Finite Group Databasebeta

← #13364895

Subgroups — #13364895

Order 1792.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#6516C211yesmaximal, characteristic
2C2×#89979C211yesmaximal, characteristic, complemented
3C2×#89501C211yesmaximal, characteristic, complemented
4C7×#1779C211yesmaximal, characteristic, complemented
5#11727712C211yesmaximal, characteristic, complemented
6#11727712C211yesmaximal, characteristic, complemented
7#11727707C211yesmaximal, characteristic, complemented
8#11727705C211yesmaximal, characteristic, complemented
9#11727703C211yesmaximal, characteristic, complemented
10#11727671C211yesmaximal, characteristic, complemented
11#11727670C211yesmaximal, characteristic, complemented
12#11727668C211yesmaximal, characteristic, complemented
13#11727667C211yesmaximal, characteristic, complemented
14#11727667C211yesmaximal, characteristic, complemented
15#11727666C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C2×#6516C411yescharacteristic
18C2×C4×C22⋊D7C2211yescharacteristic
19C2×C4×C22⋊D7C2211yescharacteristic
20C2×C4×C22⋊D7C2211yescharacteristic
21C22×#1136C2211yescharacteristic
22C22×#1136C2211yescharacteristic
23C22×#1131C2211yescharacteristic, complemented
24C2×C7×C22⋊C8C2211yescharacteristic
25C2×C7×C22⋊C8C2211yescharacteristic
26C2×C7×C22⋊C8C2211yescharacteristic
27C2×C7×C22⋊C8C2211yescharacteristic
28C2×C7×C22⋊C8C2211yescharacteristic
29C2×C7×C22⋊C8C2211yescharacteristic
30#90019C411yescharacteristic
31#89985C411yescharacteristic
32#89985C411yescharacteristic
33#89985C411yescharacteristic
34#89982C411yescharacteristic
35#89982C411yescharacteristic
36#89982C411yescharacteristic
37C4×C22⋊Dic7C2211yescharacteristic
38C4×C22⋊Dic7C2211yescharacteristic
39C4×C22⋊Dic7C2211yescharacteristic
40#89979—24no—
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43C2×C22⋊(C7⋊C8)C2211yescharacteristic
44C2×C22⋊(C7⋊C8)C2211yescharacteristic
45C2×(C2×D7)⋊C8C2211yescharacteristic, complemented
46C2×(C2×D7)⋊C8C2211yescharacteristic, complemented
47C2×(C2×D7)⋊C8C2211yescharacteristic, complemented
48C2×#6389C2211yescharacteristic, complemented
49C2×Dic7⋊C8C2211yescharacteristic, complemented
50C2×Dic7⋊C8C2211yescharacteristic, complemented
51C2×Dic7⋊C8C2211yescharacteristic, complemented
52C2×C8×Dic7C2211yescharacteristic, complemented
53C2×C8×Dic7C2211yescharacteristic, complemented
54#89501—24no—
55#89345C2211yescharacteristic, complemented
56#89345C2211yescharacteristic, complemented
57#89345C2211yescharacteristic, complemented
58#89345C2211yescharacteristic, complemented
59#89345C2211yescharacteristic, complemented
60#89345C2211yescharacteristic, complemented
61#22038—71nomaximal, Sylow
62C25×C7C2×C411yescharacteristic
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—41no—
66C23×C4×C7—41no—
67C23×C4×C7—41no—
68C23×C4×C7—41no—
69C23×C4×C7C2×C411yescharacteristic
70C23×C4×C7C2×C411yescharacteristic
