Finite Group Databasebeta

← C7×#14512 #13191728

Subgroups — C7×#14512 #13191728

Order 1792.

1298 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C7×#1442C211yesmaximal, characteristic, complemented
3C7×#1441C211yesmaximal, characteristic, complemented
4C7×#1440C211yesmaximal, characteristic
5C7×#1440C211yesmaximal, characteristic
6C7×#1439C211yesmaximal, characteristic
7C7×#1439C211yesmaximal, characteristic
8C7×#1437C211yesmaximal, characteristic
9C7×#1437C211yesmaximal, characteristic
10C7×#1436C211yesmaximal, characteristic, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C7×#1434C211yesmaximal, characteristic, complemented
13C7×#1434C211yesmaximal, characteristic, complemented
14C7×#1434C211yesmaximal, characteristic, complemented
15C7×#1434C211yesmaximal, characteristic, complemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C7×#388C418yescomplemented
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
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
52#14512C711yesmaximal, characteristic, direct product factor, Sylow
53C25×C7C2311yescharacteristic
54C23×C4×C7C2311yescharacteristic
55C23×C4×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
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—41no—
71C2×C7×C4⋊C4—41no—
72C2×C7×C4⋊C4—41no—
73C2×C7×C4⋊C4—41no—
74C2×C7×C4⋊C4—41no—
75C2×C7×C4⋊C4—41no—
76C2×C7×C4⋊C4C2×C414yes—
77C2×C7×C22⋊C4—22no—
78C2×C7×C22⋊C4—22no—
79C2×C7×C22⋊C4—22no—
80C2×C7×C22⋊C4—22no—
81C2×C7×C22⋊C4—22no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—41no—
84C2×C7×C22⋊C4—41no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4—41no—
87C2×C7×C22⋊C4—41no—
88C2×C7×C22⋊C4—41no—
89C2×C7×C22⋊C4—41no—
90C2×C7×C22⋊C4—41no—
91C2×C7×C22⋊C4—41no—
92C2×C7×C22⋊C4—41no—
93C2×C7×C22⋊C4—41no—
94C2×C7×C22⋊C4—41no—
95C2×C7×C22⋊C4C2×C414yes—
96C2×C7×C22⋊C4C2×C414yes—
97C2×C7×C22⋊C4C2×C414yes—
98C2×C42×C7—22no—
99C2×C42×C7—22no—
100C2×C42×C7—22no—
101C2×C42×C7—41no—
102C2×C42×C7—41no—
103C2×C42×C7—41no—
104C2×C42×C7—41no—
105C2×C42×C7—41no—
106C2×C42×C7C2×C414yes—
107C7×#95—22no—
108C7×#95—22no—
109C7×#95—22no—
110C7×#95—22no—
111C7×#95—22no—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—41no—
115C7×#95—41no—
116C7×#95—41no—
117C7×#95—41no—
118C7×#95—41no—
119C7×#95—41no—
120C7×#95—41no—
121C7×#95—41no—
122C7×#95—41no—
123C7×#95—41no—
124C7×#95—41no—
125C7×#95—41no—
126C7×#95—41no—
127C7×#95C2×C414yes—
128C7×#95C2×C414yes—
129C2×#388C2×C711yescharacteristic
130#1442C2×C711yescharacteristic, complemented
131#1441C2×C711yescharacteristic, complemented
132#1440C2×C711yescharacteristic
133#1440C2×C711yescharacteristic
134#1439C2×C711yescharacteristic
135#1439C2×C711yescharacteristic
136#1437C2×C711yescharacteristic
137#1437C2×C711yescharacteristic
138#1436C2×C711yescharacteristic, complemented
139C4⋊#95C2×C711yescharacteristic, complemented
140#1434C2×C711yescharacteristic, complemented
141#1434C2×C711yescharacteristic, complemented
142#1434C2×C711yescharacteristic, complemented
143#1434C2×C711yescharacteristic, complemented
144C24×C7—21no—
145C24×C7—21no—
146C24×C7—21no—
147C24×C7—21no—
148C24×C7—21no—
149C24×C7—21no—
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×C7C22×C412yes—
159C24×C7C2411yescharacteristic
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
