Finite Group Databasebeta

← #13374184

Subgroups — #13374184

Order 1792.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2341C211yesmaximal, characteristic, complemented
2C2×#90010C211yesmaximal, characteristic
3C2×#90004C211yesmaximal, characteristic, complemented
4C2×#89798C211yesmaximal, characteristic, complemented
5#11730912C211yesmaximal, characteristic, complemented
6#11729387C211yesmaximal, characteristic, complemented
7C4×#6409C211yesmaximal, characteristic, complemented
8#11729382C211yesmaximal, characteristic, complemented
9#11727411C211yesmaximal, characteristic, complemented
10#11727401C211yesmaximal, characteristic, complemented
11#11727399C211yesmaximal, characteristic, complemented
12#11727390C211yesmaximal, characteristic, complemented
13#11727271C211yesmaximal, characteristic, complemented
14#11727258C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C22×#1141C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C22×#1136C2211yescharacteristic
24C2×(C22⋊D7)⋊C4—21no—
25C2×C4×D28C2211yescharacteristic
26C7×#390—21no—
27C7×#390—21no—
28C7×#390C2211yescharacteristic
29C7×#390C2211yescharacteristic
30C7×#380—21no—
31C7×#380C2211yescharacteristic
32C4×C7×C22⋊C4—21no—
33C4×C7×C22⋊C4C2211yescharacteristic
34#90010C418yescomplemented
35#90004—24no—
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6409C2211yescharacteristic
39C2×#6406C2211yescharacteristic
40C2×#6406C2211yescharacteristic
41C2×#6406C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43#89798—24no—
44C2×#6383C2211yescharacteristic
45C2×#6383C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47C2×#6381C2211yescharacteristic
48#89730—21no—
49#89711C2211yescharacteristic
50C4×C4⋊Dic7C2211yescharacteristic
51#89700C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54#89442—21no—
55#89440—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#22863—71nomaximal, Sylow
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C2×C7×#41C2×C414yescomplemented
69C22×C7×Q8C2311yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7C2311yescharacteristic
74C22×C22⋊D7—21no—
75C23×Dic7—21no—
76C22×D28C2311yescharacteristic
77C22×C4×D7—21no—
78C4×C7×Q8—22no—
79C4×C7×Q8—22no—
80C4×C7×Q8—41no—
81C4×C7×Q8—41no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C7×C22⋊C4—21no—
91C2×C7×C22⋊C4D411yescharacteristic
92C2×C7×C22⋊C4D411yescharacteristic
93C2×C42×C7—21no—
94C2×C42×C7—21no—
95C2×C42×C7C2311yescharacteristic
96C2×C42×C7C2311yescharacteristic
97C2×#1143—22no—
98C2×#1143—22no—
99C2×#1143C2×C414yescomplemented
100C2×#1141—41no—
101C2×#1141—41no—
102C2×#1141C2×C414yescomplemented
103#6493—22no—
104#6493C2×C414yes—
105C2×(C2×D7)⋊C4—21no—
106C2×(C2×D7)⋊C4—21no—
107C2×(C2×D7)⋊C4—21no—
108C2×(C2×D7)⋊C4—21no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—21no—
111C2×C4⋊Dic7—41no—
112C2×C4⋊Dic7C2311yescharacteristic
113C2×C4⋊Dic7C2311yescharacteristic
114C2×C4⋊Dic7C2311yescharacteristic
115C2×Dic7⋊C4—21no—
116C2×C4×Dic7—21no—
117C2×#1136—22no—
118C2×#1136—22no—
119C2×#1136—41no—
