Finite Group Databasebeta

← C7×#14096 #13191312

Subgroups — C7×#14096 #13191312

Order 1792.

2266 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×#123C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic, complemented
3C2×C7×#386C211yesmaximal, characteristic
4C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C7×C22⋊C4C211yesmaximal, characteristic, complemented
6C7×#1445C211yesmaximal, characteristic, complemented
7C7×#1440C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic, complemented
9C7×#1438C211yesmaximal, characteristic
10C7×#1437C211yesmaximal, characteristic, complemented
11C7×#1436C211yesmaximal, characteristic, complemented
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×C4⋊#95C211yesmaximal, characteristic, complemented
14C7×C22⋊#95C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C2×C7×#123—24no—
20C2×C7×#123—24no—
21C2×C7×#123C418yescomplemented
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×C42×C7C2211yescharacteristic
36C22×C42×C7C2211yescharacteristic
37C22×C42×C7C2211yescharacteristic
38C7×#388—24no—
39C7×#386—24no—
40C4×C7×C22⋊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#14096C711yesmaximal, characteristic, direct product factor, Sylow
59C25×C7C2311yescharacteristic
60C25×C7C2311yescharacteristic
61C22×C7×D4—22no—
62C22×C7×D4—22no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—41no—
66C22×C7×D4—41no—
67C22×C7×D4C2×C414yes—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—22no—
71C23×C4×C7—22no—
72C23×C4×C7—22no—
73C23×C4×C7—22no—
74C23×C4×C7—22no—
75C23×C4×C7—22no—
76C23×C4×C7—22no—
77C23×C4×C7—41no—
78C23×C4×C7—41no—
79C23×C4×C7—41no—
80C23×C4×C7—41no—
81C23×C4×C7C2×C414yescomplemented
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×#123—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⋊C4C2×C414yescomplemented
104C2×C7×C4⋊C4C2×C414yescomplemented
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—22no—
121C2×C7×C22⋊C4—22no—
122C2×C7×C22⋊C4—22no—
123C2×C7×C22⋊C4—22no—
124C2×C7×C22⋊C4—22no—
125C2×C7×C22⋊C4—41no—
126C2×C7×C22⋊C4—41no—
127C2×C7×C22⋊C4—41no—
128C2×C7×C22⋊C4—41no—
129C2×C7×C22⋊C4C2×C414yes—
130C2×C7×C22⋊C4C2×C414yes—
131C2×C7×C22⋊C4C2×C414yescomplemented
132C2×C7×C22⋊C4D414yes—
133C2×C7×C22⋊C4D414yes—
134C2×C7×C22⋊C4D414yes—
135C2×C42×C7—22no—
136C2×C42×C7—22no—
137C2×C42×C7—22no—
138C2×C42×C7—22no—
139C2×C42×C7—22no—
140C2×C42×C7—22no—
141C2×C42×C7—41no—
142C2×C42×C7—41no—
143C2×C42×C7—41no—
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—22no—
154C7×#95—22no—
155C7×#95—22no—
156C7×#95—41no—
157C7×#95—41no—
158C7×#95—41no—
159C7×#95—41no—
160C22×#123C2×C711yescharacteristic
161C2×#388C2×C711yescharacteristic, complemented
162C2×#386C2×C711yescharacteristic
163C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
164C2×C4×C22⋊C4C2×C711yescharacteristic, complemented
165#1445C2×C711yescharacteristic, complemented
166#1440C2×C711yescharacteristic, complemented
167#1439C2×C711yescharacteristic, complemented
168#1438C2×C711yescharacteristic
169#1437C2×C711yescharacteristic, complemented
170#1436C2×C711yescharacteristic, complemented
171#1436C2×C711yescharacteristic, complemented
172C4⋊#95C2×C711yescharacteristic, complemented
173C22⋊#95C2×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×C7C22×C412yes—
200C24×C7C22×C412yes—
201C24×C7C2×D412yes—
202C24×C7C2×D412yes—
203C24×C7C2×D412yes—
204C24×C7#4112yes—
205C24×C7C2411yescharacteristic
206C2×C7×D4—28no—
207C2×C7×D4—28no—
208C2×C7×D4—44no—
209C2×C7×D4—44no—
210C2×C7×D4—44no—
211C2×C7×D4—44no—
212C2×C7×D4—44no—
