Finite Group Databasebeta

← #13374204

Subgroups — #13374204

Order 1792.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2362C211yesmaximal, characteristic, complemented
2C2×#89818C211yesmaximal, characteristic
3C2×#89798C211yesmaximal, characteristic, complemented
4C2×#89773C211yesmaximal, characteristic
5C22⋊C4×D28C211yesmaximal, characteristic
6#11729451C211yesmaximal, characteristic, complemented
7#11729387C211yesmaximal, characteristic, complemented
8#11729330C211yesmaximal, characteristic, complemented
9#11727441C211yesmaximal, characteristic, complemented
10#11727430C211yesmaximal, characteristic, complemented
11#11727380C211yesmaximal, characteristic, complemented
12#11727371C211yesmaximal, characteristic, complemented
13C4×#6383C211yesmaximal, characteristic, complemented
14#11727216C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C23×D28C2211yescharacteristic
17C2×C7×C22⋊Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic, complemented
19C2×C7×#117C2211yescharacteristic
20C22×#1143C2211yescharacteristic
21C22×#1143C2211yescharacteristic
22C22×#1136C2211yescharacteristic
23C2×D7×C22⋊C4—21no—
24C2×C4×D28C2211yescharacteristic
25C2×C4×D28C2211yescharacteristic
26C7×#391C2211yescharacteristic, complemented
27C7×#389C2211yescharacteristic, complemented
28C7×#388—21no—
29C7×#388—21no—
30C7×#387—21no—
31C4×C7×C4⋊C4—21no—
32C4×C7×C4⋊C4C2211yescharacteristic, complemented
33C4×C7×C22⋊C4C2211yescharacteristic
34C2×#6409C2211yescharacteristic, complemented
35C2×#6409C2211yescharacteristic, complemented
36#89984C2211yescharacteristic
37C2×C22⋊(C7⋊C8)C2211yescharacteristic
38#89818C418yescomplemented
39#89798—24no—
40#89773—24no—
41C2×#6383C2211yescharacteristic
42C2×#6383C2211yescharacteristic
43C2×#6383C2211yescharacteristic
44C2×#6383C2211yescharacteristic
45C2×#6383C2211yescharacteristic
46C2×#6383C2211yescharacteristic
47C2×#6382C2211yescharacteristic, complemented
48C2×#6381C2211yescharacteristic, complemented
49#89727—21no—
50#89711C2211yescharacteristic
51#89711C2211yescharacteristic
52C2×#6377C2211yescharacteristic, complemented
53C2×C4×C7⋊C8C2211yescharacteristic, complemented
54#89437—21no—
55#89437—21no—
56#89324C2211yescharacteristic, complemented
57#89324C2211yescharacteristic, complemented
58#89324C2211yescharacteristic, complemented
59#89324C2211yescharacteristic, complemented
60#89319C2211yescharacteristic, complemented
61#89319C2211yescharacteristic, complemented
62#22864—71nomaximal, Sylow
63C24×D7—21no—
64C22×C7×Q8C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C22×D28—22no—
67C22×D28—22no—
68C22×D28—21no—
69C22×D28—22no—
70C22×D28—41no—
71C22×D28—41no—
72C22×D28C2×C414yes—
73C22×D28C2311yescharacteristic
74C22×D28C2311yescharacteristic
75C22×C4×D7—21no—
76C22×C4×D7—21no—
77C7×C22⋊Q8—22no—
78C7×C22⋊Q8C2×C414yescomplemented
79C4×C7×Q8—22no—
80C4×C7×Q8—41no—
81C7×#117—22no—
82C7×#117—41no—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4—21no—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4C2311yescharacteristic
87C2×C7×C4⋊C4C2311yescharacteristic
88C2×C7×C4⋊C4C2311yescharacteristic
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×C7—21no—
96C2×C42×C7C2311yescharacteristic
97C2×C42×C7C2311yescharacteristic