71C23×C4×C7C2×C411yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C22×C22⋊D7C2×C411yescharacteristic
76C22×C22⋊D7C2×C411yescharacteristic
77C22×C22⋊D7C2×C411yescharacteristic
78C22×C4×D7C2311yescharacteristic
79C22×C7×C8C2311yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C22×C7×C8C2311yescharacteristic
83#6516—24no—
84C2×C22⋊Dic7C2×C411yescharacteristic
85C2×C22⋊Dic7C2×C411yescharacteristic
86C2×C22⋊Dic7C2×C411yescharacteristic
87C2×C22⋊Dic7C2×C411yescharacteristic
88C2×C22⋊Dic7C2×C411yescharacteristic
89C2×C22⋊Dic7C2×C411yescharacteristic
90C2×C22⋊Dic7C2×C411yescharacteristic
91C2×C22⋊Dic7C2×C411yescharacteristic
92C2×C22⋊Dic7C2×C411yescharacteristic
93C4×C22⋊D7—22no—
94C4×C22⋊D7—22no—
95C4×C22⋊D7—41no—
96C4×C22⋊D7—41no—
97C4×C22⋊D7—41no—
98C4×C22⋊D7—41no—
99C2×(C2×D7)⋊C4C2×C411yescharacteristic
100C2×(C2×D7)⋊C4C2×C411yescharacteristic
101C2×(C2×D7)⋊C4C2×C411yescharacteristic
102C2×Dic7⋊C4C2×C411yescharacteristic
103C2×Dic7⋊C4C2×C411yescharacteristic
104C2×Dic7⋊C4C2×C411yescharacteristic
105C2×C4×Dic7C2311yescharacteristic
106C2×C4×Dic7C2311yescharacteristic
107C2×C4×Dic7C2311yescharacteristic
108C2×#1136—22no—
109C2×#1136—41no—
110C2×#1136—41no—
111C2×#1136—41no—
112C2×#1136—41no—
113C2×#1136D414yescomplemented
114C22×C7⋊C8C2311yescharacteristic
115C22×C7⋊C8C2311yescharacteristic
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C2×#1131—22no—
119C2×#1131—41no—
120C2×#1131—41no—
121C7×C22⋊C8—22no—
122C7×C22⋊C8—22no—
123C7×C22⋊C8—41no—
124C7×C22⋊C8—41no—
125C7×C22⋊C8—41no—
126C7×C22⋊C8—41no—
127C7⋊#95C2×C411yescharacteristic
128C7⋊#95C2×C411yescharacteristic
129C7⋊#95C2×C411yescharacteristic
130C7⋊#95C2×C411yescharacteristic
131C7⋊#95C2×C411yescharacteristic
132C7⋊#95C2×C411yescharacteristic
133C22⋊(C7⋊C8)—22no—
134C22⋊(C7⋊C8)—22no—
135C22⋊(C7⋊C8)—22no—
136C22⋊(C7⋊C8)—22no—
137(C2×D7)⋊C8—22no—
138(C2×D7)⋊C8—41no—
139(C2×D7)⋊C8—41no—
140#6389—41no—
141Dic7⋊C8—22no—
142Dic7⋊C8—41no—
143Dic7⋊C8—41no—
144C8×Dic7—22no—
145C8×Dic7—41no—
146C2×#436—71no—
147C2×#407—71no—
148C4×#120—71no—
149#1955—71no—
150#1954—71no—
151#1924—71no—
152#1923—71no—
153#1923—71no—
154#1923—71no—
155#1870—71no—
156#1870—71no—
157#1870—71no—
158#1851—71no—
159#1779D711yescharacteristic, complemented
160#1753—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—41no—
165C24×C7—41no—
166C24×C7—41no—
167C24×C7—41no—
168C24×C7C22×C411yescharacteristic
169C24×C7C22×C411yescharacteristic
170C24×C7C22×C411yescharacteristic
171C23×D7C22×C411yescharacteristic
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—41no—
192C22×C4×C7—41no—
193C22×C4×C7—41no—
194C22×C4×C7—41no—
195C22×C4×C7—41no—
196C22×C4×C7—41no—
197C22×C4×C7—44no—
198C22×C4×C7—44no—
199C22×C4×C7—44no—
200C22×C4×C7—44no—
201C22×C4×C7C22×C411yescharacteristic
202C22×C4×C7C22×C411yescharacteristic
203C22×C4×C7C22×C411yescharacteristic
204C22×C4×C7C2×D412yes—
205C22×C4×C7#4112yes—
206C22×C4×C7C2411yescharacteristic
