Finite Group Databasebeta

← C7×#14112 #13191328

Subgroups — C7×#14112 #13191328

Order 1792.

1846 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×C7×#389C211yesmaximal, characteristic, complemented
2C2×C7×#388C211yesmaximal, characteristic
3C2×C7×#388C211yesmaximal, characteristic
4C2×C7×#385C211yesmaximal, characteristic
5C2×C7×#385C211yesmaximal, characteristic
6C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
7C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
8C7×#1444C211yesmaximal, characteristic, complemented
9C7×#1441C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic
11C7×#1439C211yesmaximal, characteristic
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C4⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C42×C7C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C22×C42×C7C2211yescharacteristic
34C22×C42×C7C2211yescharacteristic
35C7×#389—24no—
36C7×#388—24no—
37C7×#388C418yescomplemented
38C7×#385—24no—
39C7×#385—24no—
40C4×C7×C4⋊C4—24no—
41C4×C7×C22⋊C4—24no—
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
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57C2×C7×#95C2211yescharacteristic
58#14112C711yesmaximal, characteristic, direct product factor, Sylow
59C25×C7C2311yescharacteristic
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—22no—
65C23×C4×C7—41no—
66C23×C4×C7—41no—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—41no—
100C2×C7×C4⋊C4—41no—
101C2×C7×C4⋊C4—41no—
102C2×C7×C4⋊C4—41no—
103C2×C7×C4⋊C4C2×C414yescomplemented
104C2×C7×C4⋊C4D414yes—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
107C2×C7×C22⋊C4—22no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—22no—
111C2×C7×C22⋊C4—22no—
112C2×C7×C22⋊C4—22no—
113C2×C7×C22⋊C4—22no—
114C2×C7×C22⋊C4—22no—
115C2×C7×C22⋊C4—22no—
116C2×C7×C22⋊C4—41no—
117C2×C7×C22⋊C4—41no—
118C2×C7×C22⋊C4C2×C414yes—
119C2×C7×C22⋊C4C2×C414yes—
120C2×C7×C22⋊C4C2×C414yes—
121C2×C7×C22⋊C4D414yes—
122C2×C7×C22⋊C4Q814yes—
123C2×C42×C7—22no—
124C2×C42×C7—22no—
125C2×C42×C7—22no—
126C2×C42×C7—22no—
127C2×C42×C7—22no—
128C2×C42×C7—22no—
129C2×C42×C7—22no—
130C2×C42×C7—22no—
131C2×C42×C7—41no—
132C2×C42×C7—41no—
133C2×C42×C7—41no—
134C2×C42×C7C2×C414yescomplemented
135C7×#95—22no—
136C7×#95—22no—
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—22no—
140C7×#95—22no—
141C7×#95—22no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—22no—
146C7×#95—22no—
147C7×#95—41no—
148C7×#95C2×C414yescomplemented
149C7×#95C2×C414yescomplemented
150C7×#95D414yes—
151C2×#389C2×C711yescharacteristic, complemented
152C2×#388C2×C711yescharacteristic
153C2×#388C2×C711yescharacteristic
154C2×#385C2×C711yescharacteristic
155C2×#385C2×C711yescharacteristic
156C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
157C2×C4×C22⋊C4C2×C711yescharacteristic
158#1444C2×C711yescharacteristic, complemented
159#1441C2×C711yescharacteristic, complemented
160#1439C2×C711yescharacteristic
161#1439C2×C711yescharacteristic
162#1436C2×C711yescharacteristic, complemented
163#1436C2×C711yescharacteristic, complemented
164#1436C2×C711yescharacteristic, complemented
165C4⋊#95C2×C711yescharacteristic, complemented
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×C7C2×D412yes—
180C24×C7C2×Q812yes—
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—28no—
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×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—21no—
253C22×C4×C7—21no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—44no—
260C22×C4×C7—44no—
261C22×C4×C7—44no—
262C22×C4×C7—44no—
263C22×C4×C7—44no—
264C22×C4×C7—44no—
265C22×C4×C7C22×C412yes—
