Finite Group Databasebeta

← C7×#14421 #13191637

Subgroups — C7×#14421 #13191637

Order 1792.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#124C211yesmaximal, characteristic
2C2×C7×#391C211yesmaximal, characteristic, complemented
3C2×C7×#388C211yesmaximal, characteristic, complemented
4C2×C7×#386C211yesmaximal, characteristic
5C2×C7×#385C211yesmaximal, characteristic, complemented
6C7×#1446C211yesmaximal, characteristic, complemented
7C7×#1440C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1439C211yesmaximal, characteristic, complemented
10C7×#1439C211yesmaximal, characteristic, complemented
11C7×#1438C211yesmaximal, characteristic
12C7×#1437C211yesmaximal, characteristic, complemented
13C7×C4⋊#95C211yesmaximal, characteristic, complemented
14C7×#1434C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C23×C7×D4C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C2×C7×#124—24no—
20C2×C7×#124—24no—
21C2×C7×#124C418yescomplemented
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×C7×C22⋊C4C2211yescharacteristic
32C22×C7×C22⋊C4C2211yescharacteristic
33C22×C7×C22⋊C4C2211yescharacteristic
34C22×C7×C22⋊C4C2211yescharacteristic
35C22×C7×C22⋊C4C2211yescharacteristic
36C22×C42×C7C2211yescharacteristic
37C22×C42×C7C2211yescharacteristic
38C7×#391—24no—
39C7×#388—24no—
40C7×#386—24no—
41C7×#385—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#14421C711yesmaximal, characteristic, direct product factor, Sylow
59C25×C7C2311yescharacteristic
60C25×C7C2311yescharacteristic
61C22×C7×Q8—22no—
62C22×C7×Q8—22no—
63C22×C7×Q8—22no—
64C22×C7×Q8—22no—
65C22×C7×Q8—41no—
66C22×C7×Q8—41no—
67C22×C7×Q8C2×C414yescomplemented
68C22×C7×D4—22no—
69C22×C7×D4—22no—
70C22×C7×D4—22no—
71C22×C7×D4—22no—
72C22×C7×D4—41no—
73C22×C7×D4—41no—
74C22×C7×D4C2×C414yes—
75C23×C4×C7—22no—
76C23×C4×C7—22no—
77C23×C4×C7—22no—
78C23×C4×C7—41no—
79C23×C4×C7—41no—
80C23×C4×C7—41no—
81C23×C4×C7—41no—
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
93C23×C4×C7C2311yescharacteristic
94C23×C4×C7C2311yescharacteristic
95C7×#124—232no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—22no—
99C2×C7×C4⋊C4—22no—
100C2×C7×C4⋊C4—22no—
101C2×C7×C4⋊C4—22no—
102C2×C7×C4⋊C4—41no—
103C2×C7×C4⋊C4—41no—
104C2×C7×C4⋊C4—41no—
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—22no—
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—41no—
121C2×C7×C22⋊C4—41no—
122C2×C7×C22⋊C4—41no—
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⋊C4C2×C414yes—
133C2×C7×C22⋊C4C2×C414yes—
134C2×C7×C22⋊C4C2×C414yescomplemented
135C2×C7×C22⋊C4C2×C414yescomplemented
136C2×C7×C22⋊C4D414yes—
137C2×C7×C22⋊C4D414yes—
138C2×C42×C7—22no—
139C2×C42×C7—22no—
140C2×C42×C7—22no—
141C2×C42×C7—22no—
142C2×C42×C7—41no—
143C2×C42×C7C2×C414yescomplemented
144C7×#95—22no—
145C7×#95—22no—
146C7×#95—22no—
147C7×#95—22no—
148C7×#95—22no—
149C7×#95—22no—
150C7×#95—22no—
151C7×#95—22no—
152C7×#95—22no—
153C7×#95—41no—
154C7×#95—41no—
155C7×#95—41no—
156C7×#95—41no—
157C7×#95—41no—
158C7×#95—41no—
159C7×#95D414yes—
160C22×#124C2×C711yescharacteristic
161C2×#391C2×C711yescharacteristic, complemented
162C2×#388C2×C711yescharacteristic, complemented
163C2×#386C2×C711yescharacteristic
