C2×C42—141no—
489C2×C42—141no—
490#107—22no—
491#107—142no—
492#107—142no—
493#107—142no—
494#106—22no—
495#106—142no—
496#106—142no—
497#106—142no—
498C22⋊C8—74no—
499C22⋊C8—74no—
500C22⋊C8—74no—
501C22⋊C8C4×D714yescomplemented
502#95—21no—
503#95—141no—
504#95—141no—
505#95—141no—
506C22×C7—22no—
507C22×C7—22no—
508C22×C7—22no—
509C22×C7—41no—
510C22×C7—41no—
511C22×C7—41no—
512C22×C7—41no—
513C22×C7C22×C4⋊C411yescharacteristic
514C22×C7C2×#12011yescharacteristic
515C22×C7C2×#12311yescharacteristic
516C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
517C22×C7C2×#13711yescharacteristic
518C22×C7#57511yescharacteristic
519C22×C7#57511yescharacteristic
520C2×D7—22no—
521C2×D7—22no—
522C2×D7—22no—
523C2×D7—22no—
524C2×D7—22no—
525C2×D7—22no—
526C2×D7—22no—
527C2×D7—22no—
528C2×D7—22no—
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—22no—
532C2×D7—416no—
533C2×D7#38514yes—
534C2×D7#42814yescomplemented
535C4×C7—22no—
536C4×C7—42no—
537C4×C7—42no—
538C4×C7—81no—
539C4×C7—81no—
540C4×C7C2×C4×D411yescharacteristic
541C4×C7C2×C4×D411yescharacteristic
542C4×C7C2×C22⋊Q811yescharacteristic
543C4×C7C2×C22⋊Q811yescharacteristic
544Dic7—22no—
545Dic7—42no—
546Dic7—42no—
547Dic7—81no—
548Dic7—81no—
549Dic7#38514yes—
550C24—71no—
551C24—71no—
552C24—74no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24—142no—
557C24—281no—
558C24—281no—
559C24D4×D711yescharacteristic
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—71no—
569C22×C4—72no—
570C22×C4—72no—
571C22×C4—72no—
572C22×C4—72no—
573C22×C4—72no—
574C22×C4—72no—
575C22×C4—74no—
576C22×C4—71no—
577C22×C4—74no—
578C22×C4—74no—
579C22×C4—72no—
580C22×C4—72no—
581C22×C4—142no—
582C22×C4—142no—
583C22×C4—148no—
584C22×C4—148no—
585C22×C4—148no—
586C22×C4—148no—
587C22×C4—142no—
588C22×C4—142no—
589C22×C4—144no—
590C22×C4—144no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—141no—
597C22×C4—141no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—282no—
602C22×C4—282no—
603C22×C4—282no—
604C22×C4—282no—
605C22×C4—282no—
606C22×C4—282no—
607C22×C4—282no—
608C22×C4—282no—
609C22×C4—282no—
610C22×C4—282no—
611C22×C4C2×C4×D712yes—
612C22×C4D4×D711yescharacteristic
613C22×C4Q8×D712yes—
614C22×C4C23×D711yescharacteristic
615M16—148no—
616M16—148no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—72no—
622C2×C8—72no—
623C2×C8—141no—
624C2×C8—141no—
625C2×C8—141no—
626C2×C8—141no—
627C2×C8C2×C4×D712yes—
628C2×C8C2×C4×D712yes—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—72no—
636C4⋊C4—72no—
637C4⋊C4—144no—
638C4⋊C4—144no—
639C4⋊C4—141no—
640C4⋊C4—141no—
641C4⋊C4—141no—
642C4⋊C4—141no—
643C4⋊C4—141no—
644C4⋊C4—141no—
645C4⋊C4—282no—
646C4⋊C4—282no—
647C4⋊C4D4×D712yes—
648C4⋊C4D4×D712yes—
649C22⋊C4—24no—
650C22⋊C4—42no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—282no—
655C22⋊C4—282no—
656C22⋊C4—282no—
657C42—24no—
658C42—144no—
659C42—144no—
660C42—144no—
661C2×C7—42no—
662C2×C7C2×#38511yescharacteristic
663C2×C7C2×#42811yescharacteristic
664C2×C7#291111yescharacteristic
665C2×C7#300611yescharacteristic
666C2×C7#300711yescharacteristic
667C2×C7#309411yescharacteristic
668C2×C7#309511yescharacteristic
669D7—24no—
670D7—24no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—72no—
678C23—72no—
679C23—72no—
680C23—72no—
681C23—72no—
682C23—72no—
683C23—148no—
684C23—148no—
685C23—141no—
686C23—141no—
687C23—141no—
688C23—141no—
689C23—141no—
690C23—141no—
691C23—141no—
692C23—141no—
693C23—284no—
694C23—284no—
695C23—284no—
696C23—284no—
697C23—284no—
698C23D7×C4⋊C412yes—