120C22×C7⋊C8C2311yescharacteristic
121C22×C7⋊C8C2311yescharacteristic
122C22×C7⋊C8C2311yescharacteristic
123C22×C7⋊C8C2311yescharacteristic
124(C22⋊D7)⋊C4—44no—
125C4×D28—22no—
126C4×D28—41no—
127C7×#95—21no—
128C7×#95D411yescharacteristic
129C7×#95D411yescharacteristic
130#6409—22no—
131#6409C2×C414yescomplemented
132#6409D414yescomplemented
133#6406—22no—
134#6406—22no—
135#6406C2×C414yescomplemented
136C7⋊#95—21no—
137C7⋊#95—21no—
138C22⋊(C7⋊C8)C2×C414yescomplemented
139#6383—22no—
140#6383—41no—
141#6381—22no—
142#6381—41no—
143#6377—22no—
144C4×C7⋊C8—41no—
145C2×#449—71no—
146C2×#440—71no—
147C2×#417—71no—
148#2361—71no—
149#2341D711yescharacteristic, complemented
150#1970—71no—
151#1936—71no—
152#1925—71no—
153#1895—71no—
154#1880—71no—
155#1879—71no—
156#1863—71no—
157#1852—71no—
158C4×#103—71no—
159#1753—71no—
160C24×C7—21no—
161C24×C7C2×D411yescharacteristic
162C23×D7—21no—
163C7×#41—28no—
164C7×#41—44no—
165C7×#41—44no—
166C7×#41—44no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8C22×C412yes—
171C2×C7×Q8C2×D412yes—
172C2×C7×Q8#4112yes—
173C2×C7×D4—24no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—21no—
178C2×C7×D4—21no—
179C2×C7×D4—42no—
180C2×C7×D4—42no—
181C2×C7×D4C22×C412yes—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—24no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—42no—
191C22×C4×C7—42no—
192C22×C4×C7C22×C412yes—
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7#4112yes—
199C22×C4×C7C2411yescharacteristic
200C2×C22⋊D7—24no—
201C2×C22⋊D7—42no—
202C2×C22⋊D7—42no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—42no—
207C22×Dic7—42no—
208C22×Dic7—81no—
209C2×D28—21no—
210C2×D28—21no—
211C2×D28—21no—
212C2×D28—21no—
213C2×D28—21no—
214C2×D28C22×C412yes—
215C2×C4×D7—42no—
216C2×C4×D7—42no—
217C2×C4×D7—81no—
218C7×C4⋊C4—21no—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—42no—
223C7×C4⋊C4—42no—
224C7×C22⋊C4—22no—
225C7×C22⋊C4—41no—
226C7×C22⋊C4—42no—
227C7×C22⋊C4—42no—
228C7×C22⋊C4—81no—
229C7×C22⋊C4—81no—
230C7×C22⋊C4—81no—
231C42×C7—21no—
232C42×C7—21no—
233C42×C7—21no—
234C42×C7—21no—
235C42×C7—42no—
236C42×C7—42no—
237#1143—28no—
238#1141—44no—
239(C2×D7)⋊C4—24no—
240(C2×D7)⋊C4—42no—
241(C2×D7)⋊C4—42no—
242(C2×D7)⋊C4—81no—
243C4⋊Dic7—21no—
244C4⋊Dic7—21no—
245C4⋊Dic7—21no—
246C4⋊Dic7—21no—
247C4⋊Dic7—42no—
248C4⋊Dic7C22×C412yes—
249C4⋊Dic7C2×D412yes—
250Dic7⋊C4—42no—
251C4×Dic7—42no—
252#1136—44no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8—21no—
256C2×C7⋊C8—21no—
257C2×C7⋊C8—21no—
258C2×C7⋊C8—21no—
259C2×C7⋊C8—21no—
260C2×C7⋊C8—21no—
261C2×C7⋊C8—21no—
262C2×C7⋊C8C22×C412yes—
263C2×C7⋊C8C22×C412yes—
264C2×C7⋊C8C2×D412yes—
265C22×#41C2×D711yescharacteristic
266C22×SD16—71no—
267C22×D8—71no—
268C22×M16—71no—
269C2×#121—71no—
270C2×C4×Q8C2×D711yescharacteristic
271C2×C4×Q8C2×D711yescharacteristic
272C2×C4×D4—71no—
273C2×C4×D4—141no—
274C22×C4⋊C4—71no—
275#449—78no—
276#440—144no—
277C2×#107—71no—
278C2×#107—71no—
279#417—144no—
280C2×#103—71no—
281C2×#103—71no—
282C2×#103—71no—
283C2×#102—71no—