98C2×C22⋊Dic7—21no—
99C2×#1143—22no—
100C2×#1143—22no—
101C2×#1143—41no—
102C2×#1143—41no—
103C2×#1143C2×C414yes—
104C2×#1143C2×C414yescomplemented
105C2×(C2×D7)⋊C4—21no—
106C2×(C2×D7)⋊C4—21no—
107C2×(C2×D7)⋊C4—21no—
108C2×(C2×D7)⋊C4—21no—
109C2×(C2×D7)⋊C4—21no—
110C2×(C2×D7)⋊C4—21no—
111C2×C4⋊Dic7C2311yescharacteristic
112C2×C4⋊Dic7C2311yescharacteristic
113C2×#1136—22no—
114C2×#1136—22no—
115C2×#1136—41no—
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C22×C7⋊C8C2311yescharacteristic
119C22×C7⋊C8C2311yescharacteristic
120D7×C22⋊C4—44no—
121C4×D28—22no—
122C4×D28—22no—
123C4×D28—41no—
124C4×D28—41no—
125C7×#95—21no—
126C7×#95—21no—
127C7×#95—21no—
128C7×#95—21no—
129C7×#95D411yescharacteristic
130C7×#95D411yescharacteristic
131#6409—22no—
132#6409—41no—
133C7⋊#95—21no—
134C22⋊(C7⋊C8)C2×C414yescomplemented
135#6383—22no—
136#6383—22no—
137#6383—22no—
138#6383C2×C414yes—
139#6383C2×C414yescomplemented
140#6383D414yes—
141#6382—41no—
142#6381—22no—
143#6377—22no—
144C4×C7⋊C8—41no—
145C2×#450—71no—
146C2×#440—71no—
147C2×#418—71no—
148#2362D711yescharacteristic, complemented
149D4×C22⋊C4—71no—
150#1968—71no—
151#1936—71no—
152#1925—71no—
153#1894—71no—
154#1880—71no—
155#1877—71no—
156#1864—71no—
157#1854—71no—
158C4×#102—71no—
159#1753—71no—
160C24×C7C2×D411yescharacteristic
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—24no—
164C23×D7—42no—
165C23×D7—42no—
166C23×D7—42no—
167C23×D7—42no—
168C23×D7—81no—
169C23×D7—81no—
170C2×C7×Q8—21no—
171C2×C7×Q8—21no—
172C2×C7×Q8—21no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8C22×C412yes—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
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×C7C22×C412yes—
185C22×C4×C7C2×D411yescharacteristic
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7#4112yes—
191C22×C4×C7C2411yescharacteristic
192C22×Dic7—21no—
193C22×Dic7—21no—
194C2×D28—21no—
195C2×D28—21no—
196C2×D28—21no—
197C2×D28—21no—
198C2×D28—21no—
199C2×D28—21no—
200C2×D28—21no—
201C2×D28—28no—
202C2×D28—24no—
203C2×D28—21no—
204C2×D28—44no—
205C2×D28—44no—
206C2×D28—44no—
207C2×D28—42no—
208C2×D28—42no—
209C2×D28C22×C412yes—
210C2×D28C22×C412yes—
211C2×D28C2×D412yes—
212C2×D28#4112yes—
213C2×C4×D7—42no—
214C2×C4×D7—42no—
215C2×C4×D7—42no—
216C2×C4×D7—42no—
217C2×C4×D7—81no—
218C2×C4×D7—81no—
219C7×C4⋊C4—24no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—21no—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—42no—
225C7×C4⋊C4—42no—
226C7×C4⋊C4C22×C412yes—
227C7×C4⋊C4C2×D412yes—
228C7×C22⋊C4—24no—
229C7×C22⋊C4—22no—
230C7×C22⋊C4—41no—
231C7×C22⋊C4—42no—
232C42×C7—21no—
233C42×C7—21no—
234C42×C7—21no—
235C42×C7—21no—
236C42×C7—42no—
237C42×C7—42no—
238C42×C7—42no—
239C22⋊Dic7—42no—
240#1143—28no—
241#1143—44no—
242(C2×D7)⋊C4—42no—
243(C2×D7)⋊C4—42no—
244(C2×D7)⋊C4—42no—
245(C2×D7)⋊C4—42no—
246(C2×D7)⋊C4—81no—
247(C2×D7)⋊C4—81no—
248C4⋊Dic7—21no—
249C4⋊Dic7—21no—
250C4⋊Dic7—21no—
251C4⋊Dic7—21no—
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—
265C23×D4—71no—
266C22×SD16—71no—
267C22×SD16—71no—
268C22×M16—71no—
269C2×C22⋊Q8C2×D711yescharacteristic
270C2×C4×Q8C2×D711yescharacteristic, complemented
271C2×C4×D4—71no—
272C2×C4×D4—71no—
273C2×#117C2×D711yescharacteristic
