Finite Group Databasebeta

← #13279165

Subgroups — #13279165

Order 1792.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#89764C211yesmaximal, characteristic
3C2×#89761C211yesmaximal, characteristic
4C2×#89705C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
6#11729323C211yesmaximal, characteristic, complemented
7#11729318C211yesmaximal, characteristic, complemented
8#11729291C211yesmaximal, characteristic
9#11729291C211yesmaximal, characteristic
10#11729290C211yesmaximal, characteristic, complemented
11#11729290C211yesmaximal, characteristic, complemented
12#11727182C211yesmaximal, characteristic
13(C2×D7)⋊#95C211yesmaximal, characteristic
14#11727163C211yesmaximal, characteristic, complemented
15Dic7⋊#95C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C4×C7×C4⋊C4—24no—
34C2×C7×#95C2211yescharacteristic
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
51C2×C7⋊#95C2211yescharacteristic
52#89764C418yescomplemented
53#89761—24no—
54C4×(C2×D7)⋊C4—24no—
55#89705—24no—
56#14178—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7—41no—
78C22×C4×D7—41no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4C2×C414yescomplemented
84C2×C7×C4⋊C4D414yes—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7—22no—
90C2×C42×C7—22no—
91C2×C42×C7—22no—
92C2×C42×C7—41no—
93C2×C42×C7—41no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—22no—
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—41no—
105C2×(C2×D7)⋊C4—41no—
106C2×(C2×D7)⋊C4—41no—
107C2×(C2×D7)⋊C4—41no—
108C2×(C2×D7)⋊C4C2×C414yes—
109C2×(C2×D7)⋊C4C2×C414yes—
110C2×(C2×D7)⋊C4C2×C414yes—
111C2×(C2×D7)⋊C4Q814yes—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—41no—
119C2×Dic7⋊C4—41no—
120C2×Dic7⋊C4—41no—
121C2×Dic7⋊C4—41no—
122C2×Dic7⋊C4C2×C414yescomplemented
123C2×Dic7⋊C4C2×C414yescomplemented
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—41no—
127C7×#95—22no—
128C7×#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95C2×C414yescomplemented
144C7⋊#95D414yes—
145C2×#399—71no—
146C2×#387—71no—
147C2×#385—71no—
148C2×C4×C4⋊C4D711yescharacteristic, complemented
149C2×C4×C22⋊C4—71no—
150#1445—71no—
151#1441—71no—
152#1439—71no—
153#1437—71no—
154#1437—71no—
155#1436—71no—
156#1436—71no—
157#1436—71no—
158C4⋊#95—71no—
159C22⋊#95—71no—
160C24×C7C2411yescharacteristic
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7C22×C412yes—
174C23×D7C2×Q812yes—
175C23×D7#4112yes—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
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—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×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×Q812yes—
220C22×C4×C7#4112yes—
221C22×C4×C7#4112yes—
222C22×C4×C7#4112yes—
223C22×C4×C7#4112yes—
224C22×C4×C7#4112yes—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
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×Dic7C2×D412yes—
271C22×Dic7C2×D412yes—
272C22×Dic7C2×Q812yes—
273C22×Dic7#4112yes—
274C2×C4×D7—28no—
275C2×C4×D7—44no—
276C2×C4×D7—44no—
277C2×C4×D7—44no—
278C2×C4×D7—44no—
279C2×C4×D7—44no—
280C2×C4×D7—44no—
281C7×C4⋊C4—28no—
282C7×C4⋊C4—28no—
283C42×C7—28no—
284C42×C7—44no—
285C42×C7—44no—
286(C2×D7)⋊C4—28no—
287(C2×D7)⋊C4—28no—
288(C2×D7)⋊C4—28no—
289(C2×D7)⋊C4—44no—
290(C2×D7)⋊C4—44no—
291(C2×D7)⋊C4—44no—
292Dic7⋊C4—28no—
293Dic7⋊C4—44no—
294Dic7⋊C4—44no—
295Dic7⋊C4—44no—
296C4×Dic7—44no—
297C24×C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4C2×D711yescharacteristic
303C22×C4⋊C4C2×D711yescharacteristic
