Finite Group Databasebeta

← C7×#14407 #13191623

Subgroups — C7×#14407 #13191623

Order 1792.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#390C211yesmaximal, characteristic
2C2×C7×#386C211yesmaximal, characteristic
3C2×C7×#386C211yesmaximal, characteristic
4C2×C7×#385C211yesmaximal, characteristic, complemented
5C2×C7×#380C211yesmaximal, characteristic, complemented
6C7×#1444C211yesmaximal, characteristic, complemented
7C7×#1442C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×#1439C211yesmaximal, characteristic, complemented
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×C22⋊#95C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊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×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2211yescharacteristic
33C22×C7×C22⋊C4C2211yescharacteristic
34C22×C42×C7C2211yescharacteristic
35C7×#390—24no—
36C7×#386—24no—
37C7×#386C418yescomplemented
38C7×#385—24no—
39C7×#380—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
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56#14407C711yesmaximal, characteristic, direct product factor, Sylow
57C25×C7C2311yescharacteristic
58C25×C7C2311yescharacteristic
59C22×C7×D4—41no—
60C22×C7×D4—41no—
61C22×C7×D4—41no—
62C22×C7×D4—41no—
63C22×C7×D4C2×C414yes—
64C22×C7×D4D414yes—
65C22×C7×D4Q814yes—
66C23×C4×C7—22no—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—22no—
71C23×C4×C7—41no—
72C23×C4×C7—41no—
73C23×C4×C7—41no—
74C23×C4×C7—41no—
75C23×C4×C7—41no—
76C23×C4×C7—41no—
77C23×C4×C7—41no—
78C23×C4×C7—41no—
79C23×C4×C7C2×C414yescomplemented
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C23×C4×C7C2311yescharacteristic
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—41no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4—41no—
100C2×C7×C4⋊C4—41no—
101C2×C7×C4⋊C4—41no—
102C2×C7×C4⋊C4—41no—
103C2×C7×C4⋊C4—41no—
104C2×C7×C4⋊C4—41no—
105C2×C7×C4⋊C4—41no—
106C2×C7×C4⋊C4—41no—
107C2×C7×C4⋊C4D414yescomplemented
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—22no—
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—22no—
121C2×C7×C22⋊C4—22no—
122C2×C7×C22⋊C4—22no—
123C2×C7×C22⋊C4—41no—
124C2×C7×C22⋊C4—41no—
125C2×C7×C22⋊C4—41no—
126C2×C7×C22⋊C4—41no—
127C2×C7×C22⋊C4—41no—
128C2×C7×C22⋊C4—41no—
129C2×C7×C22⋊C4—41no—
130C2×C7×C22⋊C4—41no—
131C2×C7×C22⋊C4—41no—
132C2×C7×C22⋊C4—41no—
133C2×C7×C22⋊C4—41no—
134C2×C7×C22⋊C4—41no—
135C2×C7×C22⋊C4C2×C414yes—
136C2×C7×C22⋊C4C2×C414yes—
137C2×C7×C22⋊C4C2×C414yescomplemented
138C2×C42×C7—22no—
139C2×C42×C7—41no—
140C2×C42×C7—41no—
141C7×#95—22no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—22no—
146C7×#95—22no—
147C7×#95—22no—
148C7×#95—22no—
149C7×#95—41no—
150C7×#95—41no—
151C7×#95—41no—
152C7×#95—41no—
153C7×#95—41no—
154C7×#95—41no—
155C7×#95C2×C414yescomplemented
156C7×#95C2×C414yescomplemented
157C2×#390C2×C711yescharacteristic
158C2×#386C2×C711yescharacteristic
159C2×#386C2×C711yescharacteristic
160C2×#385C2×C711yescharacteristic, complemented
161C2×#380C2×C711yescharacteristic, complemented
162#1444C2×C711yescharacteristic, complemented
163#1442C2×C711yescharacteristic, complemented
