Finite Group Databasebeta

← #13275387

Subgroups — #13275387

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×C4×C7×C22⋊C4C211yesmaximal, characteristic
2C2×#89982C211yesmaximal, characteristic
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic
4C2×#89717C211yesmaximal, characteristic
5C2×#89716C211yesmaximal, characteristic
6C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
7C2×#89421C211yesmaximal, characteristic, complemented
8#11729299C211yesmaximal, characteristic
9#11729299C211yesmaximal, characteristic
10#11729290C211yesmaximal, characteristic, complemented
11#11729290C211yesmaximal, characteristic, complemented
12C4×C7⋊#95C211yesmaximal, characteristic, complemented
13#11727160C211yesmaximal, characteristic, complemented
14#11727159C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C4×C7×C22⋊C4—24no—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38#89982C418yescomplemented
39C4×C22⋊Dic7—24no—
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
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89717C418yescomplemented
55#89716C418yescomplemented
56C4×Dic7⋊C4—24no—
57#89421—24no—
58#13823—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—41no—
65C23×C4×C7—41no—
66C23×C4×C7C2×C414yes—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4C2×C414yes—
86C2×C7×C22⋊C4C2×C414yes—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C42×C7—41no—
92C2×C42×C7—41no—
93C2×C22⋊Dic7—22no—
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—41no—
98C2×C22⋊Dic7—41no—
99C2×C22⋊Dic7C2×C414yes—
100C2×C22⋊Dic7C2×C414yes—
101C2×C22⋊Dic7C2×C414yes—
102C2×C22⋊Dic7C2×C414yes—
103C2×C22⋊Dic7C2×C414yes—
104C2×C22⋊Dic7C2×C414yes—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4C2×C414yes—
114C2×Dic7⋊C4C2×C414yes—
115C2×Dic7⋊C4C2×C414yescomplemented
116C2×Dic7⋊C4C2×C414yescomplemented
117C2×C4×Dic7—22no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
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—41no—
130C2×C4×Dic7—41no—
131C2×C4×Dic7—41no—
132C2×C4×Dic7—41no—
133C2×C4×Dic7C2×C414yescomplemented
134C2×C4×Dic7C2×C414yescomplemented
135C7×#95—22no—
136C7×#95D414yes—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95C2×C414yes—
145C7⋊#95C2×C414yes—
146C7⋊#95C2×C414yescomplemented
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⋊C4D711yescharacteristic
158#1437—71no—
159#1437—71no—
160#1436—71no—
161#1436—71no—
162#1436—71no—
163#1436—71no—
164C4×#95—71no—
165C4×#95—71no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7C22×C412yes—
179C24×C7C22×C412yes—
180C24×C7C22×C412yes—
181C24×C7C2411yescharacteristic
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—28no—
211C22×C4×C7—28no—
212C22×C4×C7—44no—
213C22×C4×C7—44no—
214C22×C4×C7—44no—
215C22×C4×C7—44no—
216C22×C4×C7—44no—
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×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C22×C412yes—
274C22×Dic7C22×C412yes—
275C22×Dic7C22×C412yes—
276C22×Dic7C22×C412yes—
277C22×Dic7C22×C412yes—
278C22×Dic7C22×C412yes—
279C22×Dic7C22×C412yes—
280C22×Dic7C22×C412yes—
281C22×Dic7C22×C412yes—
282C22×Dic7C22×C412yes—
283C22×Dic7C2×D412yes—
284C22×Dic7C2×D412yes—
285C22×Dic7#4112yes—
286C22×Dic7#4112yes—
287C7×C22⋊C4—28no—
288C7×C22⋊C4—28no—
289C42×C7—44no—
290C42×C7—44no—
291C22⋊Dic7—28no—
292C22⋊Dic7—28no—
293C22⋊Dic7—44no—
294C22⋊Dic7C42116yescomplemented
295Dic7⋊C4—28no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4—28no—
299C4×Dic7—28no—
300C4×Dic7—28no—
301C4×Dic7—44no—
302C4×Dic7—44no—
303C4×Dic7—44no—
304C4×Dic7—44no—
305C24×C4C2×D711yescharacteristic
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⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C42—71no—
317C22×C42—71no—
318C22×C42—71no—
319C22×C42—71no—
320C22×C42—71no—
321C22×C42—71no—
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—24no—
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×#95—71no—
344C2×#95—71no—
345C2×#95C2×D711yescharacteristic
346C2×#95C2×D711yescharacteristic
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—41no—
373C23×C7—41no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7—41no—
377C23×C7—41no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7C2×C4214yes—
382C23×C7C23×C411yescharacteristic
383C23×C7C23×C411yescharacteristic
384C23×C7C23×C411yescharacteristic
385C23×C7C22×D411yescharacteristic
386C23×C7C22×D411yescharacteristic
387C23×C7C2×#4111yescharacteristic