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C42—71no—
311C22×C42C2×D711yescharacteristic
312C22×C42C2×D711yescharacteristic
313C22×C42C2×D711yescharacteristic
314#399—78no—
315#387—144no—
316#385—144no—
317C4×C4⋊C4—24no—
318C4×C22⋊C4—144no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95C2×D711yescharacteristic
336C2×#95C2×D711yescharacteristic
337C23×C7C23×C411yescharacteristic
338C23×C7C22×D411yescharacteristic
339C23×C7C22×D411yescharacteristic
340C23×C7C22×Q811yescharacteristic
341C23×C7C2×#4111yescharacteristic
342C23×C7C2×#4111yescharacteristic
343C23×C7C2×#4111yescharacteristic
344C23×C7C2×#4111yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7H(5,𝔽2)11yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C72−1+411yescharacteristic
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
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—41no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7C4×Q814yes—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
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—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7C4×D414yes—
434C2×C4×C7C22⋊Q814yes—
435C2×C4×C7#12314yes—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
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—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
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×Dic7C4×D414yes—
485C4×D7—416no—
486C25—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—142no—
495C23×C4—142no—
496C23×C4—142no—
497C23×C4—142no—
498C23×C4—142no—
499C23×C4—281no—
500C23×C4—281no—
501C23×C4C22×D711yescharacteristic
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—74no—
513C2×C4⋊C4—74no—
514C2×C4⋊C4—142no—
515C2×C4⋊C4—142no—
516C2×C4⋊C4—142no—
517C2×C4⋊C4—142no—
518C2×C4⋊C4—142no—
519C2×C4⋊C4—142no—
520C2×C4⋊C4—281no—
521C2×C4⋊C4—281no—
522C2×C4⋊C4—281no—
523C2×C4⋊C4—281no—
524C2×C4⋊C4C4×D714yescomplemented
525C2×C4⋊C4C22⋊D714yes—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—142no—
531C2×C22⋊C4—142no—
532C2×C22⋊C4—142no—
533C2×C22⋊C4—142no—
534C2×C22⋊C4—142no—
535C2×C22⋊C4—142no—
536C2×C22⋊C4—142no—
537C2×C22⋊C4—142no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—281no—
541C2×C22⋊C4—281no—
542C2×C22⋊C4—281no—
543C2×C22⋊C4—281no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—41no—
552C2×C42—41no—
553C2×C42—142no—
554C2×C42—142no—
555C2×C42—281no—
556#95—22no—
557#95—22no—
558#95—74no—
559#95—74no—
560#95—142no—
561#95—142no—
562#95—142no—
563#95—142no—
564#95—142no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—281no—
570#95—281no—
571#95—281no—
572#95—281no—
573#95—281no—
574C22×C7C2×C4×D411yescharacteristic
575C22×C7C2×C4×D411yescharacteristic
576C22×C7C2×C4×Q811yescharacteristic
577C22×C7C4×#4111yescharacteristic
578C22×C7C4×#4111yescharacteristic
579C22×C7#51811yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7C2×C22⋊Q811yescharacteristic
582C22×C7C2×#12311yescharacteristic
583C22×C7#52511yescharacteristic
584C22×C7#52511yescharacteristic
585C22×C7#52911yescharacteristic
586C22×C7#52911yescharacteristic
587C22×C7#52911yescharacteristic
588C22×C7#53311yescharacteristic
589C22×C7#53811yescharacteristic
590C22×C7#53911yescharacteristic
591C22×C7#54011yescharacteristic
592C22×C7#54211yescharacteristic
593C22×C7D4211yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54611yescharacteristic
596C22×C7#54711yescharacteristic
597C22×C7D4×Q811yescharacteristic
598C22×C7#55011yescharacteristic
599C22×C7#55011yescharacteristic
