Finite Group Databasebeta

← C7×#14447 #13191663

Subgroups — C7×#14447 #13191663

Order 1792.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C7×#1443C211yesmaximal, characteristic, complemented
5C7×#1441C211yesmaximal, characteristic, complemented
6C7×#1440C211yesmaximal, characteristic
7C7×#1439C211yesmaximal, characteristic
8C7×#1439C211yesmaximal, characteristic
9C7×#1439C211yesmaximal, characteristic
10C7×#1437C211yesmaximal, characteristic
11C7×#1436C211yesmaximal, characteristic, complemented
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×C4⋊#95C211yesmaximal, characteristic, complemented
14C7×C4⋊#95C211yesmaximal, characteristic, complemented
15C7×#1434C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic
30C22×C42×C7C2211yescharacteristic
31C7×#388—24no—
32C7×#388C418yescomplemented
33C7×#387—24no—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54#14447C711yesmaximal, characteristic, direct product factor, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—41no—
78C2×C7×C4⋊C4—41no—
79C2×C7×C4⋊C4—41no—
80C2×C7×C4⋊C4—41no—
81C2×C7×C4⋊C4—41no—
82C2×C7×C4⋊C4—41no—
83C2×C7×C4⋊C4C2×C414yes—
84C2×C7×C4⋊C4D414yes—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—41no—
94C2×C7×C22⋊C4—41no—
95C2×C7×C22⋊C4—41no—
96C2×C7×C22⋊C4—41no—
97C2×C7×C22⋊C4—41no—
98C2×C7×C22⋊C4—41no—
99C2×C7×C22⋊C4—41no—
100C2×C7×C22⋊C4—41no—
101C2×C7×C22⋊C4—41no—
102C2×C7×C22⋊C4—41no—
103C2×C7×C22⋊C4C2×C414yes—
104C2×C7×C22⋊C4C2×C414yes—
105C2×C7×C22⋊C4C2×C414yes—
106C2×C42×C7—22no—
107C2×C42×C7—22no—
108C2×C42×C7—22no—
109C2×C42×C7—41no—
110C2×C42×C7—41no—
111C2×C42×C7—41no—
112C2×C42×C7—41no—
113C2×C42×C7—41no—
114C2×C42×C7C2×C414yes—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—22no—
122C7×#95—22no—
123C7×#95—22no—
124C7×#95—41no—
125C7×#95—41no—
126C7×#95—41no—
127C7×#95—41no—
128C7×#95—41no—
129C7×#95—41no—
130C7×#95—41no—
131C7×#95—41no—
132C7×#95—41no—
133C7×#95C2×C414yes—
134C7×#95C2×C414yes—
135C2×#388C2×C711yescharacteristic
136C2×#388C2×C711yescharacteristic
137C2×#387C2×C711yescharacteristic, complemented
138#1443C2×C711yescharacteristic, complemented
139#1441C2×C711yescharacteristic, complemented
140#1440C2×C711yescharacteristic
141#1439C2×C711yescharacteristic
142#1439C2×C711yescharacteristic
143#1439C2×C711yescharacteristic
144#1437C2×C711yescharacteristic
145#1436C2×C711yescharacteristic, complemented
146#1436C2×C711yescharacteristic, complemented
147C4⋊#95C2×C711yescharacteristic, complemented
148C4⋊#95C2×C711yescharacteristic, complemented
149#1434C2×C711yescharacteristic, complemented
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
163C24×C7—21no—
164C24×C7C22×C412yes—
165C24×C7C2411yescharacteristic
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×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×C7C22×C412yes—
251C22×C4×C7C22×C412yes—
252C22×C4×C7C22×C412yes—
253C22×C4×C7C22×C412yes—
254C22×C4×C7C22×C412yes—
255C22×C4×C7C22×C412yes—
256C22×C4×C7C2×D412yes—
257C22×C4×C7C2×D412yes—
258C22×C4×C7C2×D412yes—
259C22×C4×C7#4112yes—
260C22×C4×C7#4112yes—
261C22×C4×C7#4112yes—
262C22×C4×C7#4112yes—
263C22×C4×C7#4112yes—
264C7×C4⋊C4—28no—
265C7×C4⋊C4—44no—
266C7×C4⋊C4—44no—
267C7×C4⋊C4—44no—
268C7×C4⋊C4—44no—
