Finite Group Databasebeta

← #13374199

Subgroups — #13374199

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×D4×C22⋊C4C211yesmaximal, characteristic
2C2×#89990C211yesmaximal, characteristic
3C2×#89987C211yesmaximal, characteristic
4C2×#89790C211yesmaximal, characteristic, complemented
5#11730913C211yesmaximal, characteristic, complemented
6#11729366C211yesmaximal, characteristic, complemented
7C4×#6406C211yesmaximal, characteristic, complemented
8#11729361C211yesmaximal, characteristic, complemented
9#11727414C211yesmaximal, characteristic, complemented
10#11727400C211yesmaximal, characteristic, complemented
11#11727399C211yesmaximal, characteristic, complemented
12#11727390C211yesmaximal, characteristic, complemented
13#11727270C211yesmaximal, characteristic, complemented
14#11727260C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×C7×C22⋊C4—21no—
20C22×#1142C2211yescharacteristic
21C22×#1142C2211yescharacteristic
22C2×#6489C2211yescharacteristic
23C2×#6487C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25C2×C4×Dic14C2211yescharacteristic, complemented
26C7×#390C2211yescharacteristic
27C7×#390C2211yescharacteristic
28C7×#386—21no—
29C7×#386—21no—
30C7×#380C2211yescharacteristic
31C7×#379—21no—
32C4×C7×C22⋊C4C2211yescharacteristic
33#89990C418yescomplemented
34#89987—24no—
35C2×#6406C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39C2×#6406C2211yescharacteristic
40C2×#6406C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89790—24no—
43C2×#6384C2211yescharacteristic, complemented
44C2×#6384C2211yescharacteristic, complemented
45C2×#6382C2211yescharacteristic, complemented
46C2×#6381C2211yescharacteristic, complemented
47#89717—21no—
48#89716—21no—
49C4×C4⋊Dic7C2211yescharacteristic, complemented
50#89701C2211yescharacteristic, complemented
51#89700C2211yescharacteristic, complemented
52C2×#6377C2211yescharacteristic, complemented
53C2×C4×C7⋊C8C2211yescharacteristic, complemented
54#89424—21no—
55#89421—21no—
56#89324C2211yescharacteristic, complemented
57#89324C2211yescharacteristic, complemented
58#89324C2211yescharacteristic, complemented
59#89324C2211yescharacteristic, complemented
60#89319C2211yescharacteristic, complemented
61#89319C2211yescharacteristic, complemented
62#22864—71nomaximal, Sylow
63C25×C7—21no—
64C22×C7×D4—22no—
65C22×C7×D4—22no—
66C22×C7×D4—21no—
67C22×C7×D4—22no—
68C22×C7×D4—41no—
69C22×C7×D4—41no—
70C22×C7×D4C2×C414yes—
71C22×C7×D4C2311yescharacteristic
72C22×C7×D4C2311yescharacteristic
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7C2311yescharacteristic
76C22×Dic14C2311yescharacteristic
77C4×C7×D4—22no—
78C4×C7×D4—22no—
79C4×C7×D4—41no—
80C4×C7×D4—41no—
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C7×C22⋊C4—44no—
91C2×C7×C22⋊C4D411yescharacteristic
92C2×C7×C22⋊C4D411yescharacteristic
93C2×C42×C7C2311yescharacteristic
94C2×C42×C7C2311yescharacteristic
95C2×C22⋊Dic7—21no—
96C2×C22⋊Dic7—21no—
97C2×#1142—22no—
98C2×#1142—22no—
99C2×#1142—41no—
100C2×#1142—41no—
101C2×#1142C2×C414yes—
102C2×#1142C2×C414yescomplemented
103#6489—22no—
104#6489—41no—
105C2×C4⋊Dic7C2311yescharacteristic
106C2×C4⋊Dic7C2311yescharacteristic
107C2×C4⋊Dic7C2311yescharacteristic
108#6487—22no—
109#6487C2×C414yescomplemented
110C2×Dic7⋊C4—21no—
111C2×Dic7⋊C4—21no—
112C2×Dic7⋊C4—21no—
113C2×C4×Dic7—21no—
114C2×C4×Dic7—21no—
115C2×C4×Dic7—21no—
116C2×#1136—22no—
117C2×#1136—22no—
118C2×#1136—41no—
119C22×C7⋊C8C2311yescharacteristic
120C22×C7⋊C8C2311yescharacteristic
121C22×C7⋊C8C2311yescharacteristic