274C22×C22⋊C4—141no—
275#450—78no—
276#440—144no—
277C2×#107—71no—
278C2×#106—71no—
279#418—144no—
280C2×#103—71no—
281C2×#103—71no—
282C2×#102—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#391C2×D711yescharacteristic, complemented
292#390—71no—
293#390—71no—
294#389C2×D711yescharacteristic, complemented
295#388—21no—
296#388—21no—
297#387—21no—
298#386—141no—
299#386—141no—
300#380—71no—
301#379—141no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4C2×D711yescharacteristic, complemented
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×C7C4×D412yes—
318C23×C7C22×D411yescharacteristic
319C22×D7—22no—
320C22×D7—22no—
321C22×D7—22no—
322C22×D7—22no—
323C22×D7—48no—
324C22×D7—41no—
325C22×D7—41no—
326C22×D7—41no—
327C22×D7—41no—
328C22×D7—48no—
329C22×D7—41no—
330C22×D7—41no—
331C22×D7—41no—
332C22×D7—41no—
333C22×D7—41no—
334C22×D7—41no—
335C22×D7—84no—
336C22×D7—84no—
337C22×D7—84no—
338C22×D7—84no—
339C22×D7—84no—
340C7×Q8—22no—
341C7×Q8—22no—
342C7×Q8—41no—
343C7×Q8—41no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—21no—
355C2×C4×C7—21no—
356C2×C4×C7—22no—
357C2×C4×C7—21no—
358C2×C4×C7—21no—
359C2×C4×C7—21no—
360C2×C4×C7—21no—
361C2×C4×C7—21no—
362C2×C4×C7—21no—
363C2×C4×C7—21no—
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×C7C4×D412yes—
374C2×C4×C7AGL(1,ℤ/8)12yes—
375C2×C4×C7C23×C411yescharacteristic
376C2×C4×C7C22×D411yescharacteristic
377C2×C4×C7C2×#4111yescharacteristic
378C2×C4×C7C2×#4111yescharacteristic
379C2×C4×C7H(5,𝔽2)11yescharacteristic
380C2×C4×C7H(5,𝔽2)11yescharacteristic
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7—41no—
387D28—22no—
388D28—22no—
389D28—22no—
390D28—22no—
391D28—22no—
392D28—48no—
393D28—41no—
394D28—41no—
395D28C4×D414yes—
396C4×D7—84no—
397C4×D7—84no—
398C7⋊C8—22no—
399C7⋊C8—22no—
400C7⋊C8—22no—
401C7⋊C8—41no—
402C25—141no—
403C22×Q8C22×D711yescharacteristic
404C22×D4—74no—
405C22×D4—71no—
406C22×D4—71no—
407C22×D4—142no—
408C22×D4—142no—
409C22×D4—142no—
410C22×D4—141no—
411C22×D4—281no—
412C22×D4—281no—
413C23×C4—141no—
414C23×C4—141no—
415C23×C4C22×D711yescharacteristic
416C2×SD16—74no—
417C2×SD16—74no—
418C2×SD16—142no—
419C2×SD16—142no—
420C2×SD16—281no—
421C2×SD16—281no—
422C2×M16—142no—
423C2×M16—142no—
424C2×M16—281no—
425C22×C8—71no—
426C22×C8—71no—
427C22×C8—71no—
428C22×C8—71no—
429C22⋊Q8—22no—
430C22⋊Q8C4×D714yescomplemented
431C4×Q8—22no—
432C4×Q8—41no—
433C4×D4—142no—
434C4×D4—142no—
435C4×D4—281no—
436C4×D4—281no—
437#117—22no—
438#117—41no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—71no—
443C2×C4⋊C4—71no—
444C2×C4⋊C4C22×D711yescharacteristic
445C2×C4⋊C4C22×D711yescharacteristic
446C2×C4⋊C4C22×D711yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—141no—
450C2×C22⋊C4—141no—
451C2×C22⋊C4—141no—
452C2×C22⋊C4—141no—
453C2×C22⋊C4—141no—
454C2×C22⋊C4—141no—
455C2×C22⋊C4—141no—
456C2×C22⋊C4—284no—
457C2×C22⋊C4C22⋊D711yescharacteristic
458C2×C22⋊C4C22⋊D711yescharacteristic
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C22×D711yescharacteristic
463C2×C42C22×D711yescharacteristic
464#107—142no—
465#106—281no—
466#103—142no—
467#103—281no—
468#102—74no—
469#102—74no—
470#102—74no—
471#102—142no—
472#102—142no—
473#102—142no—
474C22⋊C8—74no—
475#97—142no—
