Finite Group Databasebeta

← #13364899

Subgroups — #13364899

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
1C2×C7×#407C211yesmaximal, characteristic, complemented
2C4×#6516C211yesmaximal, characteristic
3C2×#89900C211yesmaximal, characteristic, complemented
4#11729880C211yesmaximal, characteristic, complemented
5#11729750C211yesmaximal, characteristic, complemented
6#11729749C211yesmaximal, characteristic, complemented
7#11729737C211yesmaximal, characteristic, complemented
8#11727712C211yesmaximal, characteristic, complemented
9#11727712C211yesmaximal, characteristic, complemented
10#11727671C211yesmaximal, characteristic, complemented
11#11727670C211yesmaximal, characteristic, complemented
12#11727669C211yesmaximal, characteristic, complemented
13#11727667C211yesmaximal, characteristic, complemented
14#11727666C211yesmaximal, characteristic, complemented
15#11727666C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×M16C2211yescharacteristic
18C22×C7×M16C2211yescharacteristic
19C2×#6516C411yescharacteristic
20C2×C4×C22⋊D7C2211yescharacteristic
21C2×C4×C22⋊D7C2211yescharacteristic
22C2×C4×C22⋊D7C2211yescharacteristic
23C22×#1131C2211yescharacteristic, complemented
24C7×#407—24no—
25C2×C7×C22⋊C8C2211yescharacteristic
26C2×C7×C22⋊C8C2211yescharacteristic
27C2×C7×C22⋊C8C2211yescharacteristic
28C2×C7×C22⋊C8C2211yescharacteristic
29#90019C411yescharacteristic
30#89985C411yescharacteristic
31#89985C411yescharacteristic
32#89985C411yescharacteristic
33#89982C411yescharacteristic
34#89982C411yescharacteristic
35#89982C411yescharacteristic
36C4×C22⋊Dic7C2211yescharacteristic
37C4×C22⋊Dic7C2211yescharacteristic
38C4×C22⋊Dic7C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43C2×C22⋊(C7⋊C8)C2211yescharacteristic
44C2×C22⋊(C7⋊C8)C2211yescharacteristic
45#89900—24no—
46C2×(C2×D7)⋊C8C2211yescharacteristic, complemented
47C2×(C2×D7)⋊C8C2211yescharacteristic, complemented
48C2×(C2×D7)⋊C8C2211yescharacteristic, complemented
49C2×#6389C2211yescharacteristic, complemented
50C2×Dic7⋊C8C2211yescharacteristic, complemented
51C2×Dic7⋊C8C2211yescharacteristic, complemented
52C2×Dic7⋊C8C2211yescharacteristic, complemented
53C2×C8×Dic7C2211yescharacteristic, complemented
54C2×C8×Dic7C2211yescharacteristic, complemented
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
79C2×C7×M16—22no—
80C2×C7×M16—41no—
81C2×C7×M16—41no—
82C2×C7×M16—41no—
83C2×C7×M16—41no—
84C2×C7×M16D414yescomplemented
85C22×C7×C8C2311yescharacteristic
86C22×C7×C8C2311yescharacteristic
87C22×C7×C8C2311yescharacteristic
88C22×C7×C8C2311yescharacteristic
89#6516—24no—
90C2×C22⋊Dic7C2×C411yescharacteristic
91C2×C22⋊Dic7C2×C411yescharacteristic
92C2×C22⋊Dic7C2×C411yescharacteristic
93C2×C22⋊Dic7C2×C411yescharacteristic
94C2×C22⋊Dic7C2×C411yescharacteristic
95C2×C22⋊Dic7C2×C411yescharacteristic
96C2×C22⋊Dic7C2×C411yescharacteristic
97C2×C22⋊Dic7C2×C411yescharacteristic
98C2×C22⋊Dic7C2×C411yescharacteristic
99C4×C22⋊D7—22no—
100C4×C22⋊D7—22no—
101C4×C22⋊D7—41no—
102C4×C22⋊D7—41no—
103C4×C22⋊D7—41no—
104C4×C22⋊D7—41no—
105C2×(C2×D7)⋊C4C2×C411yescharacteristic
106C2×(C2×D7)⋊C4C2×C411yescharacteristic
107C2×(C2×D7)⋊C4C2×C411yescharacteristic
108C2×Dic7⋊C4C2×C411yescharacteristic
109C2×Dic7⋊C4C2×C411yescharacteristic
110C2×Dic7⋊C4C2×C411yescharacteristic
111C2×C4×Dic7C2311yescharacteristic
112C2×C4×Dic7C2311yescharacteristic
113C2×C4×Dic7C2311yescharacteristic
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—22no—
124C7×C22⋊C8—22no—
125C7⋊#95C2×C411yescharacteristic
126C7⋊#95C2×C411yescharacteristic
127C7⋊#95C2×C411yescharacteristic
128C7⋊#95C2×C411yescharacteristic
129C7⋊#95C2×C411yescharacteristic
130C7⋊#95C2×C411yescharacteristic
131C22⋊(C7⋊C8)—22no—
132C22⋊(C7⋊C8)—22no—
133C22⋊(C7⋊C8)—41no—
134C22⋊(C7⋊C8)—41no—
135C22⋊(C7⋊C8)—41no—
136C22⋊(C7⋊C8)—41no—
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×#407D711yescharacteristic, complemented
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#1779—71no—
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—
229C7×M16—44no—
230C7×M16—44no—
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—
241C2×C7×C8C2×D412yes—
242C2×C7×C8C2×D412yes—
243C22⋊Dic7—22no—
244C22⋊Dic7—22no—
245C22⋊Dic7—22no—
