Finite Group Databasebeta

← #13374544

Subgroups — #13374544

Order 1792.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2880C211yesmaximal, characteristic, complemented
2#11741525C211yesmaximal, characteristic
3C2×#90008C211yesmaximal, characteristic, complemented
4C2×#89917C211yesmaximal, characteristic, complemented
5#11736041C211yesmaximal, characteristic, complemented
6#11729771C211yesmaximal, characteristic, complemented
7#11729764C211yesmaximal, characteristic, complemented
8#11729762C211yesmaximal, characteristic, complemented
9#11727765C211yesmaximal, characteristic, complemented
10#11727753C211yesmaximal, characteristic, complemented
11#11727752C211yesmaximal, characteristic, complemented
12#11727750C211yesmaximal, characteristic, complemented
13#11727738C211yesmaximal, characteristic, complemented
14#11727720C211yesmaximal, characteristic, complemented
15#11727661C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C2×C7×#131C2211yescharacteristic
18C2×C7×#131C2211yescharacteristic
19C2×#6513C2211yescharacteristic
20C2×#6513C2211yescharacteristic
21#90482C2211yescharacteristic
22C2×#6489C2211yescharacteristic
23C22×#1136C2211yescharacteristic
24C2×#6464C2211yescharacteristic, complemented
25C7×#408—21no—
26C7×#408—21no—
27C7×#408C2211yescharacteristic
28C7×#408C2211yescharacteristic
29C7×#407—21no—
30C7×#407C2211yescharacteristic
31C2×C7×C22⋊C8—21no—
32C2×C7×C22⋊C8C2211yescharacteristic
33#90011C411yescharacteristic, complemented
34#90011C411yescharacteristic, complemented
35#90010C411yescharacteristic, complemented
36#90010C411yescharacteristic, complemented
37#90008—24no—
38C2×#6411C2211yescharacteristic
39C2×#6411C2211yescharacteristic
40C2×#6411C2211yescharacteristic
41C2×#6411C2211yescharacteristic
42#90005C2211yescharacteristic
43#90005C2211yescharacteristic
44#90000C411yescharacteristic, complemented
45#89999C411yescharacteristic, complemented
46#89990C411yescharacteristic, complemented
47#89989C411yescharacteristic, complemented
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49#89917—24no—
50C2×#6399C2211yescharacteristic, complemented
51C2×#6399C2211yescharacteristic, complemented
52C2×#6396C2211yescharacteristic, complemented
53C2×#6396C2211yescharacteristic, complemented
54#89882C2211yescharacteristic, complemented
55#89874C2211yescharacteristic, complemented
56#89873C2211yescharacteristic, complemented
57C2×#6389C2211yescharacteristic, complemented
58C2×C8×Dic7C2211yescharacteristic, complemented
59#89502—21no—
60#89501—21no—
61#89500—21no—
62(C22⋊D7)⋊C8—21no—
63#89353C2211yescharacteristic, complemented
64#89353C2211yescharacteristic, complemented
65#89350C2211yescharacteristic, complemented
66#89350C2211yescharacteristic, complemented
67#89345C2211yescharacteristic, complemented
68#89345C2211yescharacteristic, complemented
69#22887—71nomaximal, Sylow
70C2×C7×#41—21no—
71C2×C7×#41—21no—
72C2×C7×#41—22no—
73C2×C7×#41—22no—
74C2×C7×#41—41no—
75C2×C7×#41—41no—
76C2×C7×#41C2×C411yescharacteristic
77C2×C7×#41C2×C411yescharacteristic
78C2×C7×#41C2311yescharacteristic
79C2×C7×#41C2311yescharacteristic
