Finite Group Databasebeta

← #13374214

Subgroups — #13374214

Order 1792.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#89999C211yesmaximal, characteristic
3C2×#89997C211yesmaximal, characteristic, complemented
4C2×#89798C211yesmaximal, characteristic, complemented
5#11730914C211yesmaximal, characteristic
6#11729387C211yesmaximal, characteristic, complemented
7C4×#6409C211yesmaximal, characteristic, complemented
8#11729383C211yesmaximal, characteristic, complemented
9#11727441C211yesmaximal, characteristic, complemented
10#11727430C211yesmaximal, characteristic, complemented
11#11727429C211yesmaximal, characteristic, complemented
12#11727421C211yesmaximal, characteristic, complemented
13#11727271C211yesmaximal, characteristic
14#11727260C211yesmaximal, characteristic, complemented
15#11727202C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C22×#1143C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×#6489C2211yescharacteristic
23C22×#1136C2211yescharacteristic
24C2×C4×D28C2211yescharacteristic
25C7×#391—21no—
26C7×#391—21no—
27C7×#391C2211yescharacteristic
28C7×#391C2211yescharacteristic
29C7×#380—21no—
30C7×#380C2211yescharacteristic
31C4×C7×C22⋊C4—21no—
32C4×C7×C22⋊C4C2211yescharacteristic
33#89999C418yescomplemented
34#89997—24no—
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6409C2211yescharacteristic
39C2×#6409C2211yescharacteristic
40C2×#6409C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89798—24no—
43C2×#6383C2211yescharacteristic
44C2×#6383C2211yescharacteristic
45C2×#6382C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47#89729—21no—
48#89728—21no—
49#89711C2211yescharacteristic
50C4×C4⋊Dic7C2211yescharacteristic
51#89700C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53C2×C4×C7⋊C8C2211yescharacteristic
54#89441—21no—
55#89438—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#22865—71nomaximal, Sylow
63C22×C7×Q8—21no—
64C22×C7×Q8—22no—
65C22×C7×Q8—22no—
66C22×C7×Q8—22no—
67C22×C7×Q8—41no—
68C22×C7×Q8—41no—
69C22×C7×Q8C2×C414yescomplemented
70C22×C7×Q8C2311yescharacteristic
71C22×C7×Q8C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7C2311yescharacteristic
74C22×C22⋊D7—21no—
75C22×D28C2311yescharacteristic
76C22×C4×D7—21no—
77C4×C7×Q8—22no—
78C4×C7×Q8—22no—
79C4×C7×Q8—41no—
80C4×C7×Q8—41no—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4—21no—
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4D411yescharacteristic
87C2×C7×C22⋊C4D411yescharacteristic
88C2×C42×C7—21no—
89C2×C42×C7—21no—
90C2×C42×C7C2311yescharacteristic
91C2×C42×C7C2311yescharacteristic
92C2×C22⋊Dic7—21no—
93C2×#1143—22no—
94C2×#1143—22no—
95C2×#1143—41no—
96C2×#1143—41no—
97C2×#1143C2×C414yes—
98C2×#1143C2×C414yes—
99#6493—22no—
100#6493C2×C414yes—
101C2×(C2×D7)⋊C4—21no—
102C2×(C2×D7)⋊C4—21no—
103C2×(C2×D7)⋊C4—21no—
104C2×(C2×D7)⋊C4—21no—
105#6489—22no—
106#6489—41no—
107C2×C4⋊Dic7C2311yescharacteristic
108C2×C4⋊Dic7C2311yescharacteristic
109C2×C4⋊Dic7C2311yescharacteristic
110C2×Dic7⋊C4—21no—
111C2×C4×Dic7—21no—
112C2×C4×Dic7—21no—
113C2×#1136—22no—
114C2×#1136—22no—
115C2×#1136—41no—
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C22×C7⋊C8C2311yescharacteristic
119C22×C7⋊C8C2311yescharacteristic
120C4×D28—22no—
121C4×D28—41no—
122C7×#95—21no—
123C7×#95—21no—
124C7×#95—21no—
125C7×#95—21no—
126C7×#95—21no—
127C7×#95D411yescharacteristic
128C7×#95D411yescharacteristic
129#6409—22no—
130#6409—22no—
131#6409—22no—
132#6409C2×C414yescomplemented
133#6409C2×C414yescomplemented
134#6409D414yescomplemented
135C7⋊#95—21no—
136C7⋊#95—21no—
137C22⋊(C7⋊C8)C2×C414yescomplemented