207C2×C22⋊D7—22no—
208C2×C22⋊D7—22no—
209C2×C22⋊D7—22no—
210C2×C22⋊D7—22no—
211C2×C22⋊D7—22no—
212C2×C22⋊D7—41no—
213C2×C22⋊D7—41no—
214C2×C22⋊D7—41no—
215C2×C22⋊D7—41no—
216C22×Dic7C22×C411yescharacteristic
217C22×Dic7C22×C411yescharacteristic
218C22×Dic7C22×C411yescharacteristic
219C22×Dic7C22×C411yescharacteristic
220C22×Dic7C22×C411yescharacteristic
221C22×Dic7C22×C411yescharacteristic
222C22×Dic7C22×C411yescharacteristic
223C2×C4×D7—21no—
224C2×C4×D7—21no—
225C2×C4×D7—21no—
226C2×C4×D7—21no—
227C2×C4×D7—21no—
228C2×C4×D7—21no—
229C2×C7×C8—21no—
230C2×C7×C8—21no—
231C2×C7×C8—21no—
232C2×C7×C8—21no—
233C2×C7×C8—21no—
234C2×C7×C8—21no—
235C2×C7×C8—21no—
236C2×C7×C8—21no—
237C2×C7×C8—21no—
238C2×C7×C8—21no—
239C2×C7×C8—21no—
240C2×C7×C8—21no—
241C22⋊Dic7—22no—
242C22⋊Dic7—22no—
243C22⋊Dic7—22no—
244C22⋊Dic7—22no—
245C22⋊Dic7—41no—
246C22⋊Dic7—41no—
247C22⋊Dic7—41no—
248C22⋊Dic7—41no—
249C22⋊Dic7M1614yescomplemented
250(C2×D7)⋊C4—22no—
251(C2×D7)⋊C4—41no—
252(C2×D7)⋊C4—41no—
253Dic7⋊C4—22no—
254Dic7⋊C4—41no—
255Dic7⋊C4—41no—
256C4×Dic7—21no—
257C4×Dic7—21no—
258C4×Dic7—21no—
259C4×Dic7—21no—
260C4×Dic7—21no—
261C4×Dic7—21no—
262#1136—44no—
263#1136—44no—
264C2×C7⋊C8—21no—
265C2×C7⋊C8—21no—
266C2×C7⋊C8—21no—
267C2×C7⋊C8—21no—
268C2×C7⋊C8—21no—
269C2×C7⋊C8—21no—
270C2×C7⋊C8—21no—
271C2×C7⋊C8—21no—
272C2×C7⋊C8—21no—
273C2×C7⋊C8—21no—
274C2×C7⋊C8C2×D412yes—
275C2×C7⋊C8C2×D412yes—
276#1131—44no—
277C24×C4C2×D711yescharacteristic
278C22×M16—71no—
279C22×M16—71no—
280C22×M16—71no—
281C2×#120—71no—
282C2×C4×D4—71no—
283C2×C4×D4—71no—
284C2×C4×D4—71no—
285#436—144no—
286C2×C4⋊C8—71no—
287C2×C4⋊C8—71no—
288C2×C4⋊C8—71no—
289#407—144no—
290C2×C22⋊C8—71no—
291C2×C22⋊C8—71no—
292C2×C22⋊C8—71no—
293C2×C22⋊C8—71no—
294C2×C22⋊C8—71no—
295C2×C22⋊C8—71no—
296C2×C22⋊C8—71no—
297C2×C22⋊C8C2×D711yescharacteristic
298C2×C22⋊C8C2×D711yescharacteristic
299C2×C22⋊C8C2×D711yescharacteristic
300C2×C22⋊C8C2×D711yescharacteristic
301C2×C22⋊C8C2×D711yescharacteristic
302C2×C22⋊C8C2×D711yescharacteristic
303C2×#97—71no—
304C2×C4×C8—71no—
305C2×C4×C8—71no—
306#386—71no—
307#386—71no—
308#386—71no—
309#385—71no—
310#385—71no—
311#385—71no—
312#379—71no—
313C4×C22⋊C4—71no—
314C4×C22⋊C4—71no—
315C4×C22⋊C4—71no—
316#336—71no—
317#336—71no—
318#336—71no—
319#336—71no—
320#336—71no—
321#336—71no—
322C23×C7—21no—
323C23×C7—21no—
324C23×C7—21no—
325C23×C7—21no—
326C23×C7—21no—
327C23×C7—21no—
328C23×C7—21no—
329C23×C7—21no—
330C23×C7—21no—
331C23×C7—21no—
332C23×C7—21no—
333C23×C7—21no—
334C23×C7—21no—
335C23×C7—21no—
336C23×C7—21no—
337C23×C7—21no—
338C23×C7—21no—
339C23×C7—21no—
340C23×C7—44no—
341C23×C7—44no—
342C23×C7—44no—
343C23×C7—44no—
344C23×C7—44no—
345C23×C7—44no—
346C23×C7—44no—
347C23×C7C4×D412yes—
348C23×C7C2×M1612yes—
349C23×C7#13112yes—
350C23×C7C23×C411yescharacteristic
351C22×D7—21no—
352C22×D7—21no—
353C22×D7—21no—
354C22×D7—21no—
355C22×D7—21no—
