Finite Group Databasebeta

← #13275392

Subgroups — #13275392

Order 1792.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89712C211yesmaximal, characteristic
2C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
4C2×#89440C211yesmaximal, characteristic
5C2×#89442C211yesmaximal, characteristic
6C2×#89421C211yesmaximal, characteristic, complemented
7C2×#89438C211yesmaximal, characteristic
8C4×C7×#95C211yesmaximal, characteristic, complemented
9#11729291C211yesmaximal, characteristic
10#11729290C211yesmaximal, characteristic, complemented
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12#11727162C211yesmaximal, characteristic
13#11727161C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727159C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C42×C7C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51#89712C418yescomplemented
52C4×(C2×D7)⋊C4—24no—
53C4×C4⋊Dic7—24no—
54#89442C418yescomplemented
55#89440C418yescomplemented
56#89438—24no—
57#89421—24no—
58#13823—71nomaximal, Sylow
59C24×D7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7—22no—
78C22×C4×D7—41no—
79C22×C4×D7—41no—
80C22×C4×D7C2×C414yes—
81C2×C42×C7—22no—
82C2×C42×C7—22no—
83C2×C42×C7—22no—
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—41no—
88C2×C42×C7—41no—
89C2×C42×C7C2×C414yescomplemented
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—22no—
92C2×(C2×D7)⋊C4—22no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—41no—
99C2×(C2×D7)⋊C4—41no—
100C2×(C2×D7)⋊C4C2×C414yes—
101C2×(C2×D7)⋊C4C2×C414yes—
102C2×(C2×D7)⋊C4C2×C414yes—
103C2×(C2×D7)⋊C4C2×C414yes—
104C2×(C2×D7)⋊C4C2×C414yes—
105C2×(C2×D7)⋊C4C2×C414yes—
106C2×(C2×D7)⋊C4C2×C414yes—
107C2×(C2×D7)⋊C4C2×C414yes—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7C2×C414yes—
113C2×C4⋊Dic7C2×C414yescomplemented
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4C2×C414yes—
119C2×Dic7⋊C4C2×C414yescomplemented
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—22no—
128C2×C4×Dic7—22no—
129C2×C4×Dic7—22no—
130C2×C4×Dic7—41no—
131C2×C4×Dic7—41no—
132C2×C4×Dic7—41no—
133C2×C4×Dic7—41no—
134C2×C4×Dic7C2×C414yescomplemented
135C7×#95—22no—
136C7×#95C2×C414yes—
137C7×#95C2×C414yescomplemented
138C7×#95D414yes—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—41no—
145C7⋊#95—41no—
146C7⋊#95C2×C414yes—
147C7⋊#95C2×C414yescomplemented
148C7⋊#95C2×C414yescomplemented
149C7⋊#95C2×C414yescomplemented
150C7⋊#95D414yes—
151C2×#388—71no—
152C2×#388—71no—
153C2×#385—71no—
154C2×C4×C4⋊C4—71no—
155C2×C4×C4⋊C4—71no—
156C2×C4×C22⋊C4—71no—
157C2×C4×C22⋊C4—71no—
158#1437—71no—
159#1437—71no—
160#1436—71no—
161#1436—71no—
162#1436—71no—
163#1436—71no—
164C4×#95—71no—
165C4×#95D711yescharacteristic, complemented
166C24×C7C2411yescharacteristic
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7—21no—
175C23×D7—21no—
176C23×D7—21no—
177C23×D7—21no—
178C23×D7—21no—
179C23×D7C22×C412yes—
180C23×D7C22×C412yes—
181C23×D7C22×C412yes—
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—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C22×C412yes—
216C22×C4×C7C22×C412yes—
217C22×C4×C7C22×C412yes—
218C22×C4×C7C22×C412yes—
219C22×C4×C7C22×C412yes—
220C22×C4×C7C22×C412yes—
221C22×C4×C7C22×C412yes—
222C22×C4×C7C22×C412yes—
223C22×C4×C7C2×D412yes—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7#4112yes—
228C22×C4×C7#4112yes—
229C22×C4×C7#4112yes—
230C22×C4×C7#4112yes—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7C22×C412yes—
268C22×Dic7C22×C412yes—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C22×C412yes—
274C22×Dic7C22×C412yes—
275C22×Dic7C22×C412yes—
276C22×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7#4112yes—
279C22×Dic7#4112yes—
280C2×C4×D7—28no—
281C2×C4×D7—28no—
282C2×C4×D7—44no—
283C2×C4×D7—44no—
284C2×C4×D7—44no—
285C2×C4×D7—44no—
286C2×C4×D7—44no—
287C42×C7—28no—