164#1439C2×C711yescharacteristic, complemented
165#1439C2×C711yescharacteristic, complemented
166#1439C2×C711yescharacteristic, complemented
167#1439C2×C711yescharacteristic, complemented
168#1436C2×C711yescharacteristic, complemented
169#1436C2×C711yescharacteristic, complemented
170C22⋊#95C2×C711yescharacteristic, complemented
171C22⋊#95C2×C711yescharacteristic, complemented
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—21no—
179C24×C7—21no—
180C24×C7—21no—
181C24×C7—21no—
182C24×C7—21no—
183C24×C7—21no—
184C24×C7—21no—
185C24×C7—21no—
186C24×C7—21no—
187C24×C7—21no—
188C24×C7—21no—
189C24×C7—21no—
190C24×C7—21no—
191C24×C7—21no—
192C24×C7—21no—
193C24×C7—21no—
194C24×C7—21no—
195C24×C7—21no—
196C24×C7C22×C412yes—
197C24×C7C22×C412yes—
198C24×C7C2×D412yes—
199C24×C7C2×D412yes—
200C24×C7C2×Q812yes—
201C24×C7C2×Q812yes—
202C24×C7C2411yescharacteristic
203C2×C7×D4—44no—
204C2×C7×D4—44no—
205C2×C7×D4—44no—
206C2×C7×D4—44no—
207C2×C7×D4—44no—
208C2×C7×D4—44no—
209C2×C7×D4C4⋊C4116yescomplemented
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—21no—
260C22×C4×C7—28no—
261C22×C4×C7—21no—
262C22×C4×C7—21no—
263C22×C4×C7—21no—
264C22×C4×C7—21no—
265C22×C4×C7—21no—
266C22×C4×C7—21no—
267C22×C4×C7—21no—
268C22×C4×C7—21no—
269C22×C4×C7—21no—
270C22×C4×C7—21no—
271C22×C4×C7—21no—
272C22×C4×C7—21no—
273C22×C4×C7—21no—
274C22×C4×C7—21no—
275C22×C4×C7—21no—
276C22×C4×C7—21no—
277C22×C4×C7—21no—
278C22×C4×C7—21no—
279C22×C4×C7—21no—
280C22×C4×C7—21no—
281C22×C4×C7—21no—
282C22×C4×C7—21no—
283C22×C4×C7—21no—
284C22×C4×C7—21no—
285C22×C4×C7—21no—
286C22×C4×C7—21no—
287C22×C4×C7—21no—
288C22×C4×C7—21no—
289C22×C4×C7—44no—
290C22×C4×C7—44no—
291C22×C4×C7—44no—
292C22×C4×C7—44no—
293C22×C4×C7—44no—
294C22×C4×C7—44no—
295C22×C4×C7—44no—
296C22×C4×C7—44no—
297C22×C4×C7—44no—
298C22×C4×C7—44no—
299C22×C4×C7—44no—
300C22×C4×C7—44no—
301C22×C4×C7—44no—
302C22×C4×C7C22×C412yes—
303C22×C4×C7C22×C412yes—
304C22×C4×C7C22×C412yes—
305C22×C4×C7C22×C412yes—
306C22×C4×C7C22×C412yes—
307C22×C4×C7C2×D412yes—
308C22×C4×C7C2×D412yes—
309C22×C4×C7C2×D412yes—
310C22×C4×C7C2×D412yes—
311C22×C4×C7C2×Q812yes—
312C22×C4×C7#4112yes—
313C22×C4×C7#4112yes—
314C22×C4×C7#4112yes—
315C7×C4⋊C4—44no—
316C7×C4⋊C4—44no—
317C7×C4⋊C4—44no—
318C7×C4⋊C4—44no—
319C7×C4⋊C4—44no—
320C7×C22⋊C4—28no—
321C7×C22⋊C4—44no—
322C7×C22⋊C4—44no—
323C7×C22⋊C4—44no—
324C7×C22⋊C4—44no—
325C7×C22⋊C4—44no—
326C7×C22⋊C4—44no—
327C7×C22⋊C4—44no—
328C7×C22⋊C4—44no—
329C7×C22⋊C4—44no—
330C42×C7—44no—
331C23×D4C22×C711yescharacteristic
332C24×C4C22×C711yescharacteristic
333C24×C4C22×C711yescharacteristic
334C22×C4⋊C4C22×C711yescharacteristic
335C22×C4⋊C4C22×C711yescharacteristic
336C22×C4⋊C4C22×C711yescharacteristic
337C22×C4⋊C4C22×C711yescharacteristic
338C22×C4⋊C4C22×C711yescharacteristic
339C22×C22⋊C4C22×C711yescharacteristic
340C22×C22⋊C4C22×C711yescharacteristic
341C22×C22⋊C4C22×C711yescharacteristic
342C22×C22⋊C4C22×C711yescharacteristic
343C22×C22⋊C4C22×C711yescharacteristic
344C22×C22⋊C4C22×C711yescharacteristic
345C22×C22⋊C4C22×C711yescharacteristic
346C22×C22⋊C4C22×C711yescharacteristic