138#6383—22no—
139#6383—41no—
140#6382—41no—
141#6381—22no—
142#6377—22no—
143C4×C7⋊C8—41no—
144C2×#448—71no—
145C2×#440—71no—
146C2×#419—71no—
147#2363—71no—
148Q8×C22⋊C4D711yescharacteristic, complemented
149#1968—71no—
150#1935—71no—
151#1928—71no—
152#1895—71no—
153#1880—71no—
154#1877—71no—
155#1865—71no—
156#1854—71no—
157C4×#103—71no—
158#1753—71no—
159C24×C7C2×D411yescharacteristic
160C23×D7—21no—
161C2×C7×Q8—24no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—28no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8—21no—
171C2×C7×Q8—42no—
172C2×C7×Q8—42no—
173C2×C7×Q8—44no—
174C2×C7×Q8—44no—
175C2×C7×Q8—44no—
176C2×C7×Q8C22×C412yes—
177C2×C7×Q8C22×C412yes—
178C2×C7×Q8C2×D412yes—
179C2×C7×Q8#4112yes—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—24no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—42no—
190C22×C4×C7—42no—
191C22×C4×C7C22×C412yes—
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7#4112yes—
198C22×C4×C7C2411yescharacteristic
199C2×C22⋊D7—24no—
200C2×C22⋊D7—81no—
201C2×C22⋊D7—81no—
202C22×Dic7—21no—
203C22×Dic7—21no—
204C22×Dic7—21no—
205C2×D28—21no—
206C2×D28—21no—
207C2×D28—21no—
208C2×D28—21no—
209C2×D28—21no—
210C2×D28C22×C412yes—
211C2×C4×D7—42no—
212C2×C4×D7—42no—
213C2×C4×D7—81no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—21no—
218C7×C4⋊C4—42no—
219C7×C4⋊C4—42no—
220C7×C22⋊C4—22no—
221C7×C22⋊C4—41no—
222C7×C22⋊C4—42no—
223C42×C7—21no—
224C42×C7—21no—
225C42×C7—21no—
226C42×C7—21no—
227C42×C7—42no—
228C42×C7—42no—
229C22⋊Dic7—42no—
230#1143—28no—
231#1143—44no—
232(C2×D7)⋊C4—24no—
233(C2×D7)⋊C4—42no—
234(C2×D7)⋊C4—42no—
235(C2×D7)⋊C4—81no—
236C4⋊Dic7—21no—
237C4⋊Dic7—21no—
238C4⋊Dic7—21no—
239C4⋊Dic7—21no—
240C4⋊Dic7C22×C412yes—
241C4⋊Dic7C2×D412yes—
242Dic7⋊C4—81no—
243C4×Dic7—42no—
244C4×Dic7—81no—
245#1136—44no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8C22×C412yes—
256C2×C7⋊C8C22×C412yes—
257C2×C7⋊C8C2×D412yes—
258C23×Q8C2×D711yescharacteristic
259C22×SD16—71no—
260C22×SD16—71no—
261C22×M16—71no—
262C2×#121—71no—
263C2×C4×Q8C2×D711yescharacteristic
264C2×C4×Q8C2×D711yescharacteristic
265C2×C4×D4—71no—
266C2×#117—71no—
267#448—78no—
268#440—144no—
269C2×#107—71no—
270C2×#106—71no—
271#419—144no—
272C2×#103—71no—
273C2×#103—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×#103—71no—
277C2×#103—71no—
278C2×#102—71no—
279C2×#102—71no—
280C2×C22⋊C8—71no—
281C2×#97—71no—
282C2×C4×C8—71no—
283#391—21no—
284#391—21no—
285#391C2×D711yescharacteristic
286#391C2×D711yescharacteristic
287#390—71no—
288#390—141no—
289#389—71no—
290#388—141no—
291#386—141no—
292#380—21no—
293#380C2×D711yescharacteristic
294C4×C4⋊C4—71no—
295C4×C22⋊C4—21no—
296C4×C22⋊C4—141no—
297C4×C22⋊C4C2×D711yescharacteristic
298#340—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#336—71no—
303#336—71no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7C4×D412yes—
311C23×C7C22×D411yescharacteristic
312C22×D7—22no—
313C22×D7—41no—
314C22×D7—41no—
315C22×D7—41no—
316C22×D7—41no—
317C22×D7—41no—
318C22×D7—41no—
319C7×Q8—22no—
320C7×Q8—22no—
321C7×Q8—22no—
322C7×Q8—22no—
323C7×Q8—22no—
324C7×Q8—48no—
325C7×Q8—41no—
326C7×Q8—41no—
327C7×Q8C4×D414yes—
328C2×C4×C7—22no—
329C2×C4×C7—21no—
330C2×C4×C7—22no—
331C2×C4×C7—21no—
332C2×C4×C7—22no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—21no—
348C2×C4×C7—21no—
349C2×C4×C7—48no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7C4×D412yes—
359C2×C4×C7#13712yes—
360C2×C4×C7C23×C411yescharacteristic
361C2×C4×C7C22×D411yescharacteristic
362C2×C4×C7C2×#4111yescharacteristic
363C2×C4×C7C2×#4111yescharacteristic