288C42×C7—44no—
289C42×C7—44no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—44no—
295(C2×D7)⋊C4C42116yescomplemented
296C4⋊Dic7—28no—
297C4⋊Dic7—28no—
298Dic7⋊C4—28no—
299Dic7⋊C4—28no—
300C4×Dic7—28no—
301C4×Dic7—44no—
302C4×Dic7—44no—
303C4×Dic7—44no—
304C4×Dic7—44no—
305C24×C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C42—71no—
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321C22×C42C2×D711yescharacteristic
322C22×C42C2×D711yescharacteristic
323C22×C42C2×D711yescharacteristic
324#388—78no—
325#388—78no—
326#385—78no—
327C4×C4⋊C4—144no—
328C4×C4⋊C4—144no—
329C4×C22⋊C4—144no—
330C4×C22⋊C4—144no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95C2×D711yescharacteristic
344C2×#95C2×D711yescharacteristic
345C2×#95C2×D711yescharacteristic
346C2×#95C2×D711yescharacteristic
347C23×C7C23×C411yescharacteristic
348C23×C7C23×C411yescharacteristic
349C23×C7C23×C411yescharacteristic
350C23×C7C22×D411yescharacteristic
351C23×C7C22×D411yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7C2×#4111yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7C2×#4111yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7H(5,𝔽2)11yescharacteristic
359C23×C7H(5,𝔽2)11yescharacteristic
360C23×C72−1+411yescharacteristic
361C23×C72−1+411yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7—41no—
388C22×D7—41no—
389C22×D7—41no—
390C22×D7—41no—
391C22×D7—41no—
392C22×D7—41no—
393C22×D7—41no—
394C22×D7—41no—
395C22×D7—41no—
396C22×D7C2×C4214yes—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7C2×C4214yes—
442C2×C4×C7C4×D414yes—
443C2×C4×C7C4×D414yes—
444C2×C4×C7C4×D414yes—
445C2×C4×C7C4×D414yes—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7C2×C4214yes—
493C2×Dic7C4×D414yes—
494C2×Dic7C4×D414yes—
495C4×D7—416no—
496C25—71no—
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—74no—
505C23×C4—142no—
506C23×C4—142no—
507C23×C4—142no—
508C23×C4—142no—
509C23×C4—281no—
510C23×C4—281no—
511C23×C4C22×D711yescharacteristic
512C23×C4C22×D711yescharacteristic
513C23×C4C22×D711yescharacteristic
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C2×C4⋊C4—74no—
519C2×C4⋊C4—74no—
520C2×C4⋊C4—74no—
521C2×C4⋊C4—74no—
522C2×C4⋊C4—142no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—142no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—74no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—281no—
547C2×C22⋊C4—281no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—41no—
555C2×C42—41no—
556C2×C42—74no—
557C2×C42—142no—
558C2×C42—142no—
559C2×C42—142no—
560C2×C42—142no—
561C2×C42—142no—
562C2×C42—142no—
563C2×C42—142no—
564C2×C42—142no—
565C2×C42—142no—
566C2×C42—142no—
567C2×C42—281no—
568C2×C42—281no—
569C2×C42—281no—
570C2×C42—281no—
571C2×C42C4×D714yescomplemented
572#95—22no—
573#95—74no—
574#95—74no—
575#95—74no—
576#95—74no—
577#95—74no—
578#95—142no—
579#95—142no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—281no—
584#95—281no—
585#95C4×D714yes—
586#95C4×D714yescomplemented
587#95D2814yes—
588C22×C7C22×C4211yescharacteristic
589C22×C7C2×C4×D411yescharacteristic
590C22×C7C2×C4×D411yescharacteristic
591C22×C7C2×C4×D411yescharacteristic
592C22×C7C2×C4×D411yescharacteristic
593C22×C7C2×C4×D411yescharacteristic
594C22×C7C2×C4×D411yescharacteristic
595C22×C7C4×#4111yescharacteristic
596C22×C7C4×#4111yescharacteristic
597C22×C7C4×#4111yescharacteristic
598C22×C7C4×#4111yescharacteristic
599C22×C7C4×#4111yescharacteristic
600C22×C7C4×#4111yescharacteristic
601C22×C7#51811yescharacteristic
602C22×C7#51911yescharacteristic
603C22×C7#52011yescharacteristic
604C22×C7#52011yescharacteristic
605C22×C7#52011yescharacteristic
606C22×C7#52011yescharacteristic
607C22×C7D4211yescharacteristic
608C22×C7#54611yescharacteristic
609C22×C7#54611yescharacteristic
610C22×C7#54711yescharacteristic
611C22×C7#54711yescharacteristic