600C22×C7#55111yescharacteristic
601C22×C7#55111yescharacteristic
602C22×C7#55111yescharacteristic
603C22×C7#55211yescharacteristic
604C22×C7#55211yescharacteristic
605C22×C7#55411yescharacteristic
606C22×C7#55411yescharacteristic
607C22×C7#55411yescharacteristic
608C22×C7#55911yescharacteristic
609C2×D7—24no—
610C2×D7—24no—
611C2×D7—24no—
612C2×D7—42no—
613C2×D7—42no—
614C2×D7—42no—
615C2×D7—42no—
616C2×D7—42no—
617C2×D7—42no—
618C2×D7—42no—
619C2×D7—42no—
620C2×D7—42no—
621C2×D7—42no—
622C2×D7—42no—
623C2×D7—42no—
624C4×C7—24no—
625C4×C7—24no—
626C4×C7—24no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—42no—
631Dic7—24no—
632Dic7—42no—
633Dic7—42no—
634Dic7—42no—
635Dic7—42no—
636Dic7—81no—
637Dic7—81no—
638C24—72no—
639C24—72no—
640C24—72no—
641C24—141no—
642C24—141no—
643C24—141no—
644C24—141no—
645C24—141no—
646C24—141no—
647C24—141no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—141no—
653C24C23×D711yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
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—72no—
691C22×C4—72no—
692C22×C4—72no—
693C22×C4—72no—
694C22×C4—72no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—148no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
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—284no—
741C22×C4—284no—
742C22×C4—284no—
743C22×C4—284no—
744C22×C4—284no—
745C22×C4—284no—
746C22×C4C2×C4×D712yes—
747C22×C4C2×C4×D712yes—
748C22×C4C2×C4×D712yes—
749C22×C4#115712yes—
750C22×C4#115712yes—
751C22×C4#115712yes—
752C22×C4#115712yes—
753C22×C4#115712yes—
754C22×C4D4×D712yes—
755C22×C4Q8×D712yes—
756C22×C4C2×C22⋊D712yes—
757C22×C4C2×C22⋊D712yes—
758C22×C4C2×C22⋊D712yes—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—148no—
762C4⋊C4—284no—
763C4⋊C4—284no—
764C4⋊C4—284no—
765C22⋊C4—148no—
766C22⋊C4—148no—
767C22⋊C4—148no—
768C22⋊C4—284no—
769C22⋊C4—284no—
770C22⋊C4—284no—
771C42—28no—
772C42—44no—
773C42—44no—
774C42—284no—
775C2×C7C4×#12311yescharacteristic
776C2×C7C4×C22⋊Q811yescharacteristic
777C2×C7#233511yescharacteristic
778C2×C7#235911yescharacteristic
779C2×C7#236011yescharacteristic
780C2×C7#236611yescharacteristic
781C2×C7#236811yescharacteristic
782C2×C7#241811yescharacteristic
783C2×C7#242311yescharacteristic
784C2×C7#244911yescharacteristic
785C2×C7#245411yescharacteristic
786C2×C7#247111yescharacteristic
787C2×C7#247911yescharacteristic
788C2×C7#257511yescharacteristic
789C2×C7#258911yescharacteristic
790D7—44no—
791C23—74no—
792C23—142no—
793C23—142no—
794C23—142no—
795C23—142no—
796C23—142no—
797C23—142no—
798C23—142no—
799C23—142no—
800C23—142no—
801C23—142no—
802C23—142no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—281no—
811C23—281no—
812C23—281no—
813C23—281no—
814C23—281no—
815C23—281no—
816C23—281no—
817C23—281no—
818C23—281no—
819C23—281no—
820C23—281no—
821C23—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23C22×C4×D711yescharacteristic
827C23C2×#115711yescharacteristic
828C23C2×#115711yescharacteristic
829C23C2×#115711yescharacteristic
830C23C2×#115711yescharacteristic
831C23C2×#115711yescharacteristic
832C23C2×D4×D711yescharacteristic
833C23#654811yescharacteristic
834C23C2×Q8×D711yescharacteristic
835C23#655111yescharacteristic
836C23D7×#4111yescharacteristic
837C23D7×#4111yescharacteristic
838C23#655311yescharacteristic
839C23#655311yescharacteristic
840C23C22×C22⋊D711yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
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—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—74no—