122C22×C7⋊C8C2311yescharacteristic
123C4×Dic14—22no—
124C4×Dic14—41no—
125C7×#95—21no—
126C7×#95D411yescharacteristic
127C7×#95D411yescharacteristic
128#6406—22no—
129#6406—22no—
130#6406—22no—
131#6406C2×C414yes—
132#6406C2×C414yescomplemented
133#6406D414yes—
134C7⋊#95—21no—
135C7⋊#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C22⋊(C7⋊C8)C2×C414yescomplemented
139#6384—22no—
140#6384—41no—
141#6382—41no—
142#6381—22no—
143#6377—22no—
144C4×C7⋊C8—41no—
145C2×#450—71no—
146C2×#440—71no—
147C2×#418—71no—
148#2362—71no—
149D4×C22⋊C4D711yescharacteristic
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×C7—21no—
161C24×C7—21no—
162C24×C7—24no—
163C24×C7—42no—
164C24×C7—42no—
165C24×C7—42no—
166C24×C7—42no—
167C24×C7—81no—
168C24×C7—81no—
169C24×C7C2×D411yescharacteristic
170C2×C7×D4—28no—
171C2×C7×D4—24no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—21no—
178C2×C7×D4—21no—
179C2×C7×D4—21no—
180C2×C7×D4—44no—
181C2×C7×D4—44no—
182C2×C7×D4—44no—
183C2×C7×D4—42no—
184C2×C7×D4—42no—
185C2×C7×D4C22×C412yes—
186C2×C7×D4C22×C412yes—
187C2×C7×D4C2×D412yes—
188C2×C7×D4#4112yes—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—42no—
196C22×C4×C7—42no—
197C22×C4×C7—42no—
198C22×C4×C7—42no—
199C22×C4×C7—81no—
200C22×C4×C7—81no—
201C22×C4×C7C22×C412yes—
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7#4112yes—
208C22×C4×C7C2411yescharacteristic
209C22×Dic7—21no—
210C22×Dic7—21no—
211C22×Dic7—21no—
212C22×Dic7—21no—
213C2×Dic14—21no—
214C2×Dic14—21no—
215C2×Dic14—21no—
216C2×Dic14—21no—
217C2×Dic14—21no—
218C2×Dic14C22×C412yes—
219C7×C4⋊C4—21no—
220C7×C4⋊C4—21no—
221C7×C4⋊C4—21no—
222C7×C4⋊C4—21no—
223C7×C22⋊C4—22no—
224C7×C22⋊C4—41no—
225C7×C22⋊C4—42no—
226C7×C22⋊C4—42no—
227C7×C22⋊C4—42no—
228C7×C22⋊C4—42no—
229C7×C22⋊C4—42no—
230C7×C22⋊C4—81no—
231C7×C22⋊C4—81no—
232C42×C7—21no—
233C42×C7—21no—
234C42×C7—21no—
235C42×C7—21no—
236C22⋊Dic7—24no—
237C22⋊Dic7—42no—
238#1142—28no—
239#1142—44no—
240C4⋊Dic7—21no—
241C4⋊Dic7—21no—
242C4⋊Dic7—21no—
243C4⋊Dic7—21no—
244C4⋊Dic7C22×C412yes—
245C4⋊Dic7C2×D412yes—
246Dic7⋊C4—24no—
247Dic7⋊C4—42no—
248Dic7⋊C4—42no—
249C4×Dic7—42no—
250C4×Dic7—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—
265C23×D4C2×D711yescharacteristic
266C22×SD16—71no—
267C22×SD16—71no—
268C22×M16—71no—
269C2×C22⋊Q8—71no—
270C2×C4×Q8—71no—
271C2×C4×D4C2×D711yescharacteristic
272C2×C4×D4C2×D711yescharacteristic
273C2×#117—71no—
274C22×C22⋊C4—21no—
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#391—71no—
292#390C2×D711yescharacteristic
293#390C2×D711yescharacteristic
294#389—71no—
295#388—141no—
296#388—141no—
297#387—141no—
298#386—21no—
299#386—21no—
300#380C2×D711yescharacteristic
301#379—21no—
302C4×C4⋊C4—71no—
303C4×C4⋊C4—141no—
304C4×C22⋊C4C2×D711yescharacteristic
305#340—71no—
306#340—71no—
307#340—71no—
308#340—71no—
309#336—71no—
310#336—71no—
311C23×C7—22no—
312C23×C7—21no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7—21no—
316C23×C7—21no—
317C23×C7—21no—
318C23×C7—21no—
319C23×C7—21no—
320C23×C7—22no—
321C23×C7—48no—
322C23×C7—48no—
323C23×C7—41no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—84no—
334C23×C7—84no—
335C23×C7—84no—
336C23×C7—84no—
337C23×C7—84no—
338C23×C7C4×D412yes—
339C23×C7C22×D411yescharacteristic
340C7×D4—22no—
341C7×D4—22no—
342C7×D4—22no—
343C7×D4—22no—
344C7×D4—22no—
345C7×D4—48no—
346C7×D4—41no—
347C7×D4—41no—
348C7×D4C4×D414yes—
349C2×C4×C7—21no—
350C2×C4×C7—21no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