80C22×C7×Q8C2×C411yescharacteristic
81C22×C7×D4—21no—
82C22×C7×D4C2×C411yescharacteristic
83C23×C4×C7—21no—
84C23×C4×C7C2311yescharacteristic
85C2×#1157C2311yescharacteristic
86C7×#131—22no—
87C7×#131—22no—
88C7×#131—41no—
89C7×#131—41no—
90C2×C7×M16—21no—
91C2×C7×M16—21no—
92C2×C7×M16C2311yescharacteristic
93C2×C7×M16C2311yescharacteristic
94C22×C7×C8—21no—
95C22×C7×C8—21no—
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98#6516—21no—
99C2×C22⋊Dic7—21no—
100#6513—22no—
101#6513—22no—
102#6513—41no—
103#6513—41no—
104C2×#1144C2×C411yescharacteristic
105C2×#1144C2×C411yescharacteristic
106C2×#1143C2×C411yescharacteristic
107C2×#1143C2×C411yescharacteristic
108C2×#1142C2×C411yescharacteristic
109C2×#1142C2×C411yescharacteristic
110C2×#1141C2×C411yescharacteristic
111C2×#1141C2×C411yescharacteristic
112#6493C2×C411yescharacteristic
113#6493C2×C411yescharacteristic
114#6492—21no—
115C4×C22⋊D7—21no—
116C4×C22⋊D7—21no—
117#6489—22no—
118#6489—41no—
119#6489C2311yescharacteristic
120C2×C4⋊Dic7—21no—
121#6487C2×C411yescharacteristic
122#6487C2×C411yescharacteristic
123C2×C4×Dic7C2311yescharacteristic
124C2×C4×Dic7C2311yescharacteristic
125C2×#1136—21no—
126C2×#1136—22no—
127C2×#1136—41no—
128C2×#1136C2311yescharacteristic
129C2×#1136C2311yescharacteristic
130C22×C7⋊C8—21no—
131C22×C7⋊C8C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133#6464—22no—
134#6464—41no—
135C2×#1131—21no—
136C2×C8×D7—21no—
137C7×C22⋊C8—21no—
138C7×C22⋊C8—21no—
139C7×C22⋊C8—21no—
140C7×C22⋊C8—21no—
141C7×C22⋊C8—21no—
142C7×C22⋊C8—21no—
143C7×C22⋊C8D411yescharacteristic
144C7×C22⋊C8D411yescharacteristic
145C7×C22⋊C8D411yescharacteristic
146C7×C22⋊C8D411yescharacteristic
147#6411—22no—
148#6411—22no—
149#6411—22no—
150#6411D414yescomplemented
151#6409C2×C411yescharacteristic
152#6409C2×C411yescharacteristic
153#6409C2×C411yescharacteristic
154#6409C2×C411yescharacteristic
155#6406C2×C411yescharacteristic
156#6406C2×C411yescharacteristic
157#6406C2×C411yescharacteristic
158#6406C2×C411yescharacteristic
159C22⋊(C7⋊C8)C2×C411yescharacteristic
160C22⋊(C7⋊C8)C2×C411yescharacteristic
161C22⋊(C7⋊C8)C2×C411yescharacteristic
162C22⋊(C7⋊C8)C2×C411yescharacteristic
163#6399—22no—
164#6399—41no—
165#6396—22no—
166#6396—41no—
167(C2×D7)⋊C8—21no—
168(C2×D7)⋊C8—21no—
169#6389—21no—
170#6389—22no—
171Dic7⋊C8—21no—
172Dic7⋊C8—21no—
173C8×Dic7—21no—
174C8×Dic7—41no—
175#3002—71no—
176C2×#444—71no—
177#2933—71no—
178C2×#421—71no—
179#2880D711yescharacteristic, complemented
180#1974—71no—
181#1938—71no—
182#1929—71no—
183#1897—71no—
184#1876—71no—
185#1876—71no—
186#1866—71no—
187#1855—71no—
188#1764—71no—
189#1750—71no—
190C24×C7—21no—
191C24×C7#4111yescharacteristic
192C7×#41—21no—
193C7×#41—21no—
194C7×#41—22no—
195C7×#41—22no—
196C7×#41—21no—
197C7×#41—21no—
198C7×#41—21no—
199C7×#41—21no—
200C7×#41—42no—
201C7×#41—42no—
202C7×#41—41no—
203C7×#41—41no—
204C7×#41—42no—
205C7×#41—42no—
206C7×#41C2×D412yes—
207C7×#41#4112yes—
208C2×C7×Q8—21no—
209C2×C7×Q8—22no—
210C2×C7×Q8—41no—
211C2×C7×Q8C22×C411yescharacteristic
212C2×C7×Q8C22×C411yescharacteristic
213C2×C7×D4—21no—