269C7×C22⋊C4—28no—
270C7×C22⋊C4—28no—
271C7×C22⋊C4—44no—
272C7×C22⋊C4—44no—
273C7×C22⋊C4—44no—
274C7×C22⋊C4—44no—
275C7×C22⋊C4—44no—
276C42×C7—44no—
277C42×C7—44no—
278C42×C7—44no—
279C22×C4⋊C4C22×C711yescharacteristic
280C22×C4⋊C4C22×C711yescharacteristic
281C22×C4⋊C4C22×C711yescharacteristic
282C22×C4⋊C4C22×C711yescharacteristic
283C22×C4⋊C4C22×C711yescharacteristic
284C22×C22⋊C4C22×C711yescharacteristic
285C22×C22⋊C4C22×C711yescharacteristic
286C22×C22⋊C4C22×C711yescharacteristic
287C22×C22⋊C4C22×C711yescharacteristic
288C22×C22⋊C4C22×C711yescharacteristic
289C22×C22⋊C4C22×C711yescharacteristic
290C22×C22⋊C4C22×C711yescharacteristic
291C22×C42C22×C711yescharacteristic
292C22×C42C22×C711yescharacteristic
293C22×C42C22×C711yescharacteristic
294#388—24no—
295#388C4×C718yescomplemented
296#387—24no—
297C2×#95C22×C711yescharacteristic
298C2×#95C22×C711yescharacteristic
299C2×#95C22×C711yescharacteristic
300C2×#95C22×C711yescharacteristic
301C2×#95C22×C711yescharacteristic
302C2×#95C22×C711yescharacteristic
303C2×#95C22×C711yescharacteristic
304C2×#95C22×C711yescharacteristic
305C2×#95C22×C711yescharacteristic
306C2×#95C22×C711yescharacteristic
307C2×#95C22×C711yescharacteristic
308C2×#95C22×C711yescharacteristic
309C2×#95C22×C711yescharacteristic
310C2×#95C22×C711yescharacteristic
311C2×#95C22×C711yescharacteristic
312C2×#95C22×C711yescharacteristic
313C2×#95C22×C711yescharacteristic
314C2×#95C22×C711yescharacteristic
315C2×#95C22×C711yescharacteristic
316C2×#95C22×C711yescharacteristic
317C23×C7—22no—
318C23×C7—22no—
319C23×C7—22no—
320C23×C7—22no—
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—41no—
325C23×C7—41no—
326C23×C7—41no—
327C23×C7—41no—
328C23×C7—41no—
329C23×C7—41no—
330C23×C7—41no—
331C23×C7—41no—
332C23×C7—41no—
333C23×C7—41no—
334C23×C7—41no—
335C23×C7—41no—
336C23×C7—41no—
337C23×C7—41no—
338C23×C7—41no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7C23×C411yescharacteristic
353C23×C7C22×D411yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7C2×#4111yescharacteristic
356C23×C7C2×#4111yescharacteristic
357C23×C7C2×#4111yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7H(5,𝔽2)11yescharacteristic
360C23×C7H(5,𝔽2)11yescharacteristic
361C23×C7H(5,𝔽2)11yescharacteristic
362C23×C7H(5,𝔽2)11yescharacteristic
363C23×C7H(5,𝔽2)11yescharacteristic
364C23×C72−1+411yescharacteristic
365C23×C72−1+411yescharacteristic
366C23×C72−1+411yescharacteristic
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
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#11714yes—
464C2×C4×C7C4×D414yes—
465C25C23×C711yescharacteristic
466C23×C4C23×C711yescharacteristic
467C23×C4C23×C711yescharacteristic
468C23×C4C23×C711yescharacteristic
469C23×C4C23×C711yescharacteristic
470C23×C4C23×C711yescharacteristic
471C23×C4C23×C711yescharacteristic
472C23×C4C23×C711yescharacteristic
473C23×C4C23×C711yescharacteristic
474C23×C4C23×C711yescharacteristic
475C23×C4C23×C711yescharacteristic
476C23×C4C23×C711yescharacteristic
477C23×C4C23×C711yescharacteristic
478C23×C4C23×C711yescharacteristic
479C23×C4C23×C711yescharacteristic
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4C2×C4×C714yes—
494C2×C4⋊C4C7×D414yes—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4C2×C4×C714yes—