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×C7C22×C412yes—
247C22×C4×C7C22×C412yes—
248C22×C4×C7C22×C412yes—
249C22×C4×C7C22×C412yes—
250C22×C4×C7C22×C412yes—
251C22×C4×C7C22×C412yes—
252C22×C4×C7#4112yes—
253C22×C4×C7#4112yes—
254C22×C4×C7#4112yes—
255C22×C4×C7#4112yes—
256C22×C4×C7#4112yes—
257C22×C4×C7#4112yes—
258C7×C4⋊C4—44no—
259C7×C4⋊C4—44no—
260C7×C4⋊C4—44no—
261C7×C22⋊C4—28no—
262C7×C22⋊C4—44no—
263C7×C22⋊C4—44no—
264C7×C22⋊C4—44no—
265C7×C22⋊C4—44no—
266C7×C22⋊C4—44no—
267C7×C22⋊C4—44no—
268C42×C7—44no—
269C42×C7—44no—
270C42×C7—44no—
271C22×C4⋊C4C22×C711yescharacteristic
272C22×C4⋊C4C22×C711yescharacteristic
273C22×C4⋊C4C22×C711yescharacteristic
274C22×C22⋊C4C22×C711yescharacteristic
275C22×C22⋊C4C22×C711yescharacteristic
276C22×C22⋊C4C22×C711yescharacteristic
277C22×C22⋊C4C22×C711yescharacteristic
278C22×C22⋊C4C22×C711yescharacteristic
279C22×C22⋊C4C22×C711yescharacteristic
280C22×C22⋊C4C22×C711yescharacteristic
281C22×C42C22×C711yescharacteristic
282C22×C42C22×C711yescharacteristic
283C22×C42C22×C711yescharacteristic
284#388C4×C718yescomplemented
285C2×#95C22×C711yescharacteristic
286C2×#95C22×C711yescharacteristic
287C2×#95C22×C711yescharacteristic
288C2×#95C22×C711yescharacteristic
289C2×#95C22×C711yescharacteristic
290C2×#95C22×C711yescharacteristic
291C2×#95C22×C711yescharacteristic
292C2×#95C22×C711yescharacteristic
293C2×#95C22×C711yescharacteristic
294C2×#95C22×C711yescharacteristic
295C2×#95C22×C711yescharacteristic
296C2×#95C22×C711yescharacteristic
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
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—41no—
323C23×C7—41no—
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×C7C23×C411yescharacteristic
343C23×C7C2×#4111yescharacteristic
344C23×C7C2×#4111yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C7H(5,𝔽2)11yescharacteristic
352C23×C7H(5,𝔽2)11yescharacteristic
353C23×C7H(5,𝔽2)11yescharacteristic
354C23×C7H(5,𝔽2)11yescharacteristic
355C23×C72−1+411yescharacteristic
356C23×C72−1+411yescharacteristic
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
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—41no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7—41no—
398C2×C4×C7—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
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#11714yes—
455C25C23×C711yescharacteristic
456C23×C4C23×C711yescharacteristic
457C23×C4C23×C711yescharacteristic
458C23×C4C23×C711yescharacteristic
459C23×C4C23×C711yescharacteristic
460C23×C4C23×C711yescharacteristic
461C23×C4C23×C711yescharacteristic
462C23×C4C23×C711yescharacteristic
463C23×C4C23×C711yescharacteristic
464C23×C4C23×C711yescharacteristic
465C23×C4C23×C711yescharacteristic
466C23×C4C23×C711yescharacteristic
467C23×C4C23×C711yescharacteristic
468C23×C4C23×C711yescharacteristic
469C23×C4C23×C711yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—41no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4C2×C4×C714yes—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—41no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—41no—
489C2×C22⋊C4—41no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—41no—
495C2×C22⋊C4—41no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4C2×C4×C714yes—
498C2×C22⋊C4C2×C4×C714yes—