347C22×C22⋊C4C22×C711yescharacteristic
348C22×C22⋊C4C22×C711yescharacteristic
349C22×C42C22×C711yescharacteristic
350#390—24no—
351#386—24no—
352#386C4×C718yescomplemented
353#385—24no—
354#380—24no—
355C2×#95C22×C711yescharacteristic
356C2×#95C22×C711yescharacteristic
357C2×#95C22×C711yescharacteristic
358C2×#95C22×C711yescharacteristic
359C2×#95C22×C711yescharacteristic
360C2×#95C22×C711yescharacteristic
361C2×#95C22×C711yescharacteristic
362C2×#95C22×C711yescharacteristic
363C2×#95C22×C711yescharacteristic
364C2×#95C22×C711yescharacteristic
365C2×#95C22×C711yescharacteristic
366C2×#95C22×C711yescharacteristic
367C2×#95C22×C711yescharacteristic
368C2×#95C22×C711yescharacteristic
369C2×#95C22×C711yescharacteristic
370C2×#95C22×C711yescharacteristic
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
384C23×C7—22no—
385C23×C7—22no—
386C23×C7—22no—
387C23×C7—22no—
388C23×C7—22no—
389C23×C7—22no—
390C23×C7—22no—
391C23×C7—22no—
392C23×C7—22no—
393C23×C7—22no—
394C23×C7—22no—
395C23×C7—22no—
396C23×C7—22no—
397C23×C7—22no—
398C23×C7—22no—
399C23×C7—22no—
400C23×C7—22no—
401C23×C7—22no—
402C23×C7—22no—
403C23×C7—22no—
404C23×C7—22no—
405C23×C7—22no—
406C23×C7—22no—
407C23×C7—41no—
408C23×C7—41no—
409C23×C7—41no—
410C23×C7—41no—
411C23×C7—41no—
412C23×C7—41no—
413C23×C7—41no—
414C23×C7—41no—
415C23×C7—41no—
416C23×C7—41no—
417C23×C7—41no—
418C23×C7—41no—
419C23×C7—41no—
420C23×C7—41no—
421C23×C7—41no—
422C23×C7—41no—
423C23×C7—41no—
424C23×C7—41no—
425C23×C7—41no—
426C23×C7—41no—
427C23×C7—41no—
428C23×C7—41no—
429C23×C7—41no—
430C23×C7—41no—
431C23×C7—41no—
432C23×C7—41no—
433C23×C7—41no—
434C23×C7—41no—
435C23×C7—41no—
436C23×C7—41no—
437C23×C7—41no—
438C23×C7—41no—
439C23×C7C2×C4⋊C414yes—
440C23×C7C2×C4⋊C414yes—
441C23×C7C23×C411yescharacteristic
442C23×C7C22×D411yescharacteristic
443C23×C7C22×D411yescharacteristic
444C23×C7C22×Q811yescharacteristic
445C23×C7C2×#4111yescharacteristic
446C23×C7C2×#4111yescharacteristic
447C23×C7C2×#4111yescharacteristic
448C23×C7H(5,𝔽2)11yescharacteristic
449C23×C7H(5,𝔽2)11yescharacteristic
450C23×C7H(5,𝔽2)11yescharacteristic
451C23×C7H(5,𝔽2)11yescharacteristic
452C23×C7H(5,𝔽2)11yescharacteristic
453C23×C7H(5,𝔽2)11yescharacteristic
454C23×C7H(5,𝔽2)11yescharacteristic
455C23×C72−1+411yescharacteristic
456C7×D4—416no—
457C2×C4×C7—22no—
458C2×C4×C7—22no—
459C2×C4×C7—22no—
460C2×C4×C7—22no—
461C2×C4×C7—22no—
462C2×C4×C7—22no—
463C2×C4×C7—22no—
464C2×C4×C7—22no—
465C2×C4×C7—22no—
466C2×C4×C7—22no—
467C2×C4×C7—22no—
468C2×C4×C7—22no—
469C2×C4×C7—22no—
470C2×C4×C7—22no—
471C2×C4×C7—22no—
472C2×C4×C7—22no—
473C2×C4×C7—22no—
474C2×C4×C7—22no—
475C2×C4×C7—22no—
476C2×C4×C7—22no—
477C2×C4×C7—22no—
478C2×C4×C7—22no—
479C2×C4×C7—22no—
480C2×C4×C7—22no—
481C2×C4×C7—22no—
482C2×C4×C7—22no—
483C2×C4×C7—22no—
484C2×C4×C7—22no—
485C2×C4×C7—22no—
486C2×C4×C7—22no—
487C2×C4×C7—22no—
488C2×C4×C7—22no—
489C2×C4×C7—22no—
490C2×C4×C7—416no—
491C2×C4×C7—416no—
492C2×C4×C7—41no—
493C2×C4×C7—41no—
494C2×C4×C7—41no—
495C2×C4×C7—41no—
496C2×C4×C7—41no—
497C2×C4×C7—41no—
498C2×C4×C7—41no—
499C2×C4×C7—41no—
500C2×C4×C7—41no—
501C2×C4×C7—41no—