514C2×C22⋊C4C2×C4×C714yes—
515C2×C22⋊C4C2×C4×C714yes—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—41no—
520C2×C42—41no—
521C2×C42—41no—
522C2×C42—41no—
523C2×C42—41no—
524C2×C42C2×C4×C714yes—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—41no—
535#95—41no—
536#95—41no—
537#95—41no—
538#95—41no—
539#95—41no—
540#95—41no—
541#95—41no—
542#95—41no—
543#95C2×C4×C714yes—
544#95C2×C4×C714yes—
545C22×C7—42no—
546C22×C7—42no—
547C22×C7—42no—
548C22×C7—42no—
549C22×C7—42no—
550C22×C7—42no—
551C22×C7—42no—
552C22×C7—81no—
553C22×C7—81no—
554C22×C7—81no—
555C22×C7—81no—
556C22×C7—81no—
557C22×C7—81no—
558C22×C7—81no—
559C22×C7—81no—
560C22×C7C2×#11711yescharacteristic
561C22×C7C2×C4×D411yescharacteristic
562C22×C7C4×#4111yescharacteristic
563C22×C7#51811yescharacteristic
564C22×C7#52011yescharacteristic
565C22×C7#52011yescharacteristic
566C22×C7#52011yescharacteristic
567C22×C7#53411yescharacteristic
568C22×C7#53711yescharacteristic
569C22×C7#53811yescharacteristic
570C22×C7#53811yescharacteristic
571C22×C7#53911yescharacteristic
572C22×C7#53911yescharacteristic
573C22×C7#54011yescharacteristic
574C22×C7#54111yescharacteristic
575C22×C7#54111yescharacteristic
576C22×C7#54211yescharacteristic
577C22×C7#54211yescharacteristic
578C22×C7#54211yescharacteristic
579C22×C7#54611yescharacteristic
580C22×C7#54711yescharacteristic
581C22×C7#54811yescharacteristic
582C22×C7#55011yescharacteristic
583C22×C7#55111yescharacteristic
584C22×C7#55111yescharacteristic
585C22×C7#55311yescharacteristic
586C22×C7#55311yescharacteristic
587C22×C7#55511yescharacteristic
588C22×C7#55611yescharacteristic
589C22×C7#55611yescharacteristic
590C22×C7#55911yescharacteristic
591C22×C7#56011yescharacteristic
592C22×C7#56211yescharacteristic
593C22×C7#56211yescharacteristic
594C22×C7#56311yescharacteristic
595C4×C7—24no—
596C4×C7—24no—
597C4×C7—42no—
598C4×C7—42no—
599C4×C7—42no—
600C4×C7—42no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7—81no—
606C4×C7—81no—
607C4×C7—81no—
608C4×C7—81no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24C22×C4×C712yes—
624C24C24×C711yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—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×C4C22×C4×C712yes—
710C22×C4C22×C4×C712yes—
711C22×C4C22×C4×C712yes—
712C22×C4C22×C4×C712yes—
713C22×C4C22×C4×C712yes—
714C22×C4C22×C4×C712yes—
715C22×C4C2×C7×D412yes—
716C22×C4C2×C7×D412yes—
717C22×C4C2×C7×D412yes—
718C22×C4C7×#4112yes—
719C22×C4C7×#4112yes—
720C22×C4C7×#4112yes—
721C22×C4C7×#4112yes—
722C22×C4C7×#4112yes—
723C4⋊C4—28no—
724C4⋊C4—44no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C42—44no—
736C42—44no—
737C42—44no—
738C2×C7—82no—
739C2×C7#231411yescharacteristic
740C2×C7#232511yescharacteristic
741C2×C7#233411yescharacteristic
742C2×C7#235311yescharacteristic
743C2×C7#235411yescharacteristic
744C2×C7#236711yescharacteristic
745C2×C7#237611yescharacteristic
746C2×C7#270111yescharacteristic
747C2×C7#270511yescharacteristic
748C2×C7#272511yescharacteristic
749C2×C7#273011yescharacteristic
750C2×C7#275911yescharacteristic
751C2×C7#278311yescharacteristic
752C2×C7#279811yescharacteristic
753C2×C7#280311yescharacteristic