164C2×#385C2×C711yescharacteristic, complemented
165#1446C2×C711yescharacteristic, complemented
166#1440C2×C711yescharacteristic, complemented
167#1439C2×C711yescharacteristic, complemented
168#1439C2×C711yescharacteristic, complemented
169#1439C2×C711yescharacteristic, complemented
170#1438C2×C711yescharacteristic
171#1437C2×C711yescharacteristic, complemented
172C4⋊#95C2×C711yescharacteristic, complemented
173#1434C2×C711yescharacteristic, complemented
174C22⋊#95C2×C711yescharacteristic, complemented
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×C7—21no—
197C24×C7—21no—
198C24×C7—21no—
199C24×C7—21no—
200C24×C7—21no—
201C24×C7C22×C412yes—
202C24×C7C22×C412yes—
203C24×C7C2×D412yes—
204C24×C7C2×D412yes—
205C24×C7C2411yescharacteristic
206C2×C7×Q8—28no—
207C2×C7×Q8—28no—
208C2×C7×Q8—44no—
209C2×C7×Q8—44no—
210C2×C7×Q8—44no—
211C2×C7×Q8—44no—
212C2×C7×Q8—44no—
213C2×C7×D4—28no—
214C2×C7×D4—28no—
215C2×C7×D4—44no—
216C2×C7×D4—44no—
217C2×C7×D4—44no—
218C2×C7×D4—44no—
219C2×C7×D4—44no—
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—21no—
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—21no—
290C22×C4×C7—21no—
291C22×C4×C7—21no—
292C22×C4×C7—21no—
293C22×C4×C7—21no—
294C22×C4×C7—21no—
295C22×C4×C7—21no—
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×C7—44no—
303C22×C4×C7C22×C412yes—
304C22×C4×C7C22×C412yes—
305C22×C4×C7C22×C412yes—
306C22×C4×C7C22×C412yes—
307C22×C4×C7C22×C412yes—
308C22×C4×C7C2×D412yes—
309C22×C4×C7C2×D412yes—
310C22×C4×C7C2×D412yes—
311C22×C4×C7C2×D412yes—
312C22×C4×C7C2×D412yes—
313C22×C4×C7C2×D412yes—
314C22×C4×C7C2×D412yes—
315C22×C4×C7#4112yes—
316C22×C4×C7#4112yes—
317C22×C4×C7#4112yes—
318C7×C4⋊C4—44no—
319C7×C4⋊C4—44no—
320C7×C4⋊C4—44no—
321C7×C22⋊C4—28no—
322C7×C22⋊C4—28no—
323C7×C22⋊C4—28no—
324C7×C22⋊C4—44no—
325C7×C22⋊C4—44no—
326C7×C22⋊C4—44no—
327C7×C22⋊C4—44no—
328C7×C22⋊C4—44no—
329C7×C22⋊C4—44no—
330C7×C22⋊C4—44no—
331C7×C22⋊C4C22⋊C4116yescomplemented
332C42×C7—28no—
333C42×C7—44no—
334C23×Q8C22×C711yescharacteristic
335C23×D4C22×C711yescharacteristic
336C24×C4C22×C711yescharacteristic
337C2×#124—24no—
338C2×#124—24no—
339C2×#124C4×C718yescomplemented
340C22×C4⋊C4C22×C711yescharacteristic
341C22×C4⋊C4C22×C711yescharacteristic
342C22×C4⋊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×C22⋊C4C22×C711yescharacteristic
350C22×C22⋊C4C22×C711yescharacteristic
351C22×C22⋊C4C22×C711yescharacteristic
352C22×C22⋊C4C22×C711yescharacteristic
353C22×C22⋊C4C22×C711yescharacteristic
354C22×C42C22×C711yescharacteristic
355C22×C42C22×C711yescharacteristic
356#391—24no—
357#388—24no—
358#386—24no—
359#385—24no—
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
371C2×#95C22×C711yescharacteristic
372C2×#95C22×C711yescharacteristic
373C2×#95C22×C711yescharacteristic
374C2×#95C22×C711yescharacteristic
375C2×#95C22×C711yescharacteristic
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—41no—
402C23×C7—41no—
403C23×C7—41no—
404C23×C7—41no—
405C23×C7—41no—
406C23×C7—41no—
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×C7—41no—
440C23×C7—41no—
441C23×C7—41no—
442C23×C7—41no—
443C23×C7—41no—
444C23×C7—41no—
445C23×C7C2×C22⋊C414yes—
446C23×C7C23×C411yescharacteristic