888C2×C4—142no—
889C2×C4—142no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—142no—
893C2×C4—142no—
894C2×C4—142no—
895C2×C4—142no—
896C2×C4—142no—
897C2×C4—142no—
898C2×C4—142no—
899C2×C4—142no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—142no—
905C2×C4—142no—
906C2×C4—2816no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4—281no—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4—281no—
927C2×C4—281no—
928C2×C4—281no—
929C2×C4—281no—
930C2×C4—281no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4#645914yes—
938C2×C4C4×C22⋊D714yes—
939C2×C4#649214yes—
940C7#1417811yescharacteristic, complemented, Sylow
941C22—144no—
942C22—144no—
943C22—144no—
944C22—282no—
945C22—282no—
946C22—282no—
947C22—282no—
948C22—282no—
949C22—282no—
950C22—282no—
951C22—282no—
952C22—282no—
953C22—282no—
954C22—282no—
955C22—282no—
956C22C4×#115711yescharacteristic
957C22C4×#115711yescharacteristic
958C22#9017011yescharacteristic
959C22#9017011yescharacteristic
960C22#9019811yescharacteristic
961C22C2×#645911yescharacteristic
962C22#9020211yescharacteristic
963C22#9020611yescharacteristic
964C22#9021811yescharacteristic
965C22#9021811yescharacteristic
966C22#9021911yescharacteristic
967C22#9022611yescharacteristic
968C22C4×D4×D711yescharacteristic
969C22#9023611yescharacteristic
970C22#9023811yescharacteristic
971C22#9024111yescharacteristic
972C22#9024411yescharacteristic
973C22#9024711yescharacteristic
974C22#9025011yescharacteristic
975C22#9025111yescharacteristic
976C22C4×Q8×D711yescharacteristic
977C22#9026511yescharacteristic
978C22#9026911yescharacteristic
979C22#9027011yescharacteristic
980C22#9027011yescharacteristic
981C22#9027211yescharacteristic
982C22#9027211yescharacteristic
983C22#9027311yescharacteristic
984C22C2×C4×C22⋊D711yescharacteristic
985C22C2×#649211yescharacteristic
986C22#9048211yescharacteristic
987C22D4×C22⋊D711yescharacteristic
988C22Q8×C22⋊D711yescharacteristic
989C22#9052011yescharacteristic
990C22#9052511yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—144no—
999C4—282no—
1000C4—282no—
1001C4—282no—
1002C4—282no—
1003C4—561no—
1004C4—561no—
1005C2—284no—
1006C2#1173112211yescharacteristic
1007C2#1173112611yescharacteristic
1008C2C4×#645911yescharacteristic
1009C2#1173121011yescharacteristic
1010C2#1173121711yescharacteristic
1011C2#1173122011yescharacteristic
1012C2#1173125411yescharacteristic
1013C2#1173125711yescharacteristic
1014C2C4×#649211yescharacteristic
1015C2#1173961811yescharacteristic
1016C2#1173972411yescharacteristic
1017C2#1173978811yescharacteristic
1018C2#1173984911yescharacteristic
1019C2#1173993511yescharacteristic
1020C2#1173993911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C4×C7×C4⋊C4C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×C4×C4⋊C4D7
hypocenterC7#14178
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×C4⋊C4C2semidirect
4. C2×#89705C2semidirect
6. #11729323C2semidirect
7. #11729318C2semidirect
10. #11729290C2semidirect
11. #11729290C2semidirect
14. #11727163C2semidirect
15. Dic7⋊#95C2semidirect
52. #89764C4semidirect
83. C2×C7×C4⋊C4C2×C4semidirect
122. C2×Dic7⋊C4C2×C4semidirect
123. C2×Dic7⋊C4C2×C4semidirect
143. C7⋊#95C2×C4semidirect
148. C2×C4×C4⋊C4D7semidirect
524. C2×C4⋊C4C4×D7semidirect
940. C7#14178semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×C4⋊C42
C2×#897642
C2×#897612
C2×#897052
C2×C4×(C2×D7)⋊C42
#117293232
#117293182
#117292912
#117292902
#117271822
(C2×D7)⋊#952
#117271632
Dic7⋊#952
#141787