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23C23×C4×C711yescharacteristic
790C23C22×C7×D411yescharacteristic
791C23C2×C7×#4111yescharacteristic
792C23C2×C7×#4111yescharacteristic
793C23C2×C7×#4111yescharacteristic
794C23C2×C7×#4111yescharacteristic
795C23C2×C7×#4111yescharacteristic
796C23C7×H(5,𝔽2)11yescharacteristic
797C23C7×H(5,𝔽2)11yescharacteristic
798C23C7×H(5,𝔽2)11yescharacteristic
799C23C7×H(5,𝔽2)11yescharacteristic
800C23C7×H(5,𝔽2)11yescharacteristic
801C23C7×2−1+411yescharacteristic
802C23C7×2−1+411yescharacteristic
803C23C7×2−1+411yescharacteristic
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4C7×#11714yes—
901C2×C4C4×C7×D414yes—
902C7#1444711yescharacteristic, direct product factor, Sylow
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22C2×C7×#11711yescharacteristic
919C22C2×C4×C7×D411yescharacteristic
920C22C4×C7×#4111yescharacteristic
921C22C7×#51811yescharacteristic
922C22C7×#52011yescharacteristic
923C22C7×#52011yescharacteristic
924C22C7×#52011yescharacteristic
925C22C7×#53411yescharacteristic
926C22C7×#53711yescharacteristic
927C22C7×#53811yescharacteristic
928C22C7×#53811yescharacteristic
929C22C7×#53911yescharacteristic
930C22C7×#53911yescharacteristic
931C22C7×#54011yescharacteristic
932C22C7×#54111yescharacteristic
933C22C7×#54111yescharacteristic
934C22C7×#54211yescharacteristic
935C22C7×#54211yescharacteristic
936C22C7×#54211yescharacteristic
937C22C7×#54611yescharacteristic
938C22C7×#54711yescharacteristic
939C22C7×#54811yescharacteristic
940C22C7×#55011yescharacteristic
941C22C7×#55111yescharacteristic
942C22C7×#55111yescharacteristic
943C22C7×#55311yescharacteristic
944C22C7×#55311yescharacteristic
945C22C7×#55511yescharacteristic
946C22C7×#55611yescharacteristic
947C22C7×#55611yescharacteristic
948C22C7×#55911yescharacteristic
949C22C7×#56011yescharacteristic
950C22C7×#56211yescharacteristic
951C22C7×#56211yescharacteristic
952C22C7×#56311yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—81no—
964C4—81no—
965C4—81no—
966C4—81no—
967C2—82no—
968C2C7×#231411yescharacteristic
969C2C7×#232511yescharacteristic
970C2C7×#233411yescharacteristic
971C2C7×#235311yescharacteristic
972C2C7×#235411yescharacteristic
973C2C7×#236711yescharacteristic
974C2C7×#237611yescharacteristic
975C2C7×#270111yescharacteristic
976C2C7×#270511yescharacteristic
977C2C7×#272511yescharacteristic
978C2C7×#273011yescharacteristic
979C2C7×#275911yescharacteristic
980C2C7×#278311yescharacteristic
981C2C7×#279811yescharacteristic
982C2C7×#280311yescharacteristic
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
3. C2×C7×#387C2semidirect
4. C7×#1443C2semidirect
5. C7×#1441C2semidirect
11. C7×#1436C2semidirect
12. C7×#1436C2semidirect
13. C7×C4⋊#95C2semidirect
14. C7×C4⋊#95C2semidirect
15. C7×#1434C2semidirect
32. C7×#388C4semidirect
54. #14447C7direct (N × H)
137. C2×#387C2×C7semidirect
138. #1443C2×C7semidirect
139. #1441C2×C7semidirect
145. #1436C2×C7semidirect
146. #1436C2×C7semidirect
147. C4⋊#95C2×C7semidirect
148. C4⋊#95C2×C7semidirect
149. #1434C2×C7semidirect
295. #388C4×C7semidirect
902. C7#14447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C7×#3872
C7×#14432
C7×#14412
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×C4⋊#952
C7×#14342
#144477