214C2×C7×D4—22no—
215C2×C7×D4—21no—
216C2×C7×D4—21no—
217C2×C7×D4—21no—
218C2×C7×D4—21no—
219C2×C7×D4—41no—
220C2×C7×D4—42no—
221C2×C7×D4—42no—
222C2×C7×D4C22×C411yescharacteristic
223C2×C7×D4C22×C411yescharacteristic
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—42no—
234C22×C4×C7—42no—
235C22×C4×C7C22×C411yescharacteristic
236C22×C4×C7C22×C411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7#4111yescharacteristic
240C22×C4×C7C2411yescharacteristic
241C2×C22⋊D7—21no—
242C2×C22⋊D7—21no—
243C2×C22⋊D7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246#1157—21no—
247#1157—21no—
248#1157—21no—
249#1157—21no—
250C2×D28C22×C411yescharacteristic
251C2×C4×D7—21no—
252C2×Dic14C22×C411yescharacteristic
253C7×M16—21no—
254C7×M16—21no—
255C7×M16—21no—
256C7×M16—21no—
257C7×M16—42no—
258C7×M16—42no—
259C2×C7×C8—21no—
260C2×C7×C8—21no—
261C2×C7×C8—21no—
262C2×C7×C8—21no—
263C2×C7×C8—21no—
264C2×C7×C8—21no—
265C2×C7×C8—42no—
266C2×C7×C8—42no—
267C2×C7×C8C2×D411yescharacteristic
268C2×C7×C8C2×D411yescharacteristic
269C2×C7×C8C2×D411yescharacteristic
270C2×C7×C8C2×D411yescharacteristic
271C22⋊Dic7—21no—
272C22⋊Dic7—21no—
273C22⋊Dic7—21no—
274C22⋊Dic7—42no—
275#1144—22no—
276#1144—41no—
277#1143—22no—
278#1143—41no—
279#1142—22no—
280#1142—41no—
281#1141—22no—
282#1141—41no—
283(C2×D7)⋊C4—21no—
284(C2×D7)⋊C4—21no—
285C4⋊Dic7—42no—
286C4⋊Dic7C22×C411yescharacteristic
287C4⋊Dic7C22×C411yescharacteristic
288Dic7⋊C4—21no—
289Dic7⋊C4—21no—
290C4×Dic7—21no—
291C4×Dic7—21no—
292C4×Dic7—21no—
293C4×Dic7—21no—
294C4×Dic7C2×D412yes—
295#1136—21no—
296#1136—21no—
297#1136—21no—
298#1136—42no—
299#1136C2×D412yes—
300C2×C7⋊C8—21no—
301C2×C7⋊C8—21no—
302C2×C7⋊C8—21no—
303C2×C7⋊C8—21no—
304C2×C7⋊C8—21no—
305C2×C7⋊C8—21no—
306C2×C7⋊C8—42no—
307C2×C7⋊C8C22×C411yescharacteristic
308C2×C7⋊C8C22×C411yescharacteristic
309C2×C7⋊C8C22×C411yescharacteristic
310C2×C7⋊C8C22×C411yescharacteristic
311#1131—42no—
312C8×D7—42no—
313C22×#41C2×D711yescharacteristic
314C2×#135—71no—
315C2×#135—71no—
316C2×#131—71no—
317C2×#131C2×D711yescharacteristic
318C2×#131C2×D711yescharacteristic
319C22×M16—71no—
320#525—71no—
321C2×#117—71no—
322#452—71no—
323#452—71no—
324#451—71no—
325#450—71no—
326#449—71no—
327#449—71no—
328#448—71no—
329#447—71no—
330#444—144no—
331#436—141no—
332#435—141no—
333#435—141no—
334C8×D4—141no—
335C2×#108—71no—
336C2×#108—71no—
337#424—71no—
338#421—144no—
339C2×#104—71no—
340C2×#104—71no—
341C2×#104—71no—
342C2×#104—71no—
343C2×#104—71no—
344C2×#104—71no—
345#416—71no—
346#416—71no—
347#408—21no—
348#408—21no—
349#408—71no—
350#408C2×D711yescharacteristic
351#408C2×D711yescharacteristic
352#407—21no—
353#407C2×D711yescharacteristic
354C2×C22⋊C8—21no—
355C2×C22⋊C8—71no—
356C2×C22⋊C8C2×D711yescharacteristic
357#405—71no—
358C2×#97—71no—
359C2×C4×C8—71no—
360#341—71no—
361#341—71no—
362#339—71no—
363#339—71no—
364#336—71no—
365#336—71no—
366C23×C7—21no—
367C23×C7—21no—
368C23×C7—21no—
369C23×C7—21no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—42no—
373C23×C7—42no—
374C23×C7—81no—
375C23×C7C4×D411yescharacteristic