476C4×C8—281no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—141no—
482#95C22⋊D711yescharacteristic
483#95C22⋊D711yescharacteristic
484C22×C7—22no—
485C22×C7—22no—
486C22×C7—22no—
487C22×C7—41no—
488C22×C7—41no—
489C22×C7—41no—
490C22×C7—41no—
491C22×C7C2×C4×D411yescharacteristic
492C22×C7D4211yescharacteristic
493C22×C7#54611yescharacteristic
494C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
495C22×C7#57511yescharacteristic
496C22×C7#57711yescharacteristic
497C22×C7#57711yescharacteristic
498C2×D7—24no—
499C2×D7—42no—
500C2×D7—42no—
501C2×D7—42no—
502C2×D7—42no—
503C2×D7—42no—
504C2×D7—42no—
505C2×D7—42no—
506C2×D7—42no—
507C2×D7—42no—
508C2×D7—816no—
509C2×D7—81no—
510C2×D7—81no—
511C2×D7—81no—
512C2×D7—81no—
513C4×C7—22no—
514C4×C7—22no—
515C4×C7—42no—
516C4×C7—42no—
517C4×C7—41no—
518C4×C7—42no—
519C4×C7—41no—
520C4×C7—41no—
521C4×C7—81no—
522C4×C7C2×C4×D411yescharacteristic
523C4×C7#51811yescharacteristic
524C4×C7#54611yescharacteristic
525C4×C7#55111yescharacteristic
526Dic7—81no—
527Dic7—81no—
528C24—141no—
529C24—141no—
530C24—144no—
531C24—282no—
532C24—282no—
533C24—282no—
534C24—282no—
535C24—561no—
536C24—561no—
537C24C2×C22⋊D711yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C4×D712yes—
544C2×D4—72no—
545C2×D4—72no—
546C2×D4—72no—
547C2×D4—72no—
548C2×D4—148no—
549C2×D4—144no—
550C2×D4—141no—
551C2×D4—141no—
552C2×D4—141no—
553C2×D4—141no—
554C2×D4—141no—
555C2×D4—141no—
556C2×D4—141no—
557C2×D4—141no—
558C2×D4—284no—
559C2×D4—284no—
560C2×D4—284no—
561C2×D4—282no—
562C2×D4—282no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—141no—
572C22×C4—141no—
573C22×C4—282no—
574C22×C4—282no—
575C22×C4—282no—
576C22×C4—282no—
577C22×C4—561no—
578C22×C4—561no—
579C22×C4C2×C4×D712yes—
580C22×C4#115712yes—
581C22×C4C2×C22⋊D711yescharacteristic
582C22×C4C2×C22⋊D711yescharacteristic
583C22×C4C2×C22⋊D711yescharacteristic
584C22×C4C2×C22⋊D711yescharacteristic
585C22×C4C2×C22⋊D711yescharacteristic
586C22×C4C23×D711yescharacteristic
587SD16—148no—
588SD16—284no—
589M16—284no—
590C2×C8—72no—
591C2×C8—72no—
592C2×C8—72no—
593C2×C8—141no—
594C2×C8—141no—
595C2×C8—141no—
596C2×C8—141no—
597C2×C8—141no—
598C2×C8—141no—
599C2×C8—141no—
600C2×C8—141no—
601C2×C8—141no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—141no—
610C4⋊C4—141no—
611C4⋊C4—141no—
612C4⋊C4—141no—
613C4⋊C4C2×C4×D712yes—
614C4⋊C4D4×D712yes—
615C22⋊C4—24no—
616C22⋊C4—22no—
617C22⋊C4—41no—
618C22⋊C4—42no—
619C22⋊C4—282no—
620C22⋊C4—282no—
621C22⋊C4—282no—
622C22⋊C4—282no—
623C22⋊C4—282no—
624C22⋊C4—561no—
625C22⋊C4—561no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—42no—
631C42—42no—
632C42—42no—
633C2×C7—42no—
634C2×C7#235811yescharacteristic
635C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
636C2×C7#294911yescharacteristic
637C2×C7#327211yescharacteristic
638C2×C7#327511yescharacteristic
639C2×C7#331011yescharacteristic
640C2×C7#331111yescharacteristic
641D7—44no—
642D7—82no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—142no—
650C23—142no—
651C23—142no—
652C23—142no—
653C23—288no—
654C23—288no—
655C23—281no—
656C23—281no—
657C23—281no—
658C23—281no—
659C23—281no—
660C23—281no—
661C23—281no—
662C23—281no—
663C23—281no—
664C23—281no—
665C23—564no—