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—28no—
226C22×C4×C7—28no—
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—28no—
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—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×C7C22×C412yes—
302C22×C4×C7C22×C412yes—
303C22×C4×C7C22×C412yes—
304C22×C4×C7C22×C412yes—
305C22×C4×C7C22×C412yes—
306C22×C4×C7C2×D412yes—
307C22×C4×C7C2×D412yes—
308C22×C4×C7C2×D412yes—
309C22×C4×C7C2×D412yes—
310C22×C4×C7C2×D412yes—
311C22×C4×C7C2×D412yes—
312C22×C4×C7#4112yes—
313C22×C4×C7#4112yes—
314C22×C4×C7#4112yes—
315C22×C4×C7#4112yes—
316C22×C4×C7#4112yes—
317C22×C4×C7#4112yes—
318C7×C4⋊C4—28no—
319C7×C4⋊C4—28no—
320C7×C4⋊C4—44no—
321C7×C22⋊C4—28no—
322C7×C22⋊C4—28no—
323C7×C22⋊C4—28no—
324C7×C22⋊C4—28no—
325C7×C22⋊C4—28no—
326C7×C22⋊C4—44no—
327C7×C22⋊C4—44no—
328C7×C22⋊C4—44no—
329C7×C22⋊C4—44no—
330C7×C22⋊C4C22⋊C4116yescomplemented
331C42×C7—44no—
332C42×C7—44no—
333C42×C7—44no—
334C23×D4C22×C711yescharacteristic
335C24×C4C22×C711yescharacteristic
336C24×C4C22×C711yescharacteristic
337C2×#123—24no—
338C2×#123—24no—
339C2×#123C4×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×C42C22×C711yescharacteristic
354C22×C42C22×C711yescharacteristic
355C22×C42C22×C711yescharacteristic
356#388—24no—
357#386—24no—
358C4×C22⋊C4—24no—
359C4×C22⋊C4—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—22no—
402C23×C7—22no—
403C23×C7—22no—
404C23×C7—22no—
405C23×C7—22no—
406C23×C7—22no—
407C23×C7—22no—
408C23×C7—22no—
409C23×C7—22no—
410C23×C7—22no—
411C23×C7—22no—
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×C7C2×C22⋊C414yes—
445C23×C7C4×D414yes—
446C23×C7C23×C411yescharacteristic
447C23×C7C22×D411yescharacteristic
448C23×C7C22×D411yescharacteristic
449C23×C7C22×D411yescharacteristic
450C23×C7C2×#4111yescharacteristic
451C23×C7C2×#4111yescharacteristic
452C23×C7C2×#4111yescharacteristic
453C23×C7C2×#4111yescharacteristic
454C23×C7C2×#4111yescharacteristic
455C23×C7C2×#4111yescharacteristic
456C23×C7C2×#4111yescharacteristic
457C23×C7H(5,𝔽2)11yescharacteristic
458C23×C7H(5,𝔽2)11yescharacteristic
459C23×C7H(5,𝔽2)11yescharacteristic
460C23×C72−1+411yescharacteristic
461C7×D4—416no—
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—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—22no—
500C2×C4×C7—22no—
501C2×C4×C7—22no—
502C2×C4×C7—22no—
503C2×C4×C7—22no—
504C2×C4×C7—416no—
505C2×C4×C7—416no—
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×C7#12314yescomplemented
555C25C23×C711yescharacteristic
556C25C23×C711yescharacteristic
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4C2×C4×C714yes—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4—41no—
576C23×C4—41no—
577C23×C4C2×C4×C714yescomplemented
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#123—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⋊C4C2×C4×C714yescomplemented
600C2×C4⋊C4C2×C4×C714yescomplemented
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—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4C2×C4×C714yes—
626C2×C22⋊C4C2×C4×C714yes—
627C2×C22⋊C4C2×C4×C714yescomplemented
628C2×C22⋊C4C7×D414yes—
629C2×C22⋊C4C7×D414yes—
630C2×C22⋊C4C7×D414yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—41no—
638C2×C42—41no—
639C2×C42—41no—
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—22no—
650#95—22no—
651#95—22no—
652#95—41no—
653#95—41no—
654#95—41no—
655#95—41no—
656C22×C7—24no—
657C22×C7—24no—
658C22×C7—24no—
659C22×C7—24no—
660C22×C7—24no—
661C22×C7—24no—
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×C7—42no—