356C22×D7—21no—
357C22×D7—21no—
358C2×C4×C7—21no—
359C2×C4×C7—21no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—21no—
365C2×C4×C7—21no—
366C2×C4×C7—21no—
367C2×C4×C7—21no—
368C2×C4×C7—21no—
369C2×C4×C7—21no—
370C2×C4×C7—44no—
371C2×C4×C7—44no—
372C2×C4×C7—44no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7C4×D412yes—
382C2×C4×C7C22×D411yescharacteristic
383C2×C4×C7C2×#4111yescharacteristic
384C2×C4×C7H(5,𝔽2)11yescharacteristic
385C2×C4×C7H(5,𝔽2)11yescharacteristic
386C2×C4×C7H(5,𝔽2)11yescharacteristic
387C2×C4×C7H(5,𝔽2)11yescharacteristic
388C22⋊D7—44no—
389C22⋊D7—44no—
390C22⋊D7—44no—
391C2×Dic7—21no—
392C2×Dic7—21no—
393C2×Dic7—21no—
394C2×Dic7—21no—
395C2×Dic7—21no—
396C2×Dic7—21no—
397C2×Dic7—21no—
398C2×Dic7—21no—
399C2×Dic7—21no—
400C2×Dic7—21no—
401C2×Dic7—21no—
402C2×Dic7—21no—
403C2×Dic7—21no—
404C2×Dic7—21no—
405C2×Dic7—21no—
406C2×Dic7—21no—
407C2×Dic7—21no—
408C2×Dic7—21no—
409C2×Dic7—21no—
410C2×Dic7C2×M1612yes—
411C2×Dic7C2×M1612yes—
412C4×D7—41no—
413C4×D7—41no—
414C4×D7—41no—
415C4×D7—41no—
416C7×C8—41no—
417C7×C8—41no—
418C7×C8—41no—
419C7×C8—41no—
420C7⋊C8—22no—
421C7⋊C8—22no—
422C7⋊C8—41no—
423C7⋊C8—41no—
424C25C4×D711yescharacteristic
425C22×D4—71no—
426C22×D4—71no—
427C22×D4—71no—
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—41no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4—71no—
435C23×C4C4×D711yescharacteristic
436C23×C4C4×D711yescharacteristic
437C23×C4C4×D711yescharacteristic
438C23×C4C22×D711yescharacteristic
439C23×C4C22×D711yescharacteristic
440C23×C4C22×D711yescharacteristic
441C2×M16—74no—
442C2×M16—142no—
443C2×M16—142no—
444C2×M16—281no—
445C2×M16—281no—
446C2×M16—281no—
447C2×M16—281no—
448C2×M16—281no—
449C2×M16—281no—
450C22×C8—71no—
451C22×C8—71no—
452C22×C8—71no—
453C22×C8—71no—
454C22×C8C22×D711yescharacteristic
455C22×C8C22×D711yescharacteristic
456C22×C8C22×D711yescharacteristic
457C22×C8C22×D711yescharacteristic
458#120—144no—
459C4×D4—142no—
460C4×D4—142no—
461C4×D4—281no—
462C4×D4—281no—
463C4×D4—281no—
464C4×D4—281no—
465C2×C4⋊C4—71no—
466C2×C4⋊C4—71no—
467C2×C4⋊C4—71no—
468C2×C22⋊C4—71no—
469C2×C22⋊C4—71no—
470C2×C22⋊C4—71no—
471C2×C22⋊C4—71no—
472C2×C22⋊C4—71no—
473C2×C22⋊C4—71no—
474C2×C22⋊C4—71no—
475C2×C22⋊C4—71no—
476C2×C22⋊C4—71no—
477C2×C22⋊C4—71no—
478C2×C22⋊C4—71no—
479C2×C22⋊C4—71no—
480C2×C42—71no—
481C2×C42—71no—
482C2×C42—71no—
483C4⋊C8—142no—
484C4⋊C8—281no—
485C4⋊C8—281no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—142no—
493C22⋊C8—142no—
494C22⋊C8—142no—
495C22⋊C8—142no—
496C22⋊C8—142no—
497C22⋊C8—281no—
498C22⋊C8—281no—
499#97—281no—
500C4×C8—142no—
501C4×C8—281no—
502#95—71no—
503#95—71no—
504#95—71no—
505#95—71no—
506#95—71no—
507#95—71no—
508C22×C7—22no—
509C22×C7—22no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7—22no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—22no—
516C22×C7—22no—
517C22×C7—416no—
518C22×C7—41no—