266C22×C4×C7C22×C412yes—
267C22×C4×C7C22×C412yes—
268C22×C4×C7C22×C412yes—
269C22×C4×C7C22×C412yes—
270C22×C4×C7C22×C412yes—
271C22×C4×C7C2×D412yes—
272C22×C4×C7C2×D412yes—
273C22×C4×C7C2×D412yes—
274C22×C4×C7C2×D412yes—
275C22×C4×C7C2×D412yes—
276C22×C4×C7C2×D412yes—
277C22×C4×C7C2×D412yes—
278C22×C4×C7C2×D412yes—
279C22×C4×C7C2×Q812yes—
280C22×C4×C7C2×Q812yes—
281C22×C4×C7#4112yes—
282C22×C4×C7#4112yes—
283C22×C4×C7#4112yes—
284C22×C4×C7#4112yes—
285C22×C4×C7#4112yes—
286C22×C4×C7#4112yes—
287C7×C4⋊C4—28no—
288C7×C4⋊C4—28no—
289C7×C4⋊C4—28no—
290C7×C4⋊C4—44no—
291C7×C4⋊C4—44no—
292C7×C4⋊C4—44no—
293C7×C4⋊C4—44no—
294C7×C4⋊C4—44no—
295C7×C22⋊C4—28no—
296C7×C22⋊C4—28no—
297C7×C22⋊C4—28no—
298C7×C22⋊C4—44no—
299C7×C22⋊C4—44no—
300C7×C22⋊C4C4⋊C4116yescomplemented
301C42×C7—28no—
302C42×C7—44no—
303C42×C7—44no—
304C42×C7—44no—
305C24×C4C22×C711yescharacteristic
306C22×C4⋊C4C22×C711yescharacteristic
307C22×C4⋊C4C22×C711yescharacteristic
308C22×C4⋊C4C22×C711yescharacteristic
309C22×C4⋊C4C22×C711yescharacteristic
310C22×C4⋊C4C22×C711yescharacteristic
311C22×C4⋊C4C22×C711yescharacteristic
312C22×C4⋊C4C22×C711yescharacteristic
313C22×C4⋊C4C22×C711yescharacteristic
314C22×C22⋊C4C22×C711yescharacteristic
315C22×C22⋊C4C22×C711yescharacteristic
316C22×C22⋊C4C22×C711yescharacteristic
317C22×C22⋊C4C22×C711yescharacteristic
318C22×C22⋊C4C22×C711yescharacteristic
319C22×C22⋊C4C22×C711yescharacteristic
320C22×C42C22×C711yescharacteristic
321C22×C42C22×C711yescharacteristic
322C22×C42C22×C711yescharacteristic
323C22×C42C22×C711yescharacteristic
324#389—24no—
325#388—24no—
326#388C4×C718yescomplemented
327#385—24no—
328#385—24no—
329C4×C4⋊C4—24no—
330C4×C22⋊C4—24no—
331C2×#95C22×C711yescharacteristic
332C2×#95C22×C711yescharacteristic
333C2×#95C22×C711yescharacteristic
334C2×#95C22×C711yescharacteristic
335C2×#95C22×C711yescharacteristic
336C2×#95C22×C711yescharacteristic
337C2×#95C22×C711yescharacteristic
338C2×#95C22×C711yescharacteristic
339C2×#95C22×C711yescharacteristic
340C2×#95C22×C711yescharacteristic
341C2×#95C22×C711yescharacteristic
342C2×#95C22×C711yescharacteristic
343C2×#95C22×C711yescharacteristic
344C2×#95C22×C711yescharacteristic
345C2×#95C22×C711yescharacteristic
346C2×#95C22×C711yescharacteristic
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×C4⋊C414yes—
382C23×C7C23×C411yescharacteristic
383C23×C7C22×D411yescharacteristic
384C23×C7C22×D411yescharacteristic
385C23×C7C22×D411yescharacteristic
386C23×C7C22×Q811yescharacteristic
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—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—416no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—41no—
469C2×C4×C7—41no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—41no—
489C2×C4×C7—41no—
490C2×C4×C7—41no—
491C2×C4×C7C2×C4⋊C414yes—
492C2×C4×C7C2×C4⋊C414yes—
493C2×C4×C7C4×D414yes—
494C2×C4×C7C4×D414yes—
495C2×C4×C7#12114yes—
496C25C23×C711yescharacteristic
497C23×C4—22no—
498C23×C4—22no—
499C23×C4—22no—
500C23×C4—22no—
501C23×C4—22no—
502C23×C4—41no—
503C23×C4—41no—
504C23×C4C23×C711yescharacteristic
505C23×C4C23×C711yescharacteristic
506C23×C4C23×C711yescharacteristic
507C23×C4C23×C711yescharacteristic
508C23×C4C23×C711yescharacteristic
509C23×C4C23×C711yescharacteristic
510C23×C4C23×C711yescharacteristic
511C23×C4C23×C711yescharacteristic
512C23×C4C23×C711yescharacteristic
513C23×C4C23×C711yescharacteristic
514C23×C4C23×C711yescharacteristic
515C23×C4C23×C711yescharacteristic
516C23×C4C23×C711yescharacteristic
517C23×C4C23×C711yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4C2×C4×C714yescomplemented