681C22×C7—42no—
682C22×C7—42no—
683C22×C7—42no—
684C22×C7—42no—
685C22×C7—42no—
686C22×C7C22×C22⋊C411yescharacteristic
687C22×C7C2×C4×D411yescharacteristic
688C22×C7C4×#4111yescharacteristic
689C22×C7C4×#4111yescharacteristic
690C22×C7C4×#4111yescharacteristic
691C22×C7#51811yescharacteristic
692C22×C7#52011yescharacteristic
693C22×C7C2×#12311yescharacteristic
694C22×C7#52511yescharacteristic
695C22×C7#52511yescharacteristic
696C22×C7#52511yescharacteristic
697C22×C7#52911yescharacteristic
698C22×C7#52911yescharacteristic
699C22×C7#53211yescharacteristic
700C22×C7#53211yescharacteristic
701C22×C7#53811yescharacteristic
702C22×C7#53911yescharacteristic
703C22×C7#54011yescharacteristic
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#54711yescharacteristic
715C22×C7#55111yescharacteristic
716C22×C7#55111yescharacteristic
717C22×C7#55211yescharacteristic
718C22×C7#55311yescharacteristic
719C22×C7#55311yescharacteristic
720C22×C7#55911yescharacteristic
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—42no—
731C4×C7—42no—
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—
758C24C22×C4×C712yes—
759C24C22×C4×C712yes—
760C24C2×C7×D412yes—
761C24C2×C7×D412yes—
762C24C2×C7×D412yes—
763C24C7×#4112yes—
764C24C24×C711yescharacteristic
765C2×D4—28no—
766C2×D4—28no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
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—28no—
785C22×C4—28no—
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—28no—
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—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×C4—44no—
859C22×C4—44no—
860C22×C4C22×C4×C712yes—
861C22×C4C22×C4×C712yes—
862C22×C4C22×C4×C712yes—
863C22×C4C22×C4×C712yes—
864C22×C4C22×C4×C712yes—
865C22×C4C2×C7×D412yes—
866C22×C4C2×C7×D412yes—
867C22×C4C2×C7×D412yes—
868C22×C4C2×C7×D412yes—
869C22×C4C2×C7×D412yes—
870C22×C4C2×C7×D412yes—
871C22×C4C7×#4112yes—
872C22×C4C7×#4112yes—
873C22×C4C7×#4112yes—
874C22×C4C7×#4112yes—
875C22×C4C7×#4112yes—
876C22×C4C7×#4112yes—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—44no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4C7×C22⋊C4116yescomplemented
890C42—44no—
891C42—44no—
892C42—44no—
893C2×C7—44no—
894C2×C7—44no—
895C2×C7#229711yescharacteristic
896C2×C7C4×#12311yescharacteristic
897C2×C7#233511yescharacteristic
898C2×C7D4×C22⋊C411yescharacteristic
899C2×C7#233911yescharacteristic
900C2×C7#235911yescharacteristic
901C2×C7#237411yescharacteristic
902C2×C7#241811yescharacteristic
903C2×C7#242211yescharacteristic
904C2×C7#245511yescharacteristic
905C2×C7#245711yescharacteristic
906C2×C7#246411yescharacteristic
907C2×C7#247011yescharacteristic
908C2×C7#255311yescharacteristic
909C2×C7#255711yescharacteristic
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—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
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—
978C23C2×C7×C22⋊C414yes—
979C23C4×C7×D414yes—
980C23C23×C4×C711yescharacteristic
981C23C22×C7×D411yescharacteristic
982C23C22×C7×D411yescharacteristic
983C23C22×C7×D411yescharacteristic
984C23C2×C7×#4111yescharacteristic
985C23C2×C7×#4111yescharacteristic
986C23C2×C7×#4111yescharacteristic
987C23C2×C7×#4111yescharacteristic
988C23C2×C7×#4111yescharacteristic
989C23C2×C7×#4111yescharacteristic
990C23C2×C7×#4111yescharacteristic
991C23C7×H(5,𝔽2)11yescharacteristic
992C23C7×H(5,𝔽2)11yescharacteristic
993C23C7×H(5,𝔽2)11yescharacteristic
994C23C7×2−1+411yescharacteristic
995D4—416no—