612C22×C7#54811yescharacteristic
613C22×C7#54811yescharacteristic
614C22×C7#55111yescharacteristic
615C22×C7#55111yescharacteristic
616C22×C7#55211yescharacteristic
617C22×C7#55211yescharacteristic
618C22×C7#55311yescharacteristic
619C22×C7#55311yescharacteristic
620C22×C7#55611yescharacteristic
621C22×C7#55611yescharacteristic
622C22×C7#55911yescharacteristic
623C2×D7—24no—
624C2×D7—24no—
625C2×D7—24no—
626C2×D7—42no—
627C2×D7—42no—
628C2×D7—42no—
629C2×D7—42no—
630C2×D7—42no—
631C2×D7—42no—
632C2×D7—42no—
633C2×D7—42no—
634C2×D7—42no—
635C2×D7—42no—
636C2×D7—42no—
637C2×D7—42no—
638C4×C7—24no—
639C4×C7—24no—
640C4×C7—24no—
641C4×C7—24no—
642C4×C7—24no—
643C4×C7—42no—
644C4×C7—42no—
645Dic7—24no—
646Dic7—24no—
647Dic7—24no—
648Dic7—42no—
649Dic7—42no—
650Dic7—42no—
651Dic7—42no—
652C24—72no—
653C24—72no—
654C24—72no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24—141no—
659C24—141no—
660C24—141no—
661C24—141no—
662C24—141no—
663C24—141no—
664C24—141no—
665C24—141no—
666C24—141no—
667C24C23×D711yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—72no—
701C22×C4—72no—
702C22×C4—72no—
703C22×C4—72no—
704C22×C4—72no—
705C22×C4—72no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—72no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—72no—
713C22×C4—148no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
734C22×C4—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—148no—
751C22×C4—284no—
752C22×C4—284no—
753C22×C4—284no—
754C22×C4—284no—
755C22×C4—284no—
756C22×C4C2×C4×D712yes—
757C22×C4C2×C4×D712yes—
758C22×C4C2×C4×D712yes—
759C22×C4C2×C4×D712yes—
760C22×C4C2×C4×D712yes—
761C22×C4C2×C4×D712yes—
762C22×C4C2×C4×D712yes—
763C22×C4C2×C4×D712yes—
764C22×C4C2×C4×D712yes—
765C22×C4C2×D2812yes—
766C22×C4C2×D2812yes—
767C22×C4C2×D2812yes—
768C22×C4#115712yes—
769C22×C4#115712yes—
770C22×C4#115712yes—
771C22×C4D4×D712yes—
772C22×C4#115912yes—
773C4⋊C4—148no—
774C4⋊C4—148no—
775C4⋊C4—148no—
776C4⋊C4—148no—
777C22⋊C4—716no—
778C22⋊C4—148no—
779C22⋊C4—148no—
780C22⋊C4—148no—
781C22⋊C4—148no—
782C22⋊C4—284no—
783C42—28no—
784C42—44no—
785C42—44no—
786C42—148no—
787C42—284no—
788C42—284no—
789C42—284no—
790C42—284no—
791C2×C7C42×D411yescharacteristic
792C2×C7C42×D411yescharacteristic
793C2×C7#227411yescharacteristic
794C2×C7#235811yescharacteristic
795C2×C7#235911yescharacteristic
796C2×C7#235911yescharacteristic
797C2×C7#236111yescharacteristic
798C2×C7#236111yescharacteristic
799C2×C7#236211yescharacteristic
800C2×C7#236211yescharacteristic
801C2×C7#236711yescharacteristic
802C2×C7#236711yescharacteristic
803C2×C7#237311yescharacteristic
804C2×C7#237311yescharacteristic
805C2×C7#237411yescharacteristic
806D7—44no—
807C23—74no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—142no—
812C23—142no—
813C23—142no—
814C23—142no—
815C23—142no—
816C23—142no—
817C23—142no—
818C23—142no—
819C23—142no—
820C23—142no—
821C23—142no—
822C23—142no—
823C23—142no—
824C23—142no—
825C23—142no—
826C23—281no—
827C23—281no—
828C23—281no—
829C23—281no—
830C23—281no—
831C23—281no—
832C23—281no—
833C23—281no—
834C23—281no—
835C23—281no—
836C23—281no—
837C23—281no—
838C23—281no—
839C23—281no—
840C23—281no—
841C23—281no—
842C23C22×C4×D711yescharacteristic
843C23C22×C4×D711yescharacteristic
844C23C22×C4×D711yescharacteristic
845C23C22×D2811yescharacteristic
846C23C2×#115711yescharacteristic
847C23C2×#115711yescharacteristic
848C23C2×#115711yescharacteristic
849C23C2×D4×D711yescharacteristic
850C23C2×#115911yescharacteristic
851C23#654811yescharacteristic
852C23#655111yescharacteristic
853C23D7×#4111yescharacteristic
854C23D7×#4111yescharacteristic
855C23#655311yescharacteristic
856C23#655411yescharacteristic
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—74no—
902C2×C4—74no—
903C2×C4—74no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—142no—