541C2×C4⋊C4C7×D414yes—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4C2×C4×C714yes—
556C2×C22⋊C4C2×C4×C714yes—
557C2×C22⋊C4C2×C4×C714yes—
558C2×C22⋊C4C7×D414yes—
559C2×C22⋊C4C7×Q814yes—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—41no—
569C2×C42—41no—
570C2×C42—41no—
571C2×C42C2×C4×C714yescomplemented
572#95—22no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—41no—
585#95C2×C4×C714yescomplemented
586#95C2×C4×C714yescomplemented
587#95C7×D414yes—
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×C4⋊C411yescharacteristic
604C22×C7C2×C4×D411yescharacteristic
605C22×C7C2×C4×D411yescharacteristic
606C22×C7C4×#4111yescharacteristic
607C22×C7C4×#4111yescharacteristic
608C22×C7#52011yescharacteristic
609C22×C7#52011yescharacteristic
610C22×C7C2×#12111yescharacteristic
611C22×C7#52511yescharacteristic
612C22×C7#52511yescharacteristic
613C22×C7#52511yescharacteristic
614C22×C7#52911yescharacteristic
615C22×C7#53211yescharacteristic
616C22×C7#53311yescharacteristic
617C22×C7#53311yescharacteristic
618C22×C7#53811yescharacteristic
619C22×C7#53911yescharacteristic
620C22×C7#54111yescharacteristic
621C22×C7#54211yescharacteristic
622C22×C7D4211yescharacteristic
623C22×C7D4211yescharacteristic
624C22×C7#54611yescharacteristic
625C22×C7#54611yescharacteristic
626C22×C7#54711yescharacteristic
627C22×C7#54711yescharacteristic
628C22×C7#54711yescharacteristic
629C22×C7#54811yescharacteristic
630C22×C7D4×Q811yescharacteristic
631C22×C7D4×Q811yescharacteristic
632C22×C7#55111yescharacteristic
633C22×C7#55211yescharacteristic
634C22×C7#55411yescharacteristic
635C22×C7#55411yescharacteristic
636C22×C7#55611yescharacteristic
637C22×C7#55911yescharacteristic
638C4×C7—24no—
639C4×C7—24no—
640C4×C7—24no—
641C4×C7—24no—
642C4×C7—24no—
643C4×C7—42no—
644C4×C7—42no—
645C4×C7—42no—
646C4×C7—42no—
647C4×C7—42no—
648C4×C7—42no—
649C4×C7—42no—
650C4×C7—81no—
651C4×C7—81no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24C22×C4×C712yes—
665C24C2×C7×D412yes—
666C24C2×C7×Q812yes—
667C24C24×C711yescharacteristic
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—28no—
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—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4C22×C4×C712yes—
752C22×C4C22×C4×C712yes—
753C22×C4C22×C4×C712yes—
754C22×C4C22×C4×C712yes—
755C22×C4C22×C4×C712yes—
756C22×C4C22×C4×C712yes—
757C22×C4C2×C7×D412yes—
758C22×C4C2×C7×D412yes—
759C22×C4C2×C7×D412yes—
760C22×C4C2×C7×D412yes—
761C22×C4C2×C7×D412yes—
762C22×C4C2×C7×D412yes—
763C22×C4C2×C7×D412yes—
764C22×C4C2×C7×D412yes—
765C22×C4C2×C7×Q812yes—
766C22×C4C2×C7×Q812yes—
767C22×C4C7×#4112yes—
768C22×C4C7×#4112yes—
769C22×C4C7×#4112yes—
770C22×C4C7×#4112yes—
771C22×C4C7×#4112yes—
772C22×C4C7×#4112yes—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—28no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4C7×C4⋊C4116yescomplemented
787C42—28no—
788C42—44no—
789C42—44no—
790C42—44no—
791C2×C7—44no—
792C2×C7#229611yescharacteristic
793C2×C7C4×#12111yescharacteristic
794C2×C7#233411yescharacteristic
795C2×C7D4×C4⋊C411yescharacteristic
796C2×C7D4×C4⋊C411yescharacteristic
797C2×C7#235911yescharacteristic
798C2×C7#236711yescharacteristic
799C2×C7#242411yescharacteristic
800C2×C7#242911yescharacteristic
801C2×C7#245511yescharacteristic
802C2×C7#246111yescharacteristic
803C2×C7#246511yescharacteristic
804C2×C7#247811yescharacteristic
805C2×C7#255611yescharacteristic
806C2×C7#258911yescharacteristic
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—
841C23C2×C7×C4⋊C414yes—
842C23C23×C4×C711yescharacteristic
843C23C22×C7×D411yescharacteristic