284C2×#102—71no—
285C2×#102—71no—
286C2×#102—71no—
287C2×#102—71no—
288C2×C22⋊C8—71no—
289C2×#97—71no—
290C2×C4×C8—71no—
291#390—21no—
292#390—21no—
293#390—71no—
294#390C2×D711yescharacteristic
295#390C2×D711yescharacteristic
296#389—71no—
297#388—141no—
298#386—141no—
299#385—141no—
300#380—21no—
301#380C2×D711yescharacteristic
302C4×C4⋊C4—71no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4C2×D711yescharacteristic
305#340—71no—
306#340—71no—
307#340—71no—
308#340—71no—
309#336—71no—
310#336—71no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7—21no—
317C23×C7—22no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
324C23×C7C4×D412yes—
325C23×C7C22×D411yescharacteristic
326C22×D7—22no—
327C22×D7—41no—
328C22×D7—41no—
329C22×D7—41no—
330C22×D7—41no—
331C22×D7—41no—
332C22×D7—41no—
333C7×Q8—22no—
334C7×Q8—22no—
335C7×Q8—22no—
336C7×Q8C4×D414yescomplemented
337C7×D4—22no—
338C7×D4—22no—
339C7×D4—48no—
340C7×D4—41no—
341C7×D4—41no—
342C2×C4×C7—22no—
343C2×C4×C7—21no—
344C2×C4×C7—22no—
345C2×C4×C7—21no—
346C2×C4×C7—22no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—21no—
354C2×C4×C7—21no—
355C2×C4×C7—21no—
356C2×C4×C7—21no—
357C2×C4×C7—21no—
358C2×C4×C7—21no—
359C2×C4×C7—21no—
360C2×C4×C7—21no—
361C2×C4×C7—21no—
362C2×C4×C7—48no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7C4×D412yes—
370C2×C4×C7AGL(1,ℤ/8)12yes—
371C2×C4×C7C23×C411yescharacteristic
372C2×C4×C7C22×D411yescharacteristic
373C2×C4×C7C2×#4111yescharacteristic
374C2×C4×C7C2×#4111yescharacteristic
375C2×C4×C7H(5,𝔽2)11yescharacteristic
376C2×C4×C7H(5,𝔽2)11yescharacteristic
377C22⋊D7—48no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7—41no—
387C2×Dic7—84no—
388D28—22no—
389D28—22no—
390D28—41no—
391D28—41no—
392C4×D7—84no—
393C7⋊C8—22no—
394C7⋊C8—22no—
395C7⋊C8—22no—
396C7⋊C8—41no—
397C2×#41—22no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—41no—
401C2×#41—41no—
402C2×#41C4×D714yescomplemented
403C22×Q8C22×D711yescharacteristic
404C22×D4—21no—
405C22×D4—71no—
406C22×D4—141no—
407C22×D4C22×D711yescharacteristic
408C23×C4—21no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4C22×D711yescharacteristic
412C2×SD16—74no—
413C2×SD16—142no—
414C2×SD16—142no—
415C2×D8—74no—
416C2×D8—281no—
417C2×D8—281no—
418C2×M16—142no—
419C2×M16—142no—
420C2×M16—281no—
421C22×C8—71no—
422C22×C8—71no—
423C22×C8—71no—
424C22×C8—71no—
425#121—74no—
426#121—142no—
427C4×Q8—22no—
428C4×Q8—22no—
429C4×Q8—41no—
430C4×Q8—41no—
431C4×D4—142no—
432C4×D4—281no—
433C4×D4—284no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—71no—
437C2×C4⋊C4—71no—
438C2×C4⋊C4—71no—
439C2×C4⋊C4—142no—
440C2×C4⋊C4—141no—
441C2×C4⋊C4—141no—
442C2×C4⋊C4—281no—
443C2×C4⋊C4C22×D711yescharacteristic
444C2×C4⋊C4C22×D711yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—141no—
451C2×C22⋊C4—141no—
452C2×C22⋊C4—141no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4C22⋊D711yescharacteristic
455C2×C22⋊C4C22⋊D711yescharacteristic
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—141no—
459C2×C42C22×D711yescharacteristic