376C23×C7C4×D411yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C22×D7—21no—
379C7×Q8—21no—
380C7×Q8—21no—
381C7×Q8—21no—
382C7×Q8—42no—
383C7×Q8C4×D412yes—
384C7×D4—22no—
385C7×D4—22no—
386C7×D4—21no—
387C7×D4—21no—
388C7×D4—21no—
389C7×D4—42no—
390C7×D4—42no—
391C7×D4—42no—
392C7×D4—41no—
393C7×D4—41no—
394C7×D4C4×D412yes—
395C2×C4×C7—21no—
396C2×C4×C7—21no—
397C2×C4×C7—21no—
398C2×C4×C7—21no—
399C2×C4×C7—21no—
400C2×C4×C7—21no—
401C2×C4×C7—21no—
402C2×C4×C7—21no—
403C2×C4×C7—21no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—21no—
407C2×C4×C7—21no—
408C2×C4×C7—21no—
409C2×C4×C7—42no—
410C2×C4×C7—42no—
411C2×C4×C7—42no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7C4×D411yescharacteristic
415C2×C4×C7C4×D411yescharacteristic
416C2×C4×C7C23×C411yescharacteristic
417C2×C4×C7C22×D411yescharacteristic
418C2×C4×C7C22×D411yescharacteristic
419C2×C4×C7C2×#4111yescharacteristic
420C2×C4×C7H(5,𝔽2)11yescharacteristic
421C2×C4×C7H(5,𝔽2)11yescharacteristic
422C22⋊D7—42no—
423C22⋊D7—41no—
424C22⋊D7—41no—
425C22⋊D7—81no—
426C2×Dic7—21no—
427C2×Dic7—21no—
428C2×Dic7—21no—
429C2×Dic7—22no—
430C2×Dic7—41no—
431C2×Dic7—41no—
432C2×Dic7—41no—
433C2×Dic7—41no—
434C2×Dic7—41no—
435D28—21no—
436D28—21no—
437C4×D7—41no—
438C4×D7—41no—
439Dic14—21no—
440Dic14—21no—
441C7×C8—21no—
442C7×C8—21no—
443C7×C8—21no—
444C7×C8—21no—
445C7×C8—41no—
446C7×C8—41no—
447C7⋊C8—21no—
448C7⋊C8—21no—
449C7⋊C8—21no—
450C7⋊C8—21no—
451C7⋊C8—22no—
452C7⋊C8—41no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—41no—
458C2×#41—41no—
459C2×#41—71no—
460C2×#41C4×D711yescharacteristic
461C2×#41C4×D711yescharacteristic
462C2×#41C22×D711yescharacteristic
463C2×#41C22×D711yescharacteristic
464C22×Q8C4×D711yescharacteristic
465C22×D4—21no—
466C22×D4C4×D711yescharacteristic
467C23×C4—21no—
468C23×C4C22×D711yescharacteristic
469#135—142no—
470#135—142no—
471#135—281no—
472#135—281no—
473C2×Q16—71no—
474C2×Q16—71no—
475C2×SD16—71no—
476C2×SD16—71no—
477C2×SD16—71no—
478C2×SD16—71no—
479C2×D8—71no—
480C2×D8—71no—
481#131—22no—
482#131—22no—
483#131—41no—
484#131—41no—
485#131—142no—
486#131—281no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—71no—
490C2×M16—71no—
491C2×M16—141no—
492C2×M16—141no—
493C2×M16—142no—
494C2×M16—281no—
495C2×M16C22×D711yescharacteristic
496C2×M16C22×D711yescharacteristic
497C22×C8—21no—
498C22×C8—21no—
499C22×C8—71no—
500C22×C8—71no—
501C22×C8—141no—
502C22×C8—141no—
503C22×C8C22×D711yescharacteristic
504C22×C8C22×D711yescharacteristic
505#123—141no—
506C22⋊Q8—71no—
507C22⋊Q8—71no—
508#121—71no—
509#121—71no—
510#120—141no—
511C4×D4—141no—
512C4×D4—141no—
513#117—71no—
514#117—142no—
515#117—281no—
516C2×C4⋊C4—141no—
517C2×C22⋊C4—141no—
518C2×C42—71no—
519C2×C42—71no—
520#108—142no—
521#108—281no—
522C4⋊C8—141no—
523C4⋊C8—141no—
524#104—74no—
525#104—142no—
526#104—142no—
527#104—142no—
528#104—142no—
529#104—281no—
530#103—71no—
531#103—71no—
532#103—71no—
533#103—71no—
534#102—71no—
535#102—71no—
536#102—71no—
537#102—71no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—71no—
545C22⋊C8—71no—
546C22⋊C8—71no—
547C22⋊C8—71no—
548C22⋊C8—141no—