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—21no—
365C2×C4×C7—21no—
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—84no—
373C2×C4×C7—84no—
374C2×C4×C7C4×D412yes—
375C2×C4×C7AGL(1,ℤ/8)12yes—
376C2×C4×C7C23×C411yescharacteristic
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7C2×#4111yescharacteristic
379C2×C4×C7C2×#4111yescharacteristic
380C2×C4×C7H(5,𝔽2)11yescharacteristic
381C2×C4×C7H(5,𝔽2)11yescharacteristic
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—41no—
386C2×Dic7—41no—
387C2×Dic7—41no—
388C2×Dic7—41no—
389C2×Dic7—41no—
390C2×Dic7—41no—
391C2×Dic7—41no—
392C2×Dic7—41no—
393C2×Dic7—41no—
394Dic14—22no—
395Dic14—22no—
396Dic14—41no—
397Dic14—41no—
398C7⋊C8—22no—
399C7⋊C8—22no—
400C7⋊C8—22no—
401C7⋊C8—41no—
402C25—21no—
403C22×Q8—71no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—21no—
408C22×D4—41no—
409C22×D4—41no—
410C22×D4C4×D714yes—
411C22×D4C22×D711yescharacteristic
412C22×D4C22×D711yescharacteristic
413C23×C4—21no—
414C23×C4—21no—
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—74no—
430C22⋊Q8—142no—
431C4×Q8—142no—
432C4×Q8—281no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—41no—
436C4×D4—41no—
437#117—142no—
438#117—281no—
439C2×C4⋊C4—71no—
440C2×C4⋊C4—71no—
441C2×C4⋊C4—71no—
442C2×C4⋊C4—141no—
443C2×C4⋊C4—141no—
444C2×C4⋊C4—141no—
445C2×C4⋊C4C22×D711yescharacteristic
446C2×C4⋊C4C22×D711yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—44no—
455C2×C22⋊C4—141no—
456C2×C22⋊C4—141no—
457C2×C22⋊C4C22⋊D711yescharacteristic
458C2×C22⋊C4C22⋊D711yescharacteristic
459C2×C42—141no—
460C2×C42—141no—
461C2×C42—141no—
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—141no—
479#95—141no—
480#95—141no—
481#95—141no—
482#95C22⋊D711yescharacteristic
483#95C22⋊D711yescharacteristic
484C22×C7—22no—
485C22×C7—24no—
486C22×C7—22no—
487C22×C7—22no—
488C22×C7—42no—
489C22×C7—42no—
490C22×C7—42no—
491C22×C7—41no—
492C22×C7—41no—
493C22×C7—42no—
494C22×C7—42no—
495C22×C7—41no—
496C22×C7—41no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—816no—
502C22×C7—81no—
503C22×C7—81no—
504C22×C7—81no—
505C22×C7—81no—
506C22×C7C2×C4×D411yescharacteristic
507C22×C7D4211yescharacteristic
508C22×C7#54611yescharacteristic
509C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
510C22×C7#57511yescharacteristic
511C22×C7#57711yescharacteristic
512C22×C7#57711yescharacteristic
513C4×C7—22no—
514C4×C7—22no—
515C4×C7—41no—
516C4×C7—41no—
517C4×C7—41no—
518C4×C7—81no—
519C4×C7—81no—
520C4×C7C2×C4×D411yescharacteristic
521C4×C7#51811yescharacteristic
522C4×C7#54611yescharacteristic
523C4×C7#55111yescharacteristic
524Dic7—42no—
525Dic7—42no—
526Dic7—42no—
527Dic7—81no—
528C24—21no—
529C24—21no—
530C24—24no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×C22⋊D711yescharacteristic
538C2×Q8—72no—
539C2×Q8—141no—
540C2×Q8—141no—
541C2×Q8—141no—
542C2×Q8—141no—
543C2×Q8—141no—
544C2×D4—28no—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4C2×C4×D712yes—
560C2×D4C2×C4×D712yes—
561C2×D4D4×D712yes—
562C2×D4#115912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—81no—
574C22×C4—81no—
575C22×C4—141no—
576C22×C4—141no—
577C22×C4—141no—
578C22×C4—141no—
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—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—72no—
607C4⋊C4—72no—
608C4⋊C4—144no—
609C4⋊C4—141no—
610C4⋊C4—141no—
611C4⋊C4—141no—
612C4⋊C4—141no—
613C4⋊C4—282no—
614C4⋊C4—282no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—144no—
625C22⋊C4—282no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—282no—