499C2×C22⋊C4C2×C4×C714yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—41no—
504C2×C42—41no—
505C2×C42—41no—
506C2×C42—41no—
507C2×C42—41no—
508C2×C42C2×C4×C714yes—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—41no—
517#95—41no—
518#95—41no—
519#95—41no—
520#95—41no—
521#95—41no—
522#95—41no—
523#95—41no—
524#95—41no—
525#95—41no—
526#95—41no—
527#95—41no—
528#95—41no—
529#95C2×C4×C714yes—
530#95C2×C4×C714yes—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—81no—
539C22×C7—81no—
540C22×C7—81no—
541C22×C7—81no—
542C22×C7—81no—
543C22×C7—81no—
544C22×C7—81no—
545C22×C7—81no—
546C22×C7C2×#11711yescharacteristic
547C22×C7C4×#4111yescharacteristic
548C22×C7C4×#4111yescharacteristic
549C22×C7#51811yescharacteristic
550C22×C7#51811yescharacteristic
551C22×C7#52011yescharacteristic
552C22×C7#52011yescharacteristic
553C22×C7#53811yescharacteristic
554C22×C7#53811yescharacteristic
555C22×C7#53811yescharacteristic
556C22×C7#53911yescharacteristic
557C22×C7#54011yescharacteristic
558C22×C7#54011yescharacteristic
559C22×C7#54111yescharacteristic
560C22×C7#54211yescharacteristic
561C22×C7#54211yescharacteristic
562C22×C7#54211yescharacteristic
563C22×C7#54211yescharacteristic
564C22×C7#54211yescharacteristic
565C22×C7#55111yescharacteristic
566C22×C7#55111yescharacteristic
567C22×C7#55111yescharacteristic
568C22×C7#55211yescharacteristic
569C22×C7#55211yescharacteristic
570C22×C7#55311yescharacteristic
571C22×C7#55311yescharacteristic
572C22×C7#55311yescharacteristic
573C22×C7#55311yescharacteristic
574C22×C7#55511yescharacteristic
575C22×C7#55511yescharacteristic
576C22×C7#55911yescharacteristic
577C22×C7#56011yescharacteristic
578C22×C7#56011yescharacteristic
579C22×C7#56211yescharacteristic
580C22×C7#56211yescharacteristic
581C4×C7—24no—
582C4×C7—42no—
583C4×C7—42no—
584C4×C7—42no—
585C4×C7—42no—
586C4×C7—42no—
587C4×C7—42no—
588C4×C7—42no—
589C4×C7—42no—
590C4×C7—42no—
591C4×C7—81no—
592C4×C7—81no—
593C4×C7—81no—
594C4×C7—81no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24C22×C4×C712yes—
610C24C24×C711yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
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×C4C22×C4×C712yes—
698C22×C4C22×C4×C712yes—
699C22×C4C22×C4×C712yes—
700C22×C4C22×C4×C712yes—
701C22×C4C22×C4×C712yes—
702C22×C4C22×C4×C712yes—
703C22×C4C7×#4112yes—
704C22×C4C7×#4112yes—
705C22×C4C7×#4112yes—
706C22×C4C7×#4112yes—
707C22×C4C7×#4112yes—
708C22×C4C7×#4112yes—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C22⋊C4—28no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4—44no—
716C22⋊C4—44no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C42—44no—
720C42—44no—
721C42—44no—
722C2×C7—82no—
723C2×C7#231911yescharacteristic
724C2×C7#233411yescharacteristic
725C2×C7#233711yescharacteristic
726C2×C7#234611yescharacteristic
727C2×C7#235311yescharacteristic
728C2×C7#237411yescharacteristic
729C2×C7#237711yescharacteristic
730C2×C7#273711yescharacteristic
731C2×C7#274111yescharacteristic
732C2×C7#275411yescharacteristic
733C2×C7#275611yescharacteristic
734C2×C7#276111yescharacteristic
735C2×C7#277211yescharacteristic
736C2×C7#279511yescharacteristic
737C2×C7#280311yescharacteristic
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23C23×C4×C711yescharacteristic
774C23C2×C7×#4111yescharacteristic