460C2×C42C22×D711yescharacteristic
461#107—142no—
462#107—281no—
463#103—74no—
464#103—74no—
465#103—142no—
466#102—74no—
467#102—142no—
468#102—142no—
469#102—142no—
470#102—281no—
471C22⋊C8—74no—
472#97—142no—
473C4×C8—281no—
474#95—21no—
475#95—141no—
476#95—141no—
477#95C22⋊D711yescharacteristic
478#95C22⋊D711yescharacteristic
479C22×C7—22no—
480C22×C7—22no—
481C22×C7—22no—
482C22×C7—41no—
483C22×C7—41no—
484C22×C7—41no—
485C22×C7—41no—
486C22×C7—42no—
487C22×C7—42no—
488C22×C7—42no—
489C22×C7—81no—
490C22×C7—81no—
491C22×C7—81no—
492C22×C7—81no—
493C22×C7C2×C4×D411yescharacteristic
494C22×C7D4211yescharacteristic
495C22×C7#54611yescharacteristic
496C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
497C22×C7#57511yescharacteristic
498C22×C7#57611yescharacteristic
499C22×C7#57811yescharacteristic
500C2×D7—42no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—81no—
504C2×D7—81no—
505C2×D7—81no—
506C2×D7—81no—
507C4×C7—22no—
508C4×C7—24no—
509C4×C7—22no—
510C4×C7—41no—
511C4×C7—41no—
512C4×C7—41no—
513C4×C7—81no—
514C4×C7—81no—
515C4×C7C2×C4×D411yescharacteristic
516C4×C7#51811yescharacteristic
517C4×C7#54611yescharacteristic
518C4×C7#55111yescharacteristic
519Dic7—42no—
520Dic7—42no—
521Dic7—81no—
522C24—21no—
523C24—141no—
524C24C2×C22⋊D711yescharacteristic
525#41—28no—
526#41—44no—
527#41—44no—
528#41—44no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C2×C4×D712yes—
533C2×Q8D4×D712yes—
534C2×Q8#115912yes—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—72no—
544C2×D4—144no—
545C2×D4—141no—
546C2×D4—141no—
547C2×D4—141no—
548C2×D4—141no—
549C2×D4—141no—
550C2×D4—282no—
551C2×D4—282no—
552C2×D4C2×C4×D712yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—282no—
567C22×C4—282no—
568C22×C4—282no—
569C22×C4—282no—
570C22×C4—561no—
571C22×C4—561no—
572C22×C4C2×C4×D712yes—
573C22×C4#115712yes—
574C22×C4C2×C22⋊D711yescharacteristic
575C22×C4C2×C22⋊D711yescharacteristic
576C22×C4C2×C22⋊D711yescharacteristic
577C22×C4C2×C22⋊D711yescharacteristic
578C22×C4C2×C22⋊D711yescharacteristic
579C22×C4C23×D711yescharacteristic
580SD16—148no—
581D8—284no—
582M16—284no—
583C2×C8—72no—
584C2×C8—72no—
585C2×C8—72no—
586C2×C8—141no—
587C2×C8—141no—
588C2×C8—141no—
589C2×C8—141no—
590C2×C8—141no—
591C2×C8—141no—
592C2×C8—141no—
593C2×C8—141no—
594C2×C8—141no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—72no—
602C4⋊C4—72no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4—141no—
606C4⋊C4—141no—
607C4⋊C4—282no—
608C4⋊C4—282no—
609C22⋊C4—22no—
610C22⋊C4—41no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—144no—
617C22⋊C4—282no—
618C22⋊C4—282no—
619C22⋊C4—561no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—42no—
625C42—42no—
626C42—282no—
627C2×C7—42no—
628C2×C7—82no—
629C2×C7#235811yescharacteristic
630C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
631C2×C7#295111yescharacteristic
632C2×C7#327411yescharacteristic
633C2×C7#327711yescharacteristic
634C2×C7#330811yescharacteristic
635C2×C7#330911yescharacteristic
