Finite Group Databasebeta

← C7×#14524 #13191740

Subgroups — C7×#14524 #13191740

Order 1792.

1402 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#395C211yesmaximal, characteristic
2C2×C7×#391C211yesmaximal, characteristic
3C2×C7×#391C211yesmaximal, characteristic
4C2×C7×#389C211yesmaximal, characteristic
5C2×C7×#387C211yesmaximal, characteristic
6C7×#1445C211yesmaximal, characteristic
7C7×#1442C211yesmaximal, characteristic
8C7×#1442C211yesmaximal, characteristic
9C7×#1441C211yesmaximal, characteristic
10C7×#1441C211yesmaximal, characteristic
11C7×#1436C211yesmaximal, characteristic
12C7×#1436C211yesmaximal, characteristic
13C7×#1436C211yesmaximal, characteristic
14C7×#1434C211yesmaximal, characteristic
15C7×#1434C211yesmaximal, characteristic
16C23×C7×Q8C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C7×#395C418yescomplemented
28C7×#391—24no—
29C7×#391—24no—
30C7×#389—24no—
31C7×#387—24no—
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
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56#14524C711yesmaximal, characteristic, direct product factor, Sylow
57C22×C7×Q8—22no—
58C22×C7×Q8—22no—
59C22×C7×Q8—22no—
60C22×C7×Q8—22no—
61C22×C7×Q8—41no—
62C22×C7×Q8—41no—
63C22×C7×Q8C2×C414yes—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—22no—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—22no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—41no—
92C2×C7×C4⋊C4—41no—
93C2×C7×C4⋊C4—41no—
94C2×C7×C4⋊C4—41no—
95C2×C7×C4⋊C4—41no—
96C2×C7×C4⋊C4—41no—
97C2×C7×C4⋊C4C2×C414yes—
98C2×C7×C4⋊C4C2×C414yes—
99C2×C7×C4⋊C4C2×C414yes—
100C2×C42×C7—22no—
101C2×C42×C7—22no—
102C2×C42×C7—22no—
103C2×C42×C7—22no—
104C2×C42×C7—22no—
105C2×C42×C7—22no—
106C2×C42×C7—41no—
107C2×C42×C7—41no—
108C2×C42×C7—41no—
109C7×#95—22no—
110C7×#95—22no—
111C7×#95—22no—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—22no—
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—
129C7×#95C2×C414yes—
130C7×#95D414yes—
131C7×#95D414yes—
132C7×#95Q814yescomplemented
133C2×#395C2×C711yescharacteristic
134C2×#391C2×C711yescharacteristic
135C2×#391C2×C711yescharacteristic
136C2×#389C2×C711yescharacteristic
137C2×#387C2×C711yescharacteristic
138#1445C2×C711yescharacteristic
139#1442C2×C711yescharacteristic
140#1442C2×C711yescharacteristic
141#1441C2×C711yescharacteristic
142#1441C2×C711yescharacteristic
143#1436C2×C711yescharacteristic
144#1436C2×C711yescharacteristic
145#1436C2×C711yescharacteristic
146#1434C2×C711yescharacteristic
147#1434C2×C711yescharacteristic
148C24×C7C2411yescharacteristic
149C2×C7×Q8—28no—
150C2×C7×Q8—28no—
151C2×C7×Q8—44no—
152C2×C7×Q8—44no—
153C2×C7×Q8—44no—
154C2×C7×Q8—44no—
155C2×C7×Q8—44no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
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×C7C22×C412yes—
243C22×C4×C7C22×C412yes—
244C22×C4×C7C22×C412yes—
245C22×C4×C7C22×C412yes—
246C22×C4×C7C22×C412yes—
247C22×C4×C7C22×C412yes—
248C22×C4×C7C22×C412yes—
249C22×C4×C7C2×D412yes—
250C22×C4×C7C2×D412yes—
251C22×C4×C7C2×D412yes—
252C22×C4×C7C2×D412yes—
253C22×C4×C7C2×D412yes—
254C22×C4×C7C2×D412yes—
255C22×C4×C7C2×Q812yes—
256C22×C4×C7C2×Q812yes—
257C22×C4×C7C2×Q812yes—
258C22×C4×C7#4112yes—
259C22×C4×C7#4112yes—
260C22×C4×C7#4112yes—
261C7×C4⋊C4—28no—
262C7×C4⋊C4—28no—
263C7×C4⋊C4—44no—
264C7×C4⋊C4—44no—
265C7×C4⋊C4—44no—
266C7×C4⋊C4—44no—
267C7×C4⋊C4—44no—
268C42×C7—44no—
269C42×C7—44no—
270C42×C7—44no—
271C23×Q8C22×C711yescharacteristic
272C22×C4⋊C4C22×C711yescharacteristic
273C22×C4⋊C4C22×C711yescharacteristic
274C22×C4⋊C4C22×C711yescharacteristic
275C22×C4⋊C4C22×C711yescharacteristic
276C22×C4⋊C4C22×C711yescharacteristic
277C22×C4⋊C4C22×C711yescharacteristic
278C22×C4⋊C4C22×C711yescharacteristic
279C22×C42C22×C711yescharacteristic