447C23×C7C22×D411yescharacteristic
448C23×C7C22×D411yescharacteristic
449C23×C7C22×D411yescharacteristic
450C23×C7C2×#4111yescharacteristic
451C23×C7C2×#4111yescharacteristic
452C23×C7C2×#4111yescharacteristic
453C23×C7H(5,𝔽2)11yescharacteristic
454C23×C7H(5,𝔽2)11yescharacteristic
455C23×C7H(5,𝔽2)11yescharacteristic
456C23×C7H(5,𝔽2)11yescharacteristic
457C23×C7H(5,𝔽2)11yescharacteristic
458C23×C72−1+411yescharacteristic
459C23×C72−1+411yescharacteristic
460C23×C72−1+411yescharacteristic
461C7×Q8—416no—
462C7×D4—416no—
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—22no—
491C2×C4×C7—22no—
492C2×C4×C7—22no—
493C2×C4×C7—22no—
494C2×C4×C7—22no—
495C2×C4×C7—22no—
496C2×C4×C7—22no—
497C2×C4×C7—22no—
498C2×C4×C7—22no—
499C2×C4×C7—416no—
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×C7—41no—
549C2×C4×C7—41no—
550C2×C4×C7—41no—
551C2×C4×C7—41no—
552C2×C4×C7C2×C22⋊C414yes—
553C2×C4×C7C2×C22⋊C414yes—
554C2×C4×C7C4×D414yes—
555C25C23×C711yescharacteristic
556C25C23×C711yescharacteristic
557C22×Q8—22no—
558C22×Q8—22no—
559C22×Q8—22no—
560C22×Q8—22no—
561C22×Q8—41no—
562C22×Q8—41no—
563C22×Q8C2×C4×C714yescomplemented
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—41no—
569C22×D4—41no—
570C22×D4C2×C4×C714yes—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—41no—
575C23×C4—41no—
576C23×C4—41no—
577C23×C4—41no—
578C23×C4C23×C711yescharacteristic
579C23×C4C23×C711yescharacteristic
580C23×C4C23×C711yescharacteristic
581C23×C4C23×C711yescharacteristic
582C23×C4C23×C711yescharacteristic
583C23×C4C23×C711yescharacteristic
584C23×C4C23×C711yescharacteristic
585C23×C4C23×C711yescharacteristic
586C23×C4C23×C711yescharacteristic
587C23×C4C23×C711yescharacteristic
588C23×C4C23×C711yescharacteristic
589C23×C4C23×C711yescharacteristic
590C23×C4C23×C711yescharacteristic
591#124—232no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
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×C22⋊C4C2×C4×C714yescomplemented
632C2×C22⋊C4C7×D414yes—
633C2×C22⋊C4C7×D414yes—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—41no—
639C2×C42C2×C4×C714yescomplemented
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95—41no—
654#95—41no—
655#95C7×D414yes—
656C22×C7—24no—
657C22×C7—24no—
658C22×C7—24no—
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—81no—
679C22×C7—81no—
680C22×C7—81no—
681C22×C7—81no—
682C22×C7—81no—
683C22×C7—81no—
684C22×C7—81no—
685C22×C7—81no—
686C22×C7C22×C22⋊C411yescharacteristic
687C22×C7C2×C4×D411yescharacteristic
688C22×C7C4×#4111yescharacteristic
689C22×C7#51811yescharacteristic
690C22×C7#52011yescharacteristic
691C22×C7#52011yescharacteristic
692C22×C7#52011yescharacteristic
693C22×C7#53511yescharacteristic
694C22×C7#53511yescharacteristic
695C22×C7#53611yescharacteristic
696C22×C7#53611yescharacteristic
697C22×C7#53711yescharacteristic
698C22×C7#53711yescharacteristic
699C22×C7#53811yescharacteristic
700C22×C7#53811yescharacteristic
701C22×C7#54211yescharacteristic
702C22×C7#54211yescharacteristic
703C22×C7#54211yescharacteristic
704C22×C7#54211yescharacteristic
705C22×C7D4211yescharacteristic
706C22×C7D4211yescharacteristic
707C22×C7#54611yescharacteristic
708C22×C7#54611yescharacteristic