666C23—564no—
667C23—564no—
668C23—564no—
669C23—564no—
670C23C4×C22⋊D712yes—
671C23C22×C22⋊D711yescharacteristic
672Q8—22no—
673Q8—22no—
674Q8—41no—
675Q8—41no—
676D4—74no—
677D4—142no—
678D4—142no—
679D4—142no—
680D4—142no—
681D4—142no—
682D4—288no—
683D4—281no—
684D4—281no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—281no—
715C2×C4—281no—
716C2×C4—281no—
717C2×C4—281no—
718C2×C4—281no—
719C2×C4—281no—
720C2×C4—564no—
721C2×C4—564no—
722C2×C4C4×C22⋊D712yes—
723C2×C4#651212yes—
724C2×C4C22×C4×D711yescharacteristic
725C2×C4C2×#115711yescharacteristic
726C2×C4C2×D4×D711yescharacteristic
727C2×C4#654811yescharacteristic
728C2×C4D7×#4111yescharacteristic
729C2×C4#655311yescharacteristic
730C8—142no—
731C8—142no—
732C8—142no—
733C8—281no—
734C7#2286411yescharacteristic, complemented, Sylow
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—144no—
743C22—282no—
744C22—282no—
745C22—282no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—5616no—
753C22—561no—
754C22—561no—
755C22—561no—
756C22—561no—
757C22C2×C4×C22⋊D711yescharacteristic
758C22D4×C22⋊D711yescharacteristic
759C22C2×#651211yescharacteristic
760C22#9051311yescharacteristic
761C22#9052011yescharacteristic
762C22#9052811yescharacteristic
763C22#9052811yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—81no—
773C4—561no—
774C4—561no—
775C4C4×D4×D711yescharacteristic
776C4#9023611yescharacteristic
777C4#9024111yescharacteristic
778C4#9024711yescharacteristic
779C2—42no—
780C2—284no—
781C2—562no—
782C2#1173984311yescharacteristic
783C2C4×#651211yescharacteristic
784C2#1173999311yescharacteristic
785C2#1174096811yescharacteristic
786C2#1174098911yescharacteristic
787C2#1174104411yescharacteristic
788C2#1174111011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2362C2
socleC23×C7C22×D4
prime radicalC23×D28C22
cosocleC22×C4×C7C24
hypercenter#2362D7
hypocenterC7#22864
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
1. C7×#2362C2semidirect
3. C2×#89798C2semidirect
6. #11729451C2semidirect
7. #11729387C2semidirect
8. #11729330C2semidirect
9. #11727441C2semidirect
10. #11727430C2semidirect
11. #11727380C2semidirect
12. #11727371C2semidirect
13. C4×#6383C2semidirect
14. #11727216C2semidirect
15. #11727202C2semidirect
18. C2×C4×C7×Q8C22semidirect
26. C7×#391C22semidirect
27. C7×#389C22semidirect
32. C4×C7×C4⋊C4C22semidirect
34. C2×#6409C22semidirect
35. C2×#6409C22semidirect
38. #89818C4semidirect
47. C2×#6382C22semidirect
48. C2×#6381C22semidirect
52. C2×#6377C22semidirect
53. C2×C4×C7⋊C8C22semidirect
56. #89324C22semidirect
57. #89324C22semidirect
58. #89324C22semidirect
59. #89324C22semidirect
60. #89319C22semidirect
61. #89319C22semidirect
78. C7×C22⋊Q8C2×C4semidirect
104. C2×#1143C2×C4semidirect
134. C22⋊(C7⋊C8)C2×C4semidirect
139. #6383C2×C4semidirect
148. #2362D7semidirect
270. C2×C4×Q8C2×D7semidirect
291. #391C2×D7semidirect
294. #389C2×D7semidirect
303. C4×C4⋊C4C2×D7semidirect
430. C22⋊Q8C4×D7semidirect
734. C7#22864semidirect

Maximal subgroups

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

subgroupindex
C7×#23622
C2×#898182
C2×#897982
C2×#897732
C22⋊C4×D282
#117294512
#117293872
#117293302
#117274412
#117274302
#117273802
#117273712
C4×#63832
#117272162
#117272022
#228647