502C2×C4×C7—41no—
503C2×C4×C7—41no—
504C2×C4×C7—41no—
505C2×C4×C7—41no—
506C2×C4×C7—41no—
507C2×C4×C7—41no—
508C2×C4×C7—41no—
509C2×C4×C7—41no—
510C2×C4×C7—41no—
511C2×C4×C7—41no—
512C2×C4×C7—41no—
513C2×C4×C7—41no—
514C2×C4×C7—41no—
515C2×C4×C7—41no—
516C2×C4×C7—41no—
517C2×C4×C7—41no—
518C2×C4×C7—41no—
519C2×C4×C7—41no—
520C2×C4×C7—41no—
521C2×C4×C7—41no—
522C2×C4×C7—41no—
523C2×C4×C7—41no—
524C2×C4×C7—41no—
525C2×C4×C7—41no—
526C2×C4×C7—41no—
527C2×C4×C7—41no—
528C2×C4×C7—41no—
529C2×C4×C7—41no—
530C2×C4×C7—41no—
531C2×C4×C7—41no—
532C2×C4×C7—41no—
533C2×C4×C7—41no—
534C2×C4×C7—41no—
535C2×C4×C7—41no—
536C2×C4×C7—41no—
537C2×C4×C7—41no—
538C2×C4×C7—41no—
539C2×C4×C7—41no—
540C2×C4×C7—41no—
541C2×C4×C7—41no—
542C2×C4×C7—41no—
543C2×C4×C7—41no—
544C2×C4×C7—41no—
545C2×C4×C7—41no—
546C2×C4×C7—41no—
547C2×C4×C7—41no—
548C2×C4×C7C2×C4⋊C414yes—
549C2×C4×C7C4×D414yes—
550C25C23×C711yescharacteristic
551C25C23×C711yescharacteristic
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—41no—
555C22×D4—41no—
556C22×D4C2×C4×C714yes—
557C22×D4C7×D414yes—
558C22×D4C7×Q814yes—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—41no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4—41no—
568C23×C4—41no—
569C23×C4—41no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4C2×C4×C714yescomplemented
573C23×C4C23×C711yescharacteristic
574C23×C4C23×C711yescharacteristic
575C23×C4C23×C711yescharacteristic
576C23×C4C23×C711yescharacteristic
577C23×C4C23×C711yescharacteristic
578C23×C4C23×C711yescharacteristic
579C23×C4C23×C711yescharacteristic
580C23×C4C23×C711yescharacteristic
581C23×C4C23×C711yescharacteristic
582C23×C4C23×C711yescharacteristic
583C23×C4C23×C711yescharacteristic
584C23×C4C23×C711yescharacteristic
585C23×C4C23×C711yescharacteristic
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4C7×D414yescomplemented
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4—41no—
628C2×C22⋊C4C2×C4×C714yes—
629C2×C22⋊C4C2×C4×C714yes—
630C2×C22⋊C4C2×C4×C714yescomplemented
631C2×C42—22no—
632C2×C42—41no—
633C2×C42—41no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—41no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95C2×C4×C714yescomplemented
649#95C2×C4×C714yescomplemented
650C22×C7—24no—
651C22×C7—24no—
652C22×C7—24no—
653C22×C7—24no—
654C22×C7—24no—
655C22×C7—24no—
656C22×C7—42no—
657C22×C7—42no—
658C22×C7—42no—
659C22×C7—42no—
660C22×C7—42no—
661C22×C7—42no—
662C22×C7—42no—
663C22×C7—42no—
664C22×C7—42no—
665C22×C7—42no—
666C22×C7—42no—
667C22×C7—42no—
668C22×C7—42no—
669C22×C7—42no—
670C22×C7—42no—
671C22×C7—42no—
672C22×C7—42no—
673C22×C7—42no—
674C22×C7—42no—
675C22×C7—42no—
676C22×C7—42no—
677C22×C7—42no—
678C22×C7—42no—
679C22×C7—42no—
680C22×C7C22×C4⋊C411yescharacteristic
681C22×C7C2×C4×D411yescharacteristic
682C22×C7C4×#4111yescharacteristic
683C22×C7#51811yescharacteristic
684C22×C7#51811yescharacteristic
685C22×C7#51811yescharacteristic
686C22×C7#52011yescharacteristic
687C22×C7#53411yescharacteristic
688C22×C7#53411yescharacteristic
689C22×C7#53411yescharacteristic
690C22×C7#53511yescharacteristic
691C22×C7#53811yescharacteristic