844C23C22×C7×D411yescharacteristic
845C23C22×C7×D411yescharacteristic
846C23C22×C7×Q811yescharacteristic
847C23C2×C7×#4111yescharacteristic
848C23C2×C7×#4111yescharacteristic
849C23C2×C7×#4111yescharacteristic
850C23C2×C7×#4111yescharacteristic
851C23C2×C7×#4111yescharacteristic
852C23C2×C7×#4111yescharacteristic
853C23C7×H(5,𝔽2)11yescharacteristic
854C23C7×H(5,𝔽2)11yescharacteristic
855C23C7×2−1+411yescharacteristic
856C23C7×2−1+411yescharacteristic
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—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—416no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4C2×C7×C4⋊C414yes—
952C2×C4C2×C7×C4⋊C414yes—
953C2×C4C4×C7×D414yes—
954C2×C4C4×C7×D414yes—
955C2×C4C7×#12114yes—
956C7#1411211yescharacteristic, direct product factor, 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—
972C22C22×C7×C4⋊C411yescharacteristic
973C22C2×C4×C7×D411yescharacteristic
974C22C2×C4×C7×D411yescharacteristic
975C22C4×C7×#4111yescharacteristic
976C22C4×C7×#4111yescharacteristic
977C22C7×#52011yescharacteristic
978C22C7×#52011yescharacteristic
979C22C2×C7×#12111yescharacteristic
980C22C7×#52511yescharacteristic
981C22C7×#52511yescharacteristic
982C22C7×#52511yescharacteristic
983C22C7×#52911yescharacteristic
984C22C7×#53211yescharacteristic
985C22C7×#53311yescharacteristic
986C22C7×#53311yescharacteristic
987C22C7×#53811yescharacteristic
988C22C7×#53911yescharacteristic
989C22C7×#54111yescharacteristic
990C22C7×#54211yescharacteristic
991C22C7×D4211yescharacteristic
992C22C7×D4211yescharacteristic
993C22C7×#54611yescharacteristic
994C22C7×#54611yescharacteristic
995C22C7×#54711yescharacteristic
996C22C7×#54711yescharacteristic
997C22C7×#54711yescharacteristic
998C22C7×#54811yescharacteristic
999C22C7×D4×Q811yescharacteristic
1000C22C7×D4×Q811yescharacteristic
1001C22C7×#55111yescharacteristic
1002C22C7×#55211yescharacteristic
1003C22C7×#55411yescharacteristic
1004C22C7×#55411yescharacteristic
1005C22C7×#55611yescharacteristic
1006C22C7×#55911yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C7×#229611yescharacteristic
1023C2C4×C7×#12111yescharacteristic
1024C2C7×#233411yescharacteristic
1025C2C7×D4×C4⋊C411yescharacteristic
1026C2C7×D4×C4⋊C411yescharacteristic
1027C2C7×#235911yescharacteristic
1028C2C7×#236711yescharacteristic
1029C2C7×#242411yescharacteristic
1030C2C7×#242911yescharacteristic
1031C2C7×#245511yescharacteristic
1032C2C7×#246111yescharacteristic
1033C2C7×#246511yescharacteristic
1034C2C7×#247811yescharacteristic
1035C2C7×#255611yescharacteristic
1036C2C7×#258911yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#389C2semidirect
6. C2×C4×C7×C4⋊C4C2semidirect
8. C7×#1444C2semidirect
9. C7×#1441C2semidirect
12. C7×#1436C2semidirect
13. C7×#1436C2semidirect
14. C7×#1436C2semidirect
15. C7×C4⋊#95C2semidirect
37. C7×#388C4semidirect
58. #14112C7direct (N × H)
103. C2×C7×C4⋊C4C2×C4semidirect
134. C2×C42×C7C2×C4semidirect
148. C7×#95C2×C4semidirect
149. C7×#95C2×C4semidirect
151. C2×#389C2×C7semidirect
156. C2×C4×C4⋊C4C2×C7semidirect
158. #1444C2×C7semidirect
159. #1441C2×C7semidirect
162. #1436C2×C7semidirect
163. #1436C2×C7semidirect
164. #1436C2×C7semidirect
165. C4⋊#95C2×C7semidirect
300. C7×C22⋊C4C4⋊C4semidirect
326. #388C4×C7semidirect
540. C2×C4⋊C4C2×C4×C7semidirect
571. C2×C42C2×C4×C7semidirect
585. #95C2×C4×C7semidirect
586. #95C2×C4×C7semidirect
786. C22⋊C4C7×C4⋊C4semidirect
956. C7#14112direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×C7×#3882
C2×C7×#3852
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14442
C7×#14412
C7×#14392
C7×#14362
C7×C4⋊#952
#141127