775C23C2×C7×#4111yescharacteristic
776C23C2×C7×#4111yescharacteristic
777C23C2×C7×#4111yescharacteristic
778C23C2×C7×#4111yescharacteristic
779C23C2×C7×#4111yescharacteristic
780C23C7×H(5,𝔽2)11yescharacteristic
781C23C7×H(5,𝔽2)11yescharacteristic
782C23C7×H(5,𝔽2)11yescharacteristic
783C23C7×H(5,𝔽2)11yescharacteristic
784C23C7×H(5,𝔽2)11yescharacteristic
785C23C7×H(5,𝔽2)11yescharacteristic
786C23C7×2−1+411yescharacteristic
787C23C7×2−1+411yescharacteristic
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
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—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
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×C4C7×#11714yes—
886C7#1451211yescharacteristic, direct product factor, Sylow
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22C2×C7×#11711yescharacteristic
903C22C4×C7×#4111yescharacteristic
904C22C4×C7×#4111yescharacteristic
905C22C7×#51811yescharacteristic
906C22C7×#51811yescharacteristic
907C22C7×#52011yescharacteristic
908C22C7×#52011yescharacteristic
909C22C7×#53811yescharacteristic
910C22C7×#53811yescharacteristic
911C22C7×#53811yescharacteristic
912C22C7×#53911yescharacteristic
913C22C7×#54011yescharacteristic
914C22C7×#54011yescharacteristic
915C22C7×#54111yescharacteristic
916C22C7×#54211yescharacteristic
917C22C7×#54211yescharacteristic
918C22C7×#54211yescharacteristic
919C22C7×#54211yescharacteristic
920C22C7×#54211yescharacteristic
921C22C7×#55111yescharacteristic
922C22C7×#55111yescharacteristic
923C22C7×#55111yescharacteristic
924C22C7×#55211yescharacteristic
925C22C7×#55211yescharacteristic
926C22C7×#55311yescharacteristic
927C22C7×#55311yescharacteristic
928C22C7×#55311yescharacteristic
929C22C7×#55311yescharacteristic
930C22C7×#55511yescharacteristic
931C22C7×#55511yescharacteristic
932C22C7×#55911yescharacteristic
933C22C7×#56011yescharacteristic
934C22C7×#56011yescharacteristic
935C22C7×#56211yescharacteristic
936C22C7×#56211yescharacteristic
937C4—24no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—81no—
948C4—81no—
949C4—81no—
950C4—81no—
951C2—82no—
952C2C7×#231911yescharacteristic
953C2C7×#233411yescharacteristic
954C2C7×#233711yescharacteristic
955C2C7×#234611yescharacteristic
956C2C7×#235311yescharacteristic
957C2C7×#237411yescharacteristic
958C2C7×#237711yescharacteristic
959C2C7×#273711yescharacteristic
960C2C7×#274111yescharacteristic
961C2C7×#275411yescharacteristic
962C2C7×#275611yescharacteristic
963C2C7×#276111yescharacteristic
964C2C7×#277211yescharacteristic
965C2C7×#279511yescharacteristic
966C2C7×#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
2. C7×#1442C2semidirect
3. C7×#1441C2semidirect
10. C7×#1436C2semidirect
11. C7×C4⋊#95C2semidirect
12. C7×#1434C2semidirect
13. C7×#1434C2semidirect
14. C7×#1434C2semidirect
15. C7×#1434C2semidirect
29. C7×#388C4semidirect
52. #14512C7direct (N × H)
130. #1442C2×C7semidirect
131. #1441C2×C7semidirect
138. #1436C2×C7semidirect
139. C4⋊#95C2×C7semidirect
140. #1434C2×C7semidirect
141. #1434C2×C7semidirect
142. #1434C2×C7semidirect
143. #1434C2×C7semidirect
284. #388C4×C7semidirect
886. C7#14512direct (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
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×#14372
C7×#14362
C7×C4⋊#952
C7×#14342
#145127