631C42—282no—
632C42—282no—
633C2×C7—42no—
634C2×C7—44no—
635C2×C7—82no—
636C2×C7#235811yescharacteristic
637C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
638C2×C7#294911yescharacteristic
639C2×C7#327211yescharacteristic
640C2×C7#327511yescharacteristic
641C2×C7#331011yescharacteristic
642C2×C7#331111yescharacteristic
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—48no—
654C23—48no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—84no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23C4×C22⋊D712yes—
671C23C22×C22⋊D711yescharacteristic
672Q8—142no—
673Q8—142no—
674Q8—281no—
675Q8—281no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—48no—
682D4—41no—
683D4—41no—
684D4(C22⋊D7)⋊C414yes—
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—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—281no—
714C2×C4—281no—
715C2×C4—281no—
716C2×C4—281no—
717C2×C4—281no—
718C2×C4—281no—
719C2×C4—281no—
720C2×C4—281no—
721C2×C4—281no—
722C2×C4C4×C22⋊D712yes—
723C2×C4#649512yes—
724C2×C4C22×C4×D711yescharacteristic
725C2×C4C2×#115711yescharacteristic
726C2×C4C2×D4×D711yescharacteristic
727C2×C4C2×#115911yescharacteristic
728C2×C4#654811yescharacteristic
729C2×C4#654811yescharacteristic
730C8—142no—
731C8—142no—
732C8—142no—
733C8—281no—
734C7#2286411yescharacteristic, complemented, Sylow
735C22—22no—
736C22—22no—
737C22—22no—
738C22—24no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×C4×C22⋊D711yescharacteristic
758C22C2×#649511yescharacteristic
759C22D4×C22⋊D711yescharacteristic
760C22#9049711yescharacteristic
761C22#9051311yescharacteristic
762C22#9052711yescharacteristic
763C22#9052711yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—81no—
771C4—282no—
772C4—282no—
773C4—282no—
774C4—561no—
775C4C2×(C22⋊D7)⋊C411yescharacteristic
776C4#9017711yescharacteristic
777C4#9018111yescharacteristic
778C4#9018611yescharacteristic
779C2—42no—
780C2—44no—
781C2—82no—
782C2#1173954411yescharacteristic
783C2C4×#649511yescharacteristic
784C2#1173998811yescharacteristic
785C2#1174092911yescharacteristic
786C2#1174093411yescharacteristic
787C2#1174094211yescharacteristic
788C2#1174095311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×D4×C22⋊C4C2
socleC23×C7C22×D4
prime radicalC23×C7×D4C22
cosocleC22×C4×C7C24
hypercenterD4×C22⋊C4D7
hypocenterC7#22864
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#89790C2semidirect
5. #11730913C2semidirect
6. #11729366C2semidirect
7. C4×#6406C2semidirect
8. #11729361C2semidirect
9. #11727414C2semidirect
10. #11727400C2semidirect
11. #11727399C2semidirect
12. #11727390C2semidirect
13. #11727270C2semidirect
14. #11727260C2semidirect
15. #11727202C2semidirect
25. C2×C4×Dic14C22semidirect
33. #89990C4semidirect
43. C2×#6384C22semidirect
44. C2×#6384C22semidirect
45. C2×#6382C22semidirect
46. C2×#6381C22semidirect
49. C4×C4⋊Dic7C22semidirect
50. #89701C22semidirect
51. #89700C22semidirect
52. C2×#6377C22semidirect
53. C2×C4×C7⋊C8C22semidirect
56. #89324C22semidirect
57. #89324C22semidirect
58. #89324C22semidirect
59. #89324C22semidirect
60. #89319C22semidirect
61. #89319C22semidirect
102. C2×#1142C2×C4semidirect
109. #6487C2×C4semidirect
132. #6406C2×C4semidirect
138. C22⋊(C7⋊C8)C2×C4semidirect
734. C7#22864semidirect

Maximal subgroups

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

subgroupindex
C7×D4×C22⋊C42
C2×#899902
C2×#899872
C2×#897902
#117309132
#117293662
C4×#64062
#117293612
#117274142
#117274002
#117273992
#117273902
#117272702
#117272602
#117272022
#228647