364C2×C4×C7H(5,𝔽2)11yescharacteristic
365C2×C4×C7H(5,𝔽2)11yescharacteristic
366C22⋊D7—84no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—41no—
374C2×Dic7—41no—
375C2×Dic7—41no—
376D28—22no—
377D28—22no—
378D28—41no—
379D28—41no—
380C4×D7—84no—
381C7⋊C8—22no—
382C7⋊C8—22no—
383C7⋊C8—22no—
384C7⋊C8—41no—
385C22×Q8—22no—
386C22×Q8—21no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—41no—
390C22×Q8—41no—
391C22×Q8C4×D714yescomplemented
392C22×Q8C22×D711yescharacteristic
393C22×Q8C22×D711yescharacteristic
394C22×D4—71no—
395C22×D4—141no—
396C23×C4—21no—
397C23×C4—141no—
398C23×C4C22×D711yescharacteristic
399C2×SD16—74no—
400C2×SD16—74no—
401C2×SD16—142no—
402C2×SD16—142no—
403C2×SD16—281no—
404C2×SD16—281no—
405C2×M16—142no—
406C2×M16—142no—
407C2×M16—281no—
408C22×C8—71no—
409C22×C8—71no—
410C22×C8—71no—
411C22×C8—71no—
412#121—74no—
413#121—142no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—41no—
417C4×Q8—41no—
418C4×D4—142no—
419C4×D4—281no—
420#117—142no—
421#117—281no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—71no—
426C2×C4⋊C4—71no—
427C2×C4⋊C4—141no—
428C2×C4⋊C4C22×D711yescharacteristic
429C2×C4⋊C4C22×D711yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—141no—
432C2×C22⋊C4—141no—
433C2×C22⋊C4—141no—
434C2×C22⋊C4—141no—
435C2×C22⋊C4—141no—
436C2×C22⋊C4C22⋊D711yescharacteristic
437C2×C22⋊C4C22⋊D711yescharacteristic
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—141no—
441C2×C42—141no—
442C2×C42C22×D711yescharacteristic
443C2×C42C22×D711yescharacteristic
444#107—142no—
445#106—281no—
446#103—74no—
447#103—74no—
448#103—74no—
449#103—142no—
450#103—142no—
451#103—142no—
452#102—142no—
453#102—281no—
454C22⋊C8—74no—
455#97—142no—
456C4×C8—281no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—141no—
463#95—141no—
464#95C22⋊D711yescharacteristic
465#95C22⋊D711yescharacteristic
466C22×C7—22no—
467C22×C7—22no—
468C22×C7—22no—
469C22×C7—41no—
470C22×C7—41no—
471C22×C7—41no—
472C22×C7—41no—
473C22×C7C2×C4×D411yescharacteristic
474C22×C7D4211yescharacteristic
475C22×C7#54611yescharacteristic
476C22×C7C2×#13711yescharacteristic
477C22×C7#57511yescharacteristic
478C22×C7#57711yescharacteristic
479C22×C7#57711yescharacteristic
480C2×D7—42no—
481C2×D7—42no—
482C2×D7—42no—
483C2×D7—81no—
484C2×D7—81no—
485C2×D7—81no—
486C2×D7—81no—
487C4×C7—22no—
488C4×C7—24no—
489C4×C7—22no—
490C4×C7—42no—
491C4×C7—41no—
492C4×C7—41no—
493C4×C7—41no—
494C4×C7—81no—
495C4×C7—81no—
496C4×C7C2×C4×D411yescharacteristic
497C4×C7#51811yescharacteristic
498C4×C7#54611yescharacteristic
499C4×C7#55111yescharacteristic
500Dic7—42no—
501Dic7—42no—
502Dic7—81no—
503C24—141no—
504C24C2×C22⋊D711yescharacteristic
505C2×Q8—24no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—28no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8C2×C4×D712yes—
521C2×Q8C2×C4×D712yes—
522C2×Q8D4×D712yes—
523C2×Q8#115912yes—
524C2×D4—72no—
525C2×D4—144no—
526C2×D4—141no—
527C2×D4—141no—
528C2×D4—141no—
529C2×D4—141no—
530C2×D4—141no—
531C2×D4—561no—
532C2×D4—561no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—141no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—282no—
548C22×C4—282no—
549C22×C4—561no—
550C22×C4C2×C4×D712yes—
551C22×C4#115712yes—
552C22×C4C2×C22⋊D711yescharacteristic
553C22×C4C2×C22⋊D711yescharacteristic
554C22×C4C2×C22⋊D711yescharacteristic
555C22×C4C2×C22⋊D711yescharacteristic
556C22×C4C2×C22⋊D711yescharacteristic
557C22×C4C23×D711yescharacteristic
558SD16—148no—
559SD16—284no—
560M16—284no—
561C2×C8—72no—
562C2×C8—72no—
563C2×C8—72no—
564C2×C8—141no—
565C2×C8—141no—
566C2×C8—141no—
567C2×C8—141no—