692C22×C7#53811yescharacteristic
693C22×C7#53811yescharacteristic
694C22×C7#53911yescharacteristic
695C22×C7#54011yescharacteristic
696C22×C7#54211yescharacteristic
697C22×C7#54311yescharacteristic
698C22×C7#54311yescharacteristic
699C22×C7D4211yescharacteristic
700C22×C7#54611yescharacteristic
701C22×C7#54611yescharacteristic
702C22×C7#54611yescharacteristic
703C22×C7#54711yescharacteristic
704C22×C7D4×Q811yescharacteristic
705C22×C7#55011yescharacteristic
706C22×C7#55311yescharacteristic
707C22×C7#55411yescharacteristic
708C22×C7#55411yescharacteristic
709C22×C7#55411yescharacteristic
710C22×C7#55511yescharacteristic
711C22×C7#56011yescharacteristic
712C22×C7#56011yescharacteristic
713C22×C7#56211yescharacteristic
714C22×C7#56211yescharacteristic
715C4×C7—24no—
716C4×C7—24no—
717C4×C7—42no—
718C4×C7—42no—
719C4×C7—42no—
720C4×C7—42no—
721C4×C7—42no—
722C4×C7—42no—
723C4×C7—42no—
724C4×C7—81no—
725C4×C7—81no—
726C4×C7—81no—
727C4×C7—81no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24C22×C4×C712yes—
753C24C22×C4×C712yes—
754C24C2×C7×D412yes—
755C24C2×C7×D412yes—
756C24C2×C7×Q812yes—
757C24C2×C7×Q812yes—
758C24C24×C711yescharacteristic
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4C7×C4⋊C4116yescomplemented
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—28no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4C22×C4×C712yes—
859C22×C4C22×C4×C712yes—
860C22×C4C22×C4×C712yes—
861C22×C4C22×C4×C712yes—
862C22×C4C22×C4×C712yes—
863C22×C4C2×C7×D412yes—
864C22×C4C2×C7×D412yes—
865C22×C4C2×C7×D412yes—
866C22×C4C2×C7×D412yes—
867C22×C4C2×C7×Q812yes—
868C22×C4C7×#4112yes—
869C22×C4C7×#4112yes—
870C22×C4C7×#4112yes—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C22⋊C4—28no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C42—44no—
887C2×C7—44no—
888C2×C7—44no—
889C2×C7#231511yescharacteristic
890C2×C7#232111yescharacteristic
891C2×C7#233511yescharacteristic
892C2×C7D4×C4⋊C411yescharacteristic
893C2×C7#234911yescharacteristic
894C2×C7#236311yescharacteristic
895C2×C7#237711yescharacteristic
896C2×C7#266811yescharacteristic
897C2×C7#267311yescharacteristic
898C2×C7#268611yescharacteristic
899C2×C7#269211yescharacteristic
900C2×C7#270811yescharacteristic
901C2×C7#273211yescharacteristic
902C2×C7#278011yescharacteristic
903C2×C7#278411yescharacteristic
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23C2×C7×C4⋊C414yes—
973C23C2×C7×C4⋊C414yes—
974C23C23×C4×C711yescharacteristic
975C23C22×C7×D411yescharacteristic
976C23C22×C7×D411yescharacteristic
977C23C22×C7×Q811yescharacteristic
978C23C2×C7×#4111yescharacteristic
979C23C2×C7×#4111yescharacteristic
980C23C2×C7×#4111yescharacteristic
981C23C7×H(5,𝔽2)11yescharacteristic
982C23C7×H(5,𝔽2)11yescharacteristic
983C23C7×H(5,𝔽2)11yescharacteristic
984C23C7×H(5,𝔽2)11yescharacteristic
985C23C7×H(5,𝔽2)11yescharacteristic
986C23C7×H(5,𝔽2)11yescharacteristic
987C23C7×H(5,𝔽2)11yescharacteristic
988C23C7×2−1+411yescharacteristic
989D4—416no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—416no—
1024C2×C4—416no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4C2×C7×C4⋊C414yes—
1082C2×C4C4×C7×D414yes—