388C23×C7C2×#4111yescharacteristic
389C23×C7C2×#4111yescharacteristic
390C23×C7C2×#4111yescharacteristic
391C23×C7C2×#4111yescharacteristic
392C23×C7C2×#4111yescharacteristic
393C23×C7H(5,𝔽2)11yescharacteristic
394C23×C7H(5,𝔽2)11yescharacteristic
395C23×C72−1+411yescharacteristic
396C23×C72−1+411yescharacteristic
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—416no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7C4×D414yes—
437C2×C4×C7C4×D414yes—
438C2×C4×C7C4×D414yes—
439C2×C4×C7C4×D414yes—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
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×Dic7C2×C4214yes—
494C2×Dic7C4×D414yes—
495C2×Dic7C4×D414yes—
496C25C22×D711yescharacteristic
497C23×C4—22no—
498C23×C4—22no—
499C23×C4—22no—
500C23×C4—22no—
501C23×C4—41no—
502C23×C4—41no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—71no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—71no—
509C23×C4—71no—
510C23×C4—71no—
511C23×C4C4×D714yes—
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—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—74no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—74no—
539C2×C22⋊C4—74no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—281no—
545C2×C22⋊C4—281no—
546C2×C22⋊C4C4×D714yes—
547C2×C22⋊C4C4×D714yes—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—41no—
553C2×C42—41no—
554C2×C42—74no—
555C2×C42—74no—
556C2×C42—142no—
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—142no—
568C2×C42—281no—
569C2×C42—281no—
570C2×C42—281no—
571C2×C42—281no—
572#95—22no—
573#95—74no—
574#95—74no—
575#95—74no—
576#95—74no—
577#95—74no—
578#95—74no—
579#95—74no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—142no—
585#95—281no—
586#95—281no—
587#95C22⋊D714yes—
588C22×C7—24no—
589C22×C7—24no—
590C22×C7—24no—
591C22×C7—42no—
592C22×C7—42no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7—42no—
596C22×C7—42no—
597C22×C7—42no—
598C22×C7—42no—
599C22×C7—42no—
600C22×C7—42no—
601C22×C7—42no—
602C22×C7—42no—
603C22×C7C22×C4211yescharacteristic
604C22×C7C2×C4×D411yescharacteristic
605C22×C7C2×C4×D411yescharacteristic
606C22×C7C2×C4×D411yescharacteristic
607C22×C7C2×C4×D411yescharacteristic
608C22×C7C2×C4×D411yescharacteristic
609C22×C7C2×C4×D411yescharacteristic
610C22×C7C4×#4111yescharacteristic
611C22×C7C4×#4111yescharacteristic
612C22×C7C4×#4111yescharacteristic
613C22×C7C4×#4111yescharacteristic
614C22×C7C4×#4111yescharacteristic
615C22×C7C4×#4111yescharacteristic
616C22×C7#51811yescharacteristic
617C22×C7#51911yescharacteristic
618C22×C7#52011yescharacteristic
619C22×C7#52011yescharacteristic
620C22×C7#52011yescharacteristic
621C22×C7#52011yescharacteristic
622C22×C7D4211yescharacteristic
623C22×C7#54611yescharacteristic
624C22×C7#54611yescharacteristic
625C22×C7#54711yescharacteristic
626C22×C7#54711yescharacteristic
627C22×C7#54811yescharacteristic
628C22×C7#54811yescharacteristic
629C22×C7#55111yescharacteristic
630C22×C7#55111yescharacteristic
631C22×C7#55211yescharacteristic
632C22×C7#55211yescharacteristic
633C22×C7#55311yescharacteristic
634C22×C7#55311yescharacteristic
635C22×C7#55611yescharacteristic
636C22×C7#55611yescharacteristic
637C22×C7#55911yescharacteristic
638C4×C7—24no—
639C4×C7—24no—
640C4×C7—24no—
641C4×C7—24no—
642C4×C7—42no—
643C4×C7—42no—
644Dic7—24no—
645Dic7—24no—
646Dic7—24no—
647Dic7—24no—
648Dic7—42no—
649Dic7—42no—
650Dic7—42no—
651Dic7—42no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24C2×C4×D712yes—
665C24C2×C4×D712yes—
666C24C2×C4×D712yes—
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—28no—
697C22×C4—28no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
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—72no—
714C22×C4—72no—
715C22×C4—72no—
716C22×C4—72no—
717C22×C4—72no—
718C22×C4—72no—
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—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
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×C4#115712yes—
766C22×C4#115712yes—
767C22×C4#115712yes—
768C22×C4D4×D712yes—
769C22×C4#115912yes—
770C22×C4C2×C22⋊D712yes—
771C22×C4C2×C22⋊D712yes—
772C22×C4C2×C22⋊D712yes—
773C4⋊C4—148no—
774C4⋊C4—148no—
775C4⋊C4—148no—
776C4⋊C4—148no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—716no—
780C22⋊C4—148no—
781C22⋊C4—148no—
782C22⋊C4—284no—
783C42—44no—
784C42—44no—
785C42—148no—
786C42—148no—
787C42—284no—
788C42—284no—
789C42—284no—
790C42—284no—
791C2×C7—44no—