709C22×C7#54611yescharacteristic
710C22×C7#54611yescharacteristic
711C22×C7#54611yescharacteristic
712C22×C7#54711yescharacteristic
713C22×C7#54711yescharacteristic
714C22×C7#54811yescharacteristic
715C22×C7#55611yescharacteristic
716C22×C7#55911yescharacteristic
717C22×C7H(3,𝔽4)11yescharacteristic
718C22×C7#56211yescharacteristic
719C22×C7#56211yescharacteristic
720C22×C7#56311yescharacteristic
721C4×C7—24no—
722C4×C7—24no—
723C4×C7—24no—
724C4×C7—42no—
725C4×C7—42no—
726C4×C7—42no—
727C4×C7—42no—
728C4×C7—42no—
729C4×C7—42no—
730C4×C7—81no—
731C4×C7—81no—
732C4×C7—81no—
733C4×C7—81no—
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—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24C22×C4×C712yes—
761C24C22×C4×C712yes—
762C24C2×C7×D412yes—
763C24C2×C7×D412yes—
764C24C24×C711yescharacteristic
765C2×Q8—28no—
766C2×Q8—28no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
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—21no—
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—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4C22×C4×C712yes—
863C22×C4C22×C4×C712yes—
864C22×C4C22×C4×C712yes—
865C22×C4C22×C4×C712yes—
866C22×C4C22×C4×C712yes—
867C22×C4C2×C7×D412yes—
868C22×C4C2×C7×D412yes—
869C22×C4C2×C7×D412yes—
870C22×C4C2×C7×D412yes—
871C22×C4C2×C7×D412yes—
872C22×C4C2×C7×D412yes—
873C22×C4C2×C7×D412yes—
874C22×C4C7×#4112yes—
875C22×C4C7×#4112yes—
876C22×C4C7×#4112yes—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4C7×C22⋊C4116yescomplemented
891C42—28no—
892C42—44no—
893C2×C7—44no—
894C2×C7—82no—
895C2×C7#231111yescharacteristic
896C2×C7#232611yescharacteristic
897C2×C7#233711yescharacteristic
898C2×C7D4×C22⋊C411yescharacteristic
899C2×C7#233911yescharacteristic
900C2×C7#236711yescharacteristic
901C2×C7#237911yescharacteristic
902C2×C7#267011yescharacteristic
903C2×C7#267211yescharacteristic
904C2×C7#267411yescharacteristic
905C2×C7#267611yescharacteristic
906C2×C7#270011yescharacteristic
907C2×C7#271011yescharacteristic
908C2×C7#271211yescharacteristic
909C2×C7#271511yescharacteristic
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—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
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—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C2×C7×C22⋊C414yes—
980C23C23×C4×C711yescharacteristic
981C23C22×C7×D411yescharacteristic
982C23C22×C7×D411yescharacteristic
983C23C22×C7×D411yescharacteristic
984C23C2×C7×#4111yescharacteristic
985C23C2×C7×#4111yescharacteristic
986C23C2×C7×#4111yescharacteristic
987C23C7×H(5,𝔽2)11yescharacteristic
988C23C7×H(5,𝔽2)11yescharacteristic
989C23C7×H(5,𝔽2)11yescharacteristic
990C23C7×H(5,𝔽2)11yescharacteristic
991C23C7×H(5,𝔽2)11yescharacteristic
992C23C7×2−1+411yescharacteristic
993C23C7×2−1+411yescharacteristic
994C23C7×2−1+411yescharacteristic
995Q8—416no—
996D4—416no—
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—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
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×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4C2×C7×C22⋊C414yes—
1087C2×C4C2×C7×C22⋊C414yes—
1088C2×C4C4×C7×D414yes—
1089C7#1442111yescharacteristic, direct product factor, Sylow