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—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—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—416no—
1039C2×C4—416no—
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×C4C7×#12314yescomplemented
1089C7#1409611yescharacteristic, direct product factor, Sylow
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
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—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C22×C7×C22⋊C411yescharacteristic
1121C22C2×C4×C7×D411yescharacteristic
1122C22C4×C7×#4111yescharacteristic
1123C22C4×C7×#4111yescharacteristic
1124C22C4×C7×#4111yescharacteristic
1125C22C7×#51811yescharacteristic
1126C22C7×#52011yescharacteristic
1127C22C2×C7×#12311yescharacteristic
1128C22C7×#52511yescharacteristic
1129C22C7×#52511yescharacteristic
1130C22C7×#52511yescharacteristic
1131C22C7×#52911yescharacteristic
1132C22C7×#52911yescharacteristic
1133C22C7×#53211yescharacteristic
1134C22C7×#53211yescharacteristic
1135C22C7×#53811yescharacteristic
1136C22C7×#53911yescharacteristic
1137C22C7×#54011yescharacteristic
1138C22C7×#54211yescharacteristic
1139C22C7×D4211yescharacteristic
1140C22C7×D4211yescharacteristic
1141C22C7×#54611yescharacteristic
1142C22C7×#54611yescharacteristic
1143C22C7×#54611yescharacteristic
1144C22C7×#54611yescharacteristic
1145C22C7×#54611yescharacteristic
1146C22C7×#54711yescharacteristic
1147C22C7×#54711yescharacteristic
1148C22C7×#54711yescharacteristic
1149C22C7×#55111yescharacteristic
1150C22C7×#55111yescharacteristic
1151C22C7×#55211yescharacteristic
1152C22C7×#55311yescharacteristic
1153C22C7×#55311yescharacteristic
1154C22C7×#55911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—44no—
1170C2C7×#229711yescharacteristic
1171C2C4×C7×#12311yescharacteristic
1172C2C7×#233511yescharacteristic
1173C2C7×D4×C22⋊C411yescharacteristic
1174C2C7×#233911yescharacteristic
1175C2C7×#235911yescharacteristic
1176C2C7×#237411yescharacteristic
1177C2C7×#241811yescharacteristic
1178C2C7×#242211yescharacteristic
1179C2C7×#245511yescharacteristic
1180C2C7×#245711yescharacteristic
1181C2C7×#246411yescharacteristic
1182C2C7×#247011yescharacteristic
1183C2C7×#255311yescharacteristic
1184C2C7×#255711yescharacteristic
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×#388C2semidirect
4. C2×C4×C7×C22⋊C4C2semidirect
5. C2×C4×C7×C22⋊C4C2semidirect
6. C7×#1445C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
10. C7×#1437C2semidirect
11. C7×#1436C2semidirect
12. C7×#1436C2semidirect
13. C7×C4⋊#95C2semidirect
14. C7×C22⋊#95C2semidirect
15. C7×C22⋊#95C2semidirect
21. C2×C7×#123C4semidirect
58. #14096C7direct (N × H)
81. C23×C4×C7C2×C4semidirect
103. C2×C7×C4⋊C4C2×C4semidirect
104. C2×C7×C4⋊C4C2×C4semidirect
131. C2×C7×C22⋊C4C2×C4semidirect
161. C2×#388C2×C7semidirect
163. C2×C4×C22⋊C4C2×C7semidirect
164. C2×C4×C22⋊C4C2×C7semidirect
165. #1445C2×C7semidirect
166. #1440C2×C7semidirect
167. #1439C2×C7semidirect
169. #1437C2×C7semidirect
170. #1436C2×C7semidirect
171. #1436C2×C7semidirect
172. C4⋊#95C2×C7semidirect
173. C22⋊#95C2×C7semidirect
174. C22⋊#95C2×C7semidirect
330. C7×C22⋊C4C22⋊C4semidirect
339. C2×#123C4×C7semidirect
554. C2×C4×C7#123semidirect
577. C23×C4C2×C4×C7semidirect
599. C2×C4⋊C4C2×C4×C7semidirect
600. C2×C4⋊C4C2×C4×C7semidirect
627. C2×C22⋊C4C2×C4×C7semidirect
889. C22⋊C4C7×C22⋊C4semidirect
1088. C2×C4C7×#123semidirect
1089. C7#14096direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1232
C2×C7×#3882
C2×C7×#3862
C2×C4×C7×C22⋊C42
C7×#14452
C7×#14402
C7×#14392
C7×#14382
C7×#14372
C7×#14362
C7×C4⋊#952
C7×C22⋊#952
#140967