792C2×C7C42×D411yescharacteristic
793C2×C7C42×D411yescharacteristic
794C2×C7#227411yescharacteristic
795C2×C7#235811yescharacteristic
796C2×C7#235911yescharacteristic
797C2×C7#235911yescharacteristic
798C2×C7#236111yescharacteristic
799C2×C7#236111yescharacteristic
800C2×C7#236211yescharacteristic
801C2×C7#236211yescharacteristic
802C2×C7#236711yescharacteristic
803C2×C7#236711yescharacteristic
804C2×C7#237311yescharacteristic
805C2×C7#237311yescharacteristic
806C2×C7#237411yescharacteristic
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23C42×D714yes—
842C23C22×C4×D711yescharacteristic
843C23C22×C4×D711yescharacteristic
844C23C22×C4×D711yescharacteristic
845C23C2×#115711yescharacteristic
846C23C2×#115711yescharacteristic
847C23C2×#115711yescharacteristic
848C23C2×D4×D711yescharacteristic
849C23C2×#115911yescharacteristic
850C23#654811yescharacteristic
851C23#654811yescharacteristic
852C23D7×#4111yescharacteristic
853C23D7×#4111yescharacteristic
854C23#655411yescharacteristic
855C23#655411yescharacteristic
856C23C22×C22⋊D711yescharacteristic
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—416no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—74no—
897C2×C4—74no—
898C2×C4—74no—
899C2×C4—74no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
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—142no—
935C2×C4—142no—
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×C4—281no—
952C2×C4(C22⋊D7)⋊C414yes—
953C2×C4C4×C22⋊D714yes—
954C2×C4C4×C22⋊D714yes—
955C2×C4C4×C22⋊D714yes—
956C7#1382311yescharacteristic, complemented, Sylow
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×C42×D711yescharacteristic
973C22C4×#115711yescharacteristic
974C22C4×#115711yescharacteristic
975C22C4×#115711yescharacteristic
976C22C2×(C22⋊D7)⋊C411yescharacteristic
977C22#9017711yescharacteristic
978C22#9018111yescharacteristic
979C22#9018611yescharacteristic
980C22#9020711yescharacteristic
981C22#9021311yescharacteristic
982C22#9022011yescharacteristic
983C22#9022411yescharacteristic
984C22C4×#115911yescharacteristic
985C22C4×#115911yescharacteristic
986C22#9023111yescharacteristic
987C22#9023211yescharacteristic
988C22#9023311yescharacteristic
989C22C4×D4×D711yescharacteristic
990C22C4×D4×D711yescharacteristic
991C22#9023711yescharacteristic
992C22#9023711yescharacteristic
993C22#9023711yescharacteristic
994C22#9023711yescharacteristic
995C22#9024211yescharacteristic
996C22#9024311yescharacteristic
997C22#9024711yescharacteristic
998C22#9024911yescharacteristic
999C22#9025011yescharacteristic
1000C22C2×C4×C22⋊D711yescharacteristic
1001C22C2×C4×C22⋊D711yescharacteristic
1002C22C2×C4×C22⋊D711yescharacteristic
1003C22D4×C22⋊D711yescharacteristic
1004C22#9049711yescharacteristic
1005C22#9051511yescharacteristic
1006C22#9052211yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—144no—
1014C4—144no—
1015C4—144no—
1016C4—144no—
1017C4—282no—
1018C4—282no—
1019C4—282no—
1020C4—282no—
1021C2—44no—
1022C2C4×(C22⋊D7)⋊C411yescharacteristic
1023C2#1173088011yescharacteristic
1024C2#1173091311yescharacteristic
1025C2#1173091711yescharacteristic
1026C2#1173092111yescharacteristic
1027C2#1173092211yescharacteristic
1028C2#1173092311yescharacteristic
1029C2#1173102311yescharacteristic
1030C2C42×C22⋊D711yescharacteristic
1031C2#1173954411yescharacteristic
1032C2#1173968811yescharacteristic
1033C2#1173978411yescharacteristic
1034C2#1173978511yescharacteristic
1035C2#1173978911yescharacteristic
1036C2#1173984411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC2×C4×C7×C22⋊C4C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×C4×C22⋊C4D7
hypocenterC7#13823
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C2×C4×Dic7⋊C4C2semidirect
7. C2×#89421C2semidirect
10. #11729290C2semidirect
11. #11729290C2semidirect
12. C4×C7⋊#95C2semidirect
13. #11727160C2semidirect
14. #11727159C2semidirect
15. Dic7×#95C2semidirect
38. #89982C4semidirect
54. #89717C4semidirect
55. #89716C4semidirect
115. C2×Dic7⋊C4C2×C4semidirect
116. C2×Dic7⋊C4C2×C4semidirect
133. C2×C4×Dic7C2×C4semidirect
134. C2×C4×Dic7C2×C4semidirect
146. C7⋊#95C2×C4semidirect
147. C7⋊#95C2×C4semidirect
148. C7⋊#95C2×C4semidirect
149. C7⋊#95C2×C4semidirect
294. C22⋊Dic7C42semidirect
956. C7#13823semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C22⋊C42
C2×#899822
C2×C4×C22⋊Dic72
C2×#897172
C2×#897162
C2×C4×Dic7⋊C42
C2×#894212
#117292992
#117292902
C4×C7⋊#952
#117271602
#117271592
Dic7×#952
#138237