519C22×C7—41no—
520C22×C7—41no—
521C22×C7—41no—
522C22×C7—41no—
523C22×C7—41no—
524C22×C7—41no—
525C22×C7—41no—
526C22×C7—41no—
527C22×C7—41no—
528C22×C7—41no—
529C22×C7—41no—
530C22×C7C2×C4×D411yescharacteristic
531C22×C7#51811yescharacteristic
532C22×C7#51811yescharacteristic
533C22×C7C22×M1611yescharacteristic
534C22×C7C2×#13111yescharacteristic
535C22×C7#56811yescharacteristic
536C22×C7#56811yescharacteristic
537C2×D7—41no—
538C2×D7—41no—
539C2×D7—41no—
540C2×D7—41no—
541C2×D7—41no—
542C2×D7—41no—
543C2×D7—41no—
544C4×C7—22no—
545C4×C7—41no—
546C4×C7—41no—
547C4×C7#53411yescharacteristic
548C4×C7#53511yescharacteristic
549C4×C7#53811yescharacteristic
550C4×C7#53811yescharacteristic
551Dic7—22no—
552Dic7—22no—
553Dic7—41no—
554Dic7—41no—
555Dic7—41no—
556Dic7—41no—
557Dic7—41no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24—41no—
565C24—71no—
566C24C2×C4×D711yescharacteristic
567C24C2×C4×D711yescharacteristic
568C24C2×C4×D711yescharacteristic
569C2×D4—142no—
570C2×D4—142no—
571C2×D4—142no—
572C2×D4—142no—
573C2×D4—142no—
574C2×D4—281no—
575C2×D4—281no—
576C2×D4—281no—
577C2×D4—281no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—71no—
608C22×C4—71no—
609C22×C4—71no—
610C22×C4—71no—
611C22×C4—71no—
612C22×C4—71no—
613C22×C4—71no—
614C22×C4—141no—
615C22×C4—141no—
616C22×C4—141no—
617C22×C4—141no—
618C22×C4—141no—
619C22×C4—141no—
620C22×C4C2×C4×D711yescharacteristic
621C22×C4C2×C4×D711yescharacteristic
622C22×C4C2×C4×D711yescharacteristic
623C22×C4D4×D712yes—
624C22×C4#115912yes—
625C22×C4C23×D711yescharacteristic
626M16—284no—
627M16—284no—
628M16—284no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—72no—
642C2×C8—72no—
643C2×C8—141no—
644C2×C8—141no—
645C2×C8—141no—
646C2×C8—141no—
647C2×C8—141no—
648C2×C8—141no—
649C2×C8—141no—
650C2×C8—141no—
651C2×C8—141no—
652C2×C8—141no—
653C4⋊C4—142no—
654C4⋊C4—281no—
655C4⋊C4—281no—
656C22⋊C4—74no—
657C22⋊C4—142no—
658C22⋊C4—142no—
659C22⋊C4—142no—
660C22⋊C4—142no—
661C22⋊C4—142no—
662C22⋊C4—281no—
663C22⋊C4—281no—
664C22⋊C4—281no—
665C22⋊C4—281no—
666C22⋊C4—281no—
667C22⋊C4—281no—
668C42—141no—
669C42—141no—
670C42—141no—
671C42—141no—
672C42—141no—
673C42—141no—
674C2×C7—42no—
675C2×C7—42no—
676C2×C7—42no—
677C2×C7#232111yescharacteristic
678C2×C7#293311yescharacteristic
679C2×C7D4×M1611yescharacteristic
680C2×C7#297411yescharacteristic
681C2×C7#297511yescharacteristic
682C2×C7#297611yescharacteristic
683C2×C7#297811yescharacteristic
684D7—81no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—141no—
711C23—141no—
712C23—141no—
713C23—141no—
714C23—141no—
715C23—141no—
716C23—141no—
717C23(C22⋊D7)⋊C412yes—
718C23#646412yes—
719C23D7×M1612yes—
720C23C22×C4×D711yescharacteristic
721D4—284no—
722D4—284no—
723D4—284no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—72no—
748C2×C4—72no—
749C2×C4—141no—
750C2×C4—141no—
751C2×C4—141no—
752C2×C4—141no—