917C2×C4—142no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
921C2×C4—142no—
922C2×C4—142no—
923C2×C4—142no—
924C2×C4—142no—
925C2×C4—142no—
926C2×C4—142no—
927C2×C4—142no—
928C2×C4—142no—
929C2×C4—142no—
930C2×C4—142no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—2816no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4—281no—
939C2×C4—281no—
940C2×C4—281no—
941C2×C4—281no—
942C2×C4—281no—
943C2×C4—281no—
944C2×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4—281no—
950C2×C4—281no—
951C2×C4C42×D714yes—
952C2×C4C4×D2814yes—
953C2×C4C4×D2814yes—
954C2×C4C4×D2814yes—
955C2×C4(C22⋊D7)⋊C414yes—
956C7#1382311yescharacteristic, complemented, Sylow
957C22—144no—
958C22—144no—
959C22—144no—
960C22—282no—
961C22—282no—
962C22—282no—
963C22—282no—
964C22—282no—
965C22—282no—
966C22—282no—
967C22—282no—
968C22—282no—
969C22—282no—
970C22—282no—
971C22—282no—
972C22C2×C42×D711yescharacteristic
973C22C2×C4×D2811yescharacteristic
974C22C2×C4×D2811yescharacteristic
975C22C2×C4×D2811yescharacteristic
976C22C4×#115711yescharacteristic
977C22C4×#115711yescharacteristic
978C22C4×#115711yescharacteristic
979C22C2×(C22⋊D7)⋊C411yescharacteristic
980C22#9018111yescharacteristic
981C22#9018611yescharacteristic
982C22#9019511yescharacteristic
983C22#9019811yescharacteristic
984C22#9020411yescharacteristic
985C22#9021311yescharacteristic
986C22#9021411yescharacteristic
987C22#9021811yescharacteristic
988C22#9022111yescharacteristic
989C22#9022211yescharacteristic
990C22#9022411yescharacteristic
991C22C4×#115911yescharacteristic
992C22C4×#115911yescharacteristic
993C22C4×D4×D711yescharacteristic
994C22C4×D4×D711yescharacteristic
995C22#9023611yescharacteristic
996C22#9023711yescharacteristic
997C22D4×D2811yescharacteristic
998C22#9024311yescharacteristic
999C22#9024511yescharacteristic
1000C22#9024611yescharacteristic
1001C22#9025011yescharacteristic
1002C22#9025611yescharacteristic
1003C22#9025911yescharacteristic
1004C22#9026311yescharacteristic
1005C22#9026511yescharacteristic
1006C22#9026711yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—144no—
1015C4—144no—
1016C4—144no—
1017C4—282no—
1018C4—282no—
1019C4—282no—
1020C4—282no—
1021C2—284no—
1022C2C42×D2811yescharacteristic
1023C2#1173078211yescharacteristic
1024C2#1173084111yescharacteristic
1025C2C4×(C22⋊D7)⋊C411yescharacteristic
1026C2#1173090911yescharacteristic
1027C2#1173091211yescharacteristic
1028C2#1173091711yescharacteristic
1029C2#1173092411yescharacteristic
1030C2#1173102211yescharacteristic
1031C2#1173109211yescharacteristic
1032C2#1173109311yescharacteristic
1033C2#1173109911yescharacteristic
1034C2#1173111111yescharacteristic
1035C2#1173119511yescharacteristic
1036C2#1173121911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC4×C7×#95C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC4×#95D7
hypocenterC7#13823
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic7C2semidirect
6. C2×#89421C2semidirect
8. C4×C7×#95C2semidirect
10. #11729290C2semidirect
11. C4×C7⋊#95C2semidirect
13. #11727161C2semidirect
14. #11727161C2semidirect
15. #11727159C2semidirect
51. #89712C4semidirect
54. #89442C4semidirect
55. #89440C4semidirect
89. C2×C42×C7C2×C4semidirect
113. C2×C4⋊Dic7C2×C4semidirect
119. C2×Dic7⋊C4C2×C4semidirect
134. C2×C4×Dic7C2×C4semidirect
137. C7×#95C2×C4semidirect
147. C7⋊#95C2×C4semidirect
148. C7⋊#95C2×C4semidirect
149. C7⋊#95C2×C4semidirect
165. C4×#95D7semidirect
295. (C2×D7)⋊C4C42semidirect
571. C2×C42C4×D7semidirect
586. #95C4×D7semidirect
956. C7#13823semidirect

Maximal subgroups

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

subgroupindex
C2×#897122
C2×C4×C4⋊Dic72
C2×C4×(C2×D7)⋊C42
C2×#894402
C2×#894422
C2×#894212
C2×#894382
C4×C7×#952
#117292912
#117292902
C4×C7⋊#952
#117271622
#117271612
#117271592
#138237