699C23C2×D4×D711yescharacteristic
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—72no—
719C2×C4—72no—
720C2×C4—72no—
721C2×C4—74no—
722C2×C4—74no—
723C2×C4—74no—
724C2×C4—74no—
725C2×C4—72no—
726C2×C4—148no—
727C2×C4—148no—
728C2×C4—148no—
729C2×C4—141no—
730C2×C4—141no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—288no—
738C2×C4—288no—
739C2×C4—281no—
740C2×C4—281no—
741C2×C4—281no—
742C2×C4—281no—
743C2×C4—281no—
744C2×C4—281no—
745C2×C4—281no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4—281no—
749C2×C4—564no—
750C2×C4—564no—
751C2×C4D7×C4⋊C412yes—
752C2×C4C22×C4×D711yescharacteristic
753C2×C4C2×D4×D711yescharacteristic
754C2×C4C2×D4×D711yescharacteristic
755C2×C4C2×Q8×D711yescharacteristic
756C2×C4D7×#4111yescharacteristic
757C2×C4D7×#4111yescharacteristic
758C8—22no—
759C8—22no—
760C8—142no—
761C8—142no—
762C7#2084611yescharacteristic, complemented, Sylow
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—74no—
771C22—74no—
772C22—142no—
773C22—142no—
774C22—142no—
775C22—142no—
776C22—142no—
777C22—142no—
778C22—142no—
779C22—142no—
780C22—142no—
781C22—142no—
782C22—142no—
783C22—142no—
784C22—2816no—
785C22C2×D7×C4⋊C411yescharacteristic
786C22D7×#12011yescharacteristic
787C22D7×#12311yescharacteristic
788C22#9045911yescharacteristic
789C22#9045911yescharacteristic
790C22D7×AGL(1,ℤ/8)11yescharacteristic
791C22D7×#13711yescharacteristic
792C4—22no—
793C4—42no—
794C4—42no—
795C4—74no—
796C4—81no—
797C4—81no—
798C4—142no—
799C4—282no—
800C4—282no—
801C4—561no—
802C4—561no—
803C4C4×D4×D711yescharacteristic
804C4C4×D4×D711yescharacteristic
805C4D7×C22⋊Q811yescharacteristic
806C4D7×C22⋊Q811yescharacteristic
807C2—42no—
808C2—144no—
809C2—144no—
810C2D7×#38511yescharacteristic
811C2#1173662211yescharacteristic
812C2D7×#42811yescharacteristic
813C2#1173752911yescharacteristic
814C2#1173767311yescharacteristic
815C2#1173881811yescharacteristic
816C2#1173896211yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1854C2
socleC23×C7C22×D4
prime radicalC24×D7D4
cosocleC22×C4×C7C24
hypercenter#1854D7
hypocenterC7#20846
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#89653C2semidirect
3. C2×#89633C2semidirect
6. C7×#1854C2semidirect
7. #11729330C2semidirect
8. #11728386C2semidirect
9. #11728333C2semidirect
10. #11727683C2semidirect
11. #11727260C2semidirect
12. #11726629C2semidirect
13. #11726628C2semidirect
14. #11726621C2semidirect
15. #11726621C2semidirect
34. C2×C7×#107C22semidirect
35. C2×C7×#106C22semidirect
42. C2×#6392C22semidirect
43. C2×#6391C22semidirect
46. C2×#6382C22semidirect
47. C2×#6382C22semidirect
48. C2×#6381C22semidirect
49. C2×#6381C22semidirect
53. #89498C4semidirect
56. C7×#340C22semidirect
57. C7×#340C22semidirect
58. #89346C22semidirect
59. #89346C22semidirect
60. #89324C22semidirect
61. #89324C22semidirect
62. #89324C22semidirect
63. #89324C22semidirect
118. C2×#1131C2×C4semidirect
119. C2×#1131C2×C4semidirect
139. C7×C22⋊C8C2×C4semidirect
144. C22⋊(C7⋊C8)C2×C4semidirect
145. (C2×D7)⋊C8C2×C4semidirect
146. (C2×D7)⋊C8C2×C4semidirect
161. #1854D7semidirect
302. C2×#107C2×D7semidirect
306. C2×#106C2×D7semidirect
325. #340C2×D7semidirect
326. #340C2×D7semidirect
501. C22⋊C8C4×D7semidirect
534. C2×D7#428semidirect
762. C7#20846semidirect

Maximal subgroups

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

subgroupindex
C2×D7×#1172
C2×#896532
C2×#896332
C2×#894982
D7×#3802
C7×#18542
#117293302
#117283862
#117283332
#117276832
#117272602
#117266292
#117266282
#117266212
#208467