549C22⋊C8—141no—
550C22⋊C8C22⋊D711yescharacteristic
551C22⋊C8C22⋊D711yescharacteristic
552C22⋊C8C22⋊D711yescharacteristic
553C22⋊C8C22⋊D711yescharacteristic
554#97—142no—
555#97—141no—
556C4×C8—141no—
557C4×C8—281no—
558C22×C7—21no—
559C22×C7—21no—
560C22×C7—21no—
561C22×C7—21no—
562C22×C7—22no—
563C22×C7—21no—
564C22×C7—21no—
565C22×C7—21no—
566C22×C7—21no—
567C22×C7—41no—
568C22×C7—41no—
569C22×C7—41no—
570C22×C7—41no—
571C22×C7—41no—
572C22×C7—81no—
573C22×C7—81no—
574C22×C7—84no—
575C22×C7C2×C4×D411yescharacteristic
576C22×C7#54611yescharacteristic
577C22×C7#55111yescharacteristic
578C2×D7—41no—
579C2×D7—41no—
580C2×D7—41no—
581C4×C7—21no—
582C4×C7—21no—
583C4×C7—22no—
584C4×C7—41no—
585C4×C7C2×C4×D411yescharacteristic
586C4×C7#51811yescharacteristic
587C4×C7D4211yescharacteristic
588C4×C7#54611yescharacteristic
589Dic7—42no—
590Dic7—41no—
591Dic7—41no—
592Dic7—41no—
593Dic7—81no—
594C24—21no—
595C24#115711yescharacteristic
596#41—21no—
597#41—21no—
598#41—22no—
599#41—22no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—42no—
609#41—42no—
610#41—141no—
611#41—141no—
612#41—141no—
613#41—141no—
614#41D4×D712yes—
615#41#115912yes—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—41no—
619C2×Q8—71no—
620C2×Q8C2×C4×D711yescharacteristic
621C2×Q8C2×C4×D711yescharacteristic
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—71no—
632C2×D4—141no—
633C2×D4—141no—
634C2×D4—141no—
635C2×D4C2×C4×D711yescharacteristic
636C2×D4C2×C4×D711yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—141no—
649C22×C4—141no—
650C22×C4—141no—
651C22×C4C2×C4×D711yescharacteristic
652C22×C4C2×C4×D711yescharacteristic
653C22×C4#115711yescharacteristic
654C22×C4C2×C22⋊D711yescharacteristic
655C22×C4C2×C22⋊D711yescharacteristic
656C22×C4C23×D711yescharacteristic
657Q16—142no—
658Q16—281no—
659SD16—142no—
660SD16—142no—
661SD16—281no—
662SD16—281no—
663D8—142no—
664D8—281no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—42no—
670M16—42no—
671M16—72no—
672M16—141no—
673M16—141no—
674M16—141no—
675M16—282no—
676M16—282no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—42no—
684C2×C8—42no—
685C2×C8—71no—
686C2×C8—71no—
687C2×C8—71no—
688C2×C8—71no—
689C2×C8—141no—
690C2×C8—141no—
691C2×C8—141no—
692C2×C8—141no—
693C2×C8—141no—
694C2×C8—141no—
695C2×C8—282no—
696C2×C8—282no—
697C2×C8C2×C22⋊D711yescharacteristic
698C2×C8C2×C22⋊D711yescharacteristic
699C2×C8C2×C22⋊D711yescharacteristic
700C2×C8C2×C22⋊D711yescharacteristic
701C4⋊C4—71no—
702C4⋊C4—71no—
703C4⋊C4—141no—
704C4⋊C4—141no—
705C4⋊C4—282no—
706C22⋊C4—141no—
707C22⋊C4—141no—
708C22⋊C4—141no—
709C22⋊C4—141no—
710C22⋊C4—141no—
711C22⋊C4—282no—
712C42—72no—
713C42—141no—
714C42—141no—
715C42—141no—
716C42—141no—
717C2×C7—21no—
718C2×C7—21no—
719C2×C7—41no—
720C2×C7—41no—
721C2×C7—42no—
722C2×C7—81no—
723C2×C7#235811yescharacteristic
724C2×C7#295511yescharacteristic
725C2×C7#295711yescharacteristic
726D7—81no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—42no—
735C23—81no—
736C23—141no—
737C23C4×C22⋊D711yescharacteristic
738C23C4×C22⋊D711yescharacteristic
739C23C2×#115711yescharacteristic