246C22⋊Dic7—22no—
247C22⋊Dic7—41no—
248C22⋊Dic7—41no—
249C22⋊Dic7—41no—
250C22⋊Dic7—41no—
251C22⋊Dic7M1614yescomplemented
252(C2×D7)⋊C4—22no—
253(C2×D7)⋊C4—41no—
254(C2×D7)⋊C4—41no—
255Dic7⋊C4—22no—
256Dic7⋊C4—41no—
257Dic7⋊C4—41no—
258C4×Dic7—21no—
259C4×Dic7—21no—
260C4×Dic7—21no—
261C4×Dic7—21no—
262C4×Dic7—21no—
263C4×Dic7—21no—
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⋊C8—21no—
275C2×C7⋊C8—21no—
276#1131—44no—
277C24×C4C2×D711yescharacteristic
278C22×M16—71no—
279C22×M16C2×D711yescharacteristic
280C22×M16C2×D711yescharacteristic
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—24no—
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⋊C8—71no—
298C2×C22⋊C8—71no—
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—22no—
417C7×C8—22no—
418C7×C8—41no—
419C7×C8—41no—
420C7⋊C8—41no—
421C7⋊C8—41no—
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—22no—
442C2×M16—41no—
443C2×M16—41no—
444C2×M16—41no—
445C2×M16—41no—
446C2×M16—142no—
447C2×M16—281no—
448C2×M16—281no—
449C2×M16C22⋊D714yescomplemented
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—22no—
489C22⋊C8—22no—
490C22⋊C8—142no—
491C22⋊C8—142no—
492C22⋊C8—142no—
493C22⋊C8—281no—
494C22⋊C8—281no—
495C22⋊C8—281no—
496C22⋊C8—281no—
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×C4#115712yes—
624C22×C4C2×C22⋊D712yes—
625C22×C4C23×D711yescharacteristic
626M16—44no—
627M16—44no—
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—141no—
640C2×C8—141no—
641C2×C8—141no—
642C2×C8—141no—
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×C8C2×C22⋊D712yes—
652C2×C8C2×C22⋊D712yes—
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—
717C23D7×M1612yes—
718C23#647012yes—
719C23C4×C22⋊D712yes—
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×C4C4×C22⋊D712yes—
773C2×C4C2×#115711yescharacteristic
774C2×C4#654811yescharacteristic
775C2×C4#654811yescharacteristic
776C2×C4#654811yescharacteristic
777C2×C4#654811yescharacteristic
778C2×C4C22×C22⋊D711yescharacteristic
779C8—22no—
780C8—22no—
781C8—41no—
782C8—41no—
783C8—281no—
784C8—281no—
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—
817C22#9017711yescharacteristic
818C22#9017711yescharacteristic
819C22C2×D7×M1611yescharacteristic
820C22C2×#647011yescharacteristic
821C22#9043611yescharacteristic
822C22#9043611yescharacteristic
823C22C2×C4×C22⋊D711yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—142no—
828C4—142no—
829C4—281no—
830C4—281no—
831C4—281no—
832C4—281no—
833C4—281no—
834C4#9018511yescharacteristic
835C4#9018511yescharacteristic
836C4#9049511yescharacteristic
837C4#9049611yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—561no—
842C2#1173607811yescharacteristic
843C2#1173607911yescharacteristic
844C2#1173608011yescharacteristic
845C2#1173608111yescharacteristic
846C2#1173954111yescharacteristic
847C2#1174120211yescharacteristic
848C2M16×C22⋊D711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D7
commutator, socleC23×C7C23×C4
FittingC2×C7×#407C2
prime radicalC2×#6516C4
cosocleC22×C4×C7C24
hypercenterC2×#407D7
hypocenterC7#22038
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×C7×#407C2semidirect
3. C2×#89900C2semidirect
4. #11729880C2semidirect
5. #11729750C2semidirect
6. #11729749C2semidirect
7. #11729737C2semidirect
8. #11727712C2semidirect
9. #11727712C2semidirect
10. #11727671C2semidirect
11. #11727670C2semidirect
12. #11727669C2semidirect
13. #11727667C2semidirect
14. #11727666C2semidirect
15. #11727666C2semidirect
23. C22×#1131C22semidirect
46. C2×(C2×D7)⋊C8C22semidirect
47. C2×(C2×D7)⋊C8C22semidirect
48. C2×(C2×D7)⋊C8C22semidirect
49. C2×#6389C22semidirect
50. C2×Dic7⋊C8C22semidirect
51. C2×Dic7⋊C8C22semidirect
52. C2×Dic7⋊C8C22semidirect
53. C2×C8×Dic7C22semidirect
54. C2×C8×Dic7C22semidirect
55. #89345C22semidirect
56. #89345C22semidirect
57. #89345C22semidirect
58. #89345C22semidirect
59. #89345C22semidirect
60. #89345C22semidirect
84. C2×C7×M16D4semidirect
147. C2×#407D7semidirect
251. C22⋊Dic7M16semidirect
449. C2×M16C22⋊D7semidirect
787. C7#22038semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4072
C4×#65162
C2×#899002
#117298802
#117297502
#117297492
#117297372
#117277122
#117276712
#117276702
#117276692
#117276672
#117276662
#220387