636D7—82no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—142no—
651C23—281no—
652C23—281no—
653C23—281no—
654C23—281no—
655C23—281no—
656C23—281no—
657C23C4×C22⋊D712yes—
658C23C22×C22⋊D711yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8(C22⋊D7)⋊C414yescomplemented
663D4—22no—
664D4—22no—
665D4—48no—
666D4—41no—
667D4—41no—
668D4—142no—
669D4—142no—
670D4—288no—
671D4—281no—
672D4—281no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—48no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—281no—
703C2×C4—281no—
704C2×C4—281no—
705C2×C4—281no—
706C2×C4—281no—
707C2×C4—281no—
708C2×C4—281no—
709C2×C4—564no—
710C2×C4—564no—
711C2×C4C4×C22⋊D712yes—
712C2×C4#651212yes—
713C2×C4C22×C4×D711yescharacteristic
714C2×C4C2×#115711yescharacteristic
715C2×C4C2×D4×D711yescharacteristic
716C2×C4C2×#115911yescharacteristic
717C2×C4#654811yescharacteristic
718C2×C4#654811yescharacteristic
719C8—142no—
720C8—142no—
721C8—142no—
722C8—281no—
723C7#2286311yescharacteristic, complemented, Sylow
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—561no—
742C22—561no—
743C22—561no—
744C22—561no—
745C22C2×C4×C22⋊D711yescharacteristic
746C22D4×C22⋊D711yescharacteristic
747C22#9049711yescharacteristic
748C22C2×#651211yescharacteristic
749C22#9051311yescharacteristic
750C22#9052611yescharacteristic
751C22#9052911yescharacteristic
752C4—22no—
753C4—22no—
754C4—24no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—282no—
761C4—282no—
762C4—561no—
763C4C2×(C22⋊D7)⋊C411yescharacteristic
764C4#9017711yescharacteristic
765C4#9018111yescharacteristic
766C4#9018611yescharacteristic
767C2—42no—
768C2—82no—
769C2—562no—
770C2#1173954411yescharacteristic
771C2C4×#651211yescharacteristic
772C2#1174000211yescharacteristic
773C2#1174098111yescharacteristic
774C2#1174099311yescharacteristic
775C2#1174101711yescharacteristic
776C2#1174102311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2341C2
socleC23×C7C22×D4
prime radicalC2×#90010C2
cosocleC22×C4×C7C24
hypercenter#2341D7
hypocenterC7#22863
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
1. C7×#2341C2semidirect
3. C2×#90004C2semidirect
4. C2×#89798C2semidirect
5. #11730912C2semidirect
6. #11729387C2semidirect
7. C4×#6409C2semidirect
8. #11729382C2semidirect
9. #11727411C2semidirect
10. #11727401C2semidirect
11. #11727399C2semidirect
12. #11727390C2semidirect
13. #11727271C2semidirect
14. #11727258C2semidirect
15. #11727202C2semidirect
34. #90010C4semidirect
68. C2×C7×#41C2×C4semidirect
99. C2×#1143C2×C4semidirect
102. C2×#1141C2×C4semidirect
131. #6409C2×C4semidirect
132. #6409D4semidirect
135. #6406C2×C4semidirect
138. C22⋊(C7⋊C8)C2×C4semidirect
149. #2341D7semidirect
336. C7×Q8C4×D4semidirect
402. C2×#41C4×D7semidirect
662. Q8(C22⋊D7)⋊C4semidirect
723. C7#22863semidirect

Maximal subgroups

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

subgroupindex
C7×#23412
C2×#900102
C2×#900042
C2×#897982
#117309122
#117293872
C4×#64092
#117293822
#117274112
#117274012
#117273992
#117273902
#117272712
#117272582
#117272022
#228637