1083C7#1440711yescharacteristic, direct product factor, Sylow
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22C22×C7×C4⋊C411yescharacteristic
1115C22C2×C4×C7×D411yescharacteristic
1116C22C4×C7×#4111yescharacteristic
1117C22C7×#51811yescharacteristic
1118C22C7×#51811yescharacteristic
1119C22C7×#51811yescharacteristic
1120C22C7×#52011yescharacteristic
1121C22C7×#53411yescharacteristic
1122C22C7×#53411yescharacteristic
1123C22C7×#53411yescharacteristic
1124C22C7×#53511yescharacteristic
1125C22C7×#53811yescharacteristic
1126C22C7×#53811yescharacteristic
1127C22C7×#53811yescharacteristic
1128C22C7×#53911yescharacteristic
1129C22C7×#54011yescharacteristic
1130C22C7×#54211yescharacteristic
1131C22C7×#54311yescharacteristic
1132C22C7×#54311yescharacteristic
1133C22C7×D4211yescharacteristic
1134C22C7×#54611yescharacteristic
1135C22C7×#54611yescharacteristic
1136C22C7×#54611yescharacteristic
1137C22C7×#54711yescharacteristic
1138C22C7×D4×Q811yescharacteristic
1139C22C7×#55011yescharacteristic
1140C22C7×#55311yescharacteristic
1141C22C7×#55411yescharacteristic
1142C22C7×#55411yescharacteristic
1143C22C7×#55411yescharacteristic
1144C22C7×#55511yescharacteristic
1145C22C7×#56011yescharacteristic
1146C22C7×#56011yescharacteristic
1147C22C7×#56211yescharacteristic
1148C22C7×#56211yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C2—44no—
1163C2—44no—
1164C2C7×#231511yescharacteristic
1165C2C7×#232111yescharacteristic
1166C2C7×#233511yescharacteristic
1167C2C7×D4×C4⋊C411yescharacteristic
1168C2C7×#234911yescharacteristic
1169C2C7×#236311yescharacteristic
1170C2C7×#237711yescharacteristic
1171C2C7×#266811yescharacteristic
1172C2C7×#267311yescharacteristic
1173C2C7×#268611yescharacteristic
1174C2C7×#269211yescharacteristic
1175C2C7×#270811yescharacteristic
1176C2C7×#273211yescharacteristic
1177C2C7×#278011yescharacteristic
1178C2C7×#278411yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C7×#385C2semidirect
5. C2×C7×#380C2semidirect
6. C7×#1444C2semidirect
7. C7×#1442C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
11. C7×#1439C2semidirect
12. C7×#1436C2semidirect
13. C7×#1436C2semidirect
14. C7×C22⋊#95C2semidirect
15. C7×C22⋊#95C2semidirect
37. C7×#386C4semidirect
56. #14407C7direct (N × H)
79. C23×C4×C7C2×C4semidirect
107. C2×C7×C4⋊C4D4semidirect
137. C2×C7×C22⋊C4C2×C4semidirect
155. C7×#95C2×C4semidirect
156. C7×#95C2×C4semidirect
160. C2×#385C2×C7semidirect
161. C2×#380C2×C7semidirect
162. #1444C2×C7semidirect
163. #1442C2×C7semidirect
164. #1439C2×C7semidirect
165. #1439C2×C7semidirect
166. #1439C2×C7semidirect
167. #1439C2×C7semidirect
168. #1436C2×C7semidirect
169. #1436C2×C7semidirect
170. C22⋊#95C2×C7semidirect
171. C22⋊#95C2×C7semidirect
209. C2×C7×D4C4⋊C4semidirect
352. #386C4×C7semidirect
572. C23×C4C2×C4×C7semidirect
600. C2×C4⋊C4C7×D4semidirect
630. C2×C22⋊C4C2×C4×C7semidirect
648. #95C2×C4×C7semidirect
649. #95C2×C4×C7semidirect
765. C2×D4C7×C4⋊C4semidirect
1083. C7#14407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3902
C2×C7×#3862
C2×C7×#3852
C2×C7×#3802
C7×#14442
C7×#14422
C7×#14392
C7×#14362
C7×C22⋊#952
#144077