753C2×C4—141no—
754C2×C4—141no—
755C2×C4—141no—
756C2×C4—141no—
757C2×C4—141no—
758C2×C4—141no—
759C2×C4—141no—
760C2×C4—141no—
761C2×C4—141no—
762C2×C4—141no—
763C2×C4—141no—
764C2×C4—141no—
765C2×C4—141no—
766C2×C4—141no—
767C2×C4—141no—
768C2×C4—281no—
769C2×C4—281no—
770C2×C4—281no—
771C2×C4—281no—
772C2×C4(C22⋊D7)⋊C412yes—
773C2×C4C2×D4×D711yescharacteristic
774C2×C4C2×#115911yescharacteristic
775C2×C4#654811yescharacteristic
776C2×C4#654811yescharacteristic
777C2×C4#654811yescharacteristic
778C2×C4#654811yescharacteristic
779C8—41no—
780C8—41no—
781C8—41no—
782C8—41no—
783C8—142no—
784C8—142no—
785C8—281no—
786C8—281no—
787C7#2203811yescharacteristic, complemented, Sylow
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—281no—
811C22—281no—
812C22—281no—
813C22—281no—
814C22—281no—
815C22—281no—
816C22—281no—
817C22C2×(C22⋊D7)⋊C411yescharacteristic
818C22#9017711yescharacteristic
819C22#9017711yescharacteristic
820C22C2×#646411yescharacteristic
821C22C2×D7×M1611yescharacteristic
822C22#9043611yescharacteristic
823C22#9043611yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—142no—
828C4—142no—
829C4—281no—
830C4—281no—
831C4—281no—
832C4—281no—
833C4—281no—
834C4#9028011yescharacteristic
835C4#9028311yescharacteristic
836C4#9028411yescharacteristic
837C4#9028411yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—561no—
842C2#1173126611yescharacteristic
843C2#1173604111yescharacteristic
844C2#1173604811yescharacteristic
845C2#1173604911yescharacteristic
846C2#1173607311yescharacteristic
847C2#1173607911yescharacteristic
848C2#1173608111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC7×#1779C2
prime radicalC2×#6516C4
cosocleC22×C4×C7C24
hypercenter#1779D7
hypocenterC7#22038
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#89979C2semidirect
3. C2×#89501C2semidirect
4. C7×#1779C2semidirect
5. #11727712C2semidirect
6. #11727712C2semidirect
7. #11727707C2semidirect
8. #11727705C2semidirect
9. #11727703C2semidirect
10. #11727671C2semidirect
11. #11727670C2semidirect
12. #11727668C2semidirect
13. #11727667C2semidirect
14. #11727667C2semidirect
15. #11727666C2semidirect
23. C22×#1131C22semidirect
45. C2×(C2×D7)⋊C8C22semidirect
46. C2×(C2×D7)⋊C8C22semidirect
47. C2×(C2×D7)⋊C8C22semidirect
48. C2×#6389C22semidirect
49. C2×Dic7⋊C8C22semidirect
50. C2×Dic7⋊C8C22semidirect
51. C2×Dic7⋊C8C22semidirect
52. C2×C8×Dic7C22semidirect
53. C2×C8×Dic7C22semidirect
55. #89345C22semidirect
56. #89345C22semidirect
57. #89345C22semidirect
58. #89345C22semidirect
59. #89345C22semidirect
60. #89345C22semidirect
113. C2×#1136D4semidirect
159. #1779D7semidirect
249. C22⋊Dic7M16semidirect
787. C7#22038semidirect

Maximal subgroups

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

subgroupindex
C4×#65162
C2×#899792
C2×#895012
C7×#17792
#117277122
#117277072
#117277052
#117277032
#117276712
#117276702
#117276682
#117276672
#117276662
#220387