1090C22—24no—
1091C22—24no—
1092C22—24no—
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—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C7×C22⋊C411yescharacteristic
1121C22C2×C4×C7×D411yescharacteristic
1122C22C4×C7×#4111yescharacteristic
1123C22C7×#51811yescharacteristic
1124C22C7×#52011yescharacteristic
1125C22C7×#52011yescharacteristic
1126C22C7×#52011yescharacteristic
1127C22C7×#53511yescharacteristic
1128C22C7×#53511yescharacteristic
1129C22C7×#53611yescharacteristic
1130C22C7×#53611yescharacteristic
1131C22C7×#53711yescharacteristic
1132C22C7×#53711yescharacteristic
1133C22C7×#53811yescharacteristic
1134C22C7×#53811yescharacteristic
1135C22C7×#54211yescharacteristic
1136C22C7×#54211yescharacteristic
1137C22C7×#54211yescharacteristic
1138C22C7×#54211yescharacteristic
1139C22C7×D4211yescharacteristic
1140C22C7×D4211yescharacteristic
1141C22C7×#54611yescharacteristic
1142C22C7×#54611yescharacteristic
1143C22C7×#54611yescharacteristic
1144C22C7×#54611yescharacteristic
1145C22C7×#54611yescharacteristic
1146C22C7×#54711yescharacteristic
1147C22C7×#54711yescharacteristic
1148C22C7×#54811yescharacteristic
1149C22C7×#55611yescharacteristic
1150C22C7×#55911yescharacteristic
1151C22C7×H(3,𝔽4)11yescharacteristic
1152C22C7×#56211yescharacteristic
1153C22C7×#56211yescharacteristic
1154C22C7×#56311yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—82no—
1170C2C7×#231111yescharacteristic
1171C2C7×#232611yescharacteristic
1172C2C7×#233711yescharacteristic
1173C2C7×D4×C22⋊C411yescharacteristic
1174C2C7×#233911yescharacteristic
1175C2C7×#236711yescharacteristic
1176C2C7×#237911yescharacteristic
1177C2C7×#267011yescharacteristic
1178C2C7×#267211yescharacteristic
1179C2C7×#267411yescharacteristic
1180C2C7×#267611yescharacteristic
1181C2C7×#270011yescharacteristic
1182C2C7×#271011yescharacteristic
1183C2C7×#271211yescharacteristic
1184C2C7×#271511yescharacteristic
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
2. C2×C7×#391C2semidirect
3. C2×C7×#388C2semidirect
5. C2×C7×#385C2semidirect
6. C7×#1446C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×#1439C2semidirect
10. C7×#1439C2semidirect
12. C7×#1437C2semidirect
13. C7×C4⋊#95C2semidirect
14. C7×#1434C2semidirect
15. C7×C22⋊#95C2semidirect
21. C2×C7×#124C4semidirect
58. #14421C7direct (N × H)
67. C22×C7×Q8C2×C4semidirect
134. C2×C7×C22⋊C4C2×C4semidirect
135. C2×C7×C22⋊C4C2×C4semidirect
143. C2×C42×C7C2×C4semidirect
161. C2×#391C2×C7semidirect
162. C2×#388C2×C7semidirect
164. C2×#385C2×C7semidirect
165. #1446C2×C7semidirect
166. #1440C2×C7semidirect
167. #1439C2×C7semidirect
168. #1439C2×C7semidirect
169. #1439C2×C7semidirect
171. #1437C2×C7semidirect
172. C4⋊#95C2×C7semidirect
173. #1434C2×C7semidirect
174. C22⋊#95C2×C7semidirect
331. C7×C22⋊C4C22⋊C4semidirect
339. C2×#124C4×C7semidirect
563. C22×Q8C2×C4×C7semidirect
630. C2×C22⋊C4C2×C4×C7semidirect
631. C2×C22⋊C4C2×C4×C7semidirect
639. C2×C42C2×C4×C7semidirect
890. C22⋊C4C7×C22⋊C4semidirect
1089. C7#14421direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1242
C2×C7×#3912
C2×C7×#3882
C2×C7×#3862
C2×C7×#3852
C7×#14462
C7×#14402
C7×#14392
C7×#14382
C7×#14372
C7×C4⋊#952
C7×#14342
C7×C22⋊#952
#144217