740Q8—21no—
741Q8—21no—
742Q8—21no—
743Q8—42no—
744Q8—141no—
745Q8—141no—
746Q8(C22⋊D7)⋊C412yes—
747D4—22no—
748D4—22no—
749D4—21no—
750D4—21no—
751D4—21no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—41no—
756D4—41no—
757D4—141no—
758D4—141no—
759D4—282no—
760D4—281no—
761D4—281no—
762D4—561no—
763D4(C22⋊D7)⋊C412yes—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—142no—
784C2×C4—141no—
785C2×C4—141no—
786C2×C4—141no—
787C2×C4—281no—
788C2×C4—281no—
789C2×C4—281no—
790C2×C4—281no—
791C2×C4—281no—
792C2×C4—281no—
793C2×C4—281no—
794C2×C4C4×C22⋊D711yescharacteristic
795C2×C4C4×C22⋊D711yescharacteristic
796C2×C4C22×C4×D711yescharacteristic
797C2×C4C2×D4×D711yescharacteristic
798C2×C4C2×#115911yescharacteristic
799C2×C4#654811yescharacteristic
800C2×C4#654811yescharacteristic
801C2×C4C22×C22⋊D711yescharacteristic
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C8—41no—
807C8—41no—
808C8—141no—
809C8—141no—
810C8—141no—
811C8—141no—
812C8—142no—
813C8—281no—
814C7#2288711yescharacteristic, complemented, Sylow
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—281no—
833C22—281no—
834C22—281no—
835C22#9018111yescharacteristic
836C22#9018611yescharacteristic
837C22C2×C4×C22⋊D711yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—282no—
843C4—281no—
844C4—281no—
845C4—281no—
846C4—561no—
847C4C2×(C22⋊D7)⋊C411yescharacteristic
848C4#9017711yescharacteristic
849C4D4×C22⋊D711yescharacteristic
850C4#9049711yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—561no—
858C2#1173954411yescharacteristic
859C2#1174123711yescharacteristic
860C2#1174125711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2880C2
socleC22×C7C2×C4×D4
prime radical#11741525C2
cosocleC22×C4×C7C24
hypercenter#2880D7
hypocenterC7#22887
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. C7×#2880C2semidirect
3. C2×#90008C2semidirect
4. C2×#89917C2semidirect
5. #11736041C2semidirect
6. #11729771C2semidirect
7. #11729764C2semidirect
8. #11729762C2semidirect
9. #11727765C2semidirect
10. #11727753C2semidirect
11. #11727752C2semidirect
12. #11727750C2semidirect
13. #11727738C2semidirect
14. #11727720C2semidirect
15. #11727661C2semidirect
24. C2×#6464C22semidirect
33. #90011C4semidirect
34. #90011C4semidirect
35. #90010C4semidirect
36. #90010C4semidirect
44. #90000C4semidirect
45. #89999C4semidirect
46. #89990C4semidirect
47. #89989C4semidirect
50. C2×#6399C22semidirect
51. C2×#6399C22semidirect
52. C2×#6396C22semidirect
53. C2×#6396C22semidirect
54. #89882C22semidirect
55. #89874C22semidirect
56. #89873C22semidirect
57. C2×#6389C22semidirect
58. C2×C8×Dic7C22semidirect
63. #89353C22semidirect
64. #89353C22semidirect
65. #89350C22semidirect
66. #89350C22semidirect
67. #89345C22semidirect
68. #89345C22semidirect
150. #6411D4semidirect
179. #2880D7semidirect
814. C7#22887semidirect

Maximal subgroups

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

subgroupindex
C7×#28802
#117415252
C2×#900082
C2×#899172
#117360412
#117297712
#117297642
#117297622
#117277652
#117277532
#117277522
#117277502
#117277382
#117277202
#117276612
#228877