568C2×C8—141no—
569C2×C8—141no—
570C2×C8—141no—
571C2×C8—141no—
572C2×C8—141no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—72no—
580C4⋊C4—72no—
581C4⋊C4—141no—
582C4⋊C4—141no—
583C4⋊C4—141no—
584C4⋊C4—141no—
585C4⋊C4—561no—
586C22⋊C4—22no—
587C22⋊C4—41no—
588C22⋊C4—42no—
589C22⋊C4—144no—
590C22⋊C4—282no—
591C22⋊C4—282no—
592C22⋊C4—282no—
593C22⋊C4—561no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—42no—
599C42—42no—
600C42—282no—
601C42—561no—
602C2×C7—42no—
603C2×C7#235811yescharacteristic
604C2×C7C4×#13711yescharacteristic
605C2×C7#294911yescharacteristic
606C2×C7#327511yescharacteristic
607C2×C7#327811yescharacteristic
608C2×C7#332011yescharacteristic
609C2×C7#332111yescharacteristic
610D7—82no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—142no—
618C23—281no—
619C23—281no—
620C23—281no—
621C23—281no—
622C23—281no—
623C23—281no—
624C23C4×C22⋊D712yes—
625C23C22×C22⋊D711yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—48no—
632Q8—41no—
633Q8—41no—
634Q8(C22⋊D7)⋊C414yes—
635D4—142no—
636D4—142no—
637D4—281no—
638D4—281no—
639D4—564no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—48no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—281no—
673C2×C4—281no—
674C2×C4—281no—
675C2×C4—281no—
676C2×C4—281no—
677C2×C4—281no—
678C2×C4—281no—
679C2×C4—564no—
680C2×C4C4×C22⋊D712yes—
681C2×C4#650512yes—
682C2×C4C22×C4×D711yescharacteristic
683C2×C4C2×#115711yescharacteristic
684C2×C4C2×D4×D711yescharacteristic
685C2×C4C2×#115911yescharacteristic
686C2×C4#654811yescharacteristic
687C2×C4#654811yescharacteristic
688C8—142no—
689C8—142no—
690C8—142no—
691C8—281no—
692C7#2286511yescharacteristic, complemented, Sylow
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—282no—
701C22—282no—
702C22—282no—
703C22—561no—
704C22—561no—
705C22—561no—
706C22—561no—
707C22C2×C4×C22⋊D711yescharacteristic
708C22D4×C22⋊D711yescharacteristic
709C22#9049711yescharacteristic
710C22C2×#650511yescharacteristic
711C22#9051311yescharacteristic
712C22#9052811yescharacteristic
713C22#9052811yescharacteristic
714C4—22no—
715C4—22no—
716C4—24no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—81no—
722C4—81no—
723C4—282no—
724C4—282no—
725C4—561no—
726C4C2×(C22⋊D7)⋊C411yescharacteristic
727C4#9017711yescharacteristic
728C4#9018111yescharacteristic
729C4#9018611yescharacteristic
730C2—42no—
731C2—562no—
732C2#1173954411yescharacteristic
733C2C4×#650511yescharacteristic
734C2#1173999311yescharacteristic
735C2#1174098411yescharacteristic
736C2#1174098911yescharacteristic
737C2#1174099811yescharacteristic
738C2#1174101111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×Q8×C22⋊C4C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenterQ8×C22⋊C4D7
hypocenterC7#22865
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C7×Q8×C22⋊C4C2semidirect
3. C2×#89997C2semidirect
4. C2×#89798C2semidirect
6. #11729387C2semidirect
7. C4×#6409C2semidirect
8. #11729383C2semidirect
9. #11727441C2semidirect
10. #11727430C2semidirect
11. #11727429C2semidirect
12. #11727421C2semidirect
14. #11727260C2semidirect
15. #11727202C2semidirect
33. #89999C4semidirect
69. C22×C7×Q8C2×C4semidirect
132. #6409C2×C4semidirect
133. #6409C2×C4semidirect
134. #6409D4semidirect
137. C22⋊(C7⋊C8)C2×C4semidirect
148. Q8×C22⋊C4D7semidirect
391. C22×Q8C4×D7semidirect
692. C7#22865semidirect

Maximal subgroups

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

subgroupindex
C7×Q8×C22⋊C42
C2×#899992
C2×#899972
C2×#897982
#117309142
#117293872
C4×#64092
#117293832
#117274412
#117274302
#117274292
#117274212
#117272712
#117272602
#117272022
#228657