280C22×C42C22×C711yescharacteristic
281C22×C42C22×C711yescharacteristic
282#395C4×C718yescomplemented
283#391—24no—
284#391—24no—
285#389—24no—
286#387—24no—
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
307C2×#95C22×C711yescharacteristic
308C2×#95C22×C711yescharacteristic
309C2×#95C22×C711yescharacteristic
310C2×#95C22×C711yescharacteristic
311C23×C7C23×C411yescharacteristic
312C23×C7C22×D411yescharacteristic
313C23×C7C22×D411yescharacteristic
314C23×C7C22×Q811yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7H(5,𝔽2)11yescharacteristic
319C23×C7H(5,𝔽2)11yescharacteristic
320C23×C7H(5,𝔽2)11yescharacteristic
321C23×C72−1+411yescharacteristic
322C23×C72−1+411yescharacteristic
323C23×C72−1+411yescharacteristic
324C23×C72−1+411yescharacteristic
325C23×C72−1+411yescharacteristic
326C7×Q8—416no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
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—41no—
376C2×C4×C7—41no—
377C2×C4×C7—41no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—41no—
381C2×C4×C7—41no—
382C2×C4×C7—41no—
383C2×C4×C7—41no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7—41no—
387C2×C4×C7—41no—
388C2×C4×C7—41no—
389C2×C4×C7—41no—
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×C7C4×D414yes—
430C2×C4×C7C4×D414yes—
431C2×C4×C7C4×Q814yes—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C2×C4×C714yes—
439C23×C4C23×C711yescharacteristic
440C23×C4C23×C711yescharacteristic
441C23×C4C23×C711yescharacteristic
442C23×C4C23×C711yescharacteristic
443C23×C4C23×C711yescharacteristic
444C23×C4C23×C711yescharacteristic
445C23×C4C23×C711yescharacteristic
446C23×C4C23×C711yescharacteristic
447C23×C4C23×C711yescharacteristic
448C23×C4C23×C711yescharacteristic
449C23×C4C23×C711yescharacteristic
450C23×C4C23×C711yescharacteristic
451C23×C4C23×C711yescharacteristic
452C23×C4C23×C711yescharacteristic
453C23×C4C23×C711yescharacteristic
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—41no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4C2×C4×C714yes—
473C2×C4⋊C4C2×C4×C714yes—
474C2×C4⋊C4C2×C4×C714yes—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—41no—
482C2×C42—41no—
483C2×C42—41no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—41no—
496#95—41no—
497#95—41no—
498#95—41no—
499#95—41no—
500#95—41no—
501#95—41no—
502#95C2×C4×C714yes—
503#95C2×C4×C714yes—
504#95C2×C4×C714yes—
505#95C7×D414yes—
506#95C7×D414yes—
507#95C7×Q814yescomplemented
508C22×C7C2×C4×D411yescharacteristic
509C22×C7C2×C4×D411yescharacteristic
510C22×C7C2×C4×Q811yescharacteristic
511C22×C7#51811yescharacteristic
512C22×C7#51911yescharacteristic
513C22×C7#51911yescharacteristic
514C22×C7#52011yescharacteristic
515C22×C7#53611yescharacteristic
516C22×C7#53611yescharacteristic
517C22×C7#53611yescharacteristic
518C22×C7#53711yescharacteristic
519C22×C7#54111yescharacteristic
520C22×C7#54111yescharacteristic
521C22×C7#54111yescharacteristic
522C22×C7#54211yescharacteristic
523C22×C7#54211yescharacteristic
524C22×C7#54211yescharacteristic
525C22×C7#54411yescharacteristic
526C22×C7#54411yescharacteristic
527C22×C7D4211yescharacteristic
528C22×C7#54611yescharacteristic
529C22×C7#54611yescharacteristic
530C22×C7#54611yescharacteristic
531C22×C7#54711yescharacteristic
532C22×C7D4×Q811yescharacteristic
533C22×C7D4×Q811yescharacteristic
534C22×C7#55111yescharacteristic
535C22×C7#55211yescharacteristic
536C22×C7#55411yescharacteristic
537C22×C7#55611yescharacteristic
538C22×C7#55711yescharacteristic
539C22×C7#56211yescharacteristic
540C22×C7#56211yescharacteristic
541C22×C7#56311yescharacteristic
542C22×C7#56311yescharacteristic
543C4×C7—24no—
544C4×C7—24no—
545C4×C7—24no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7—42no—
556C4×C7—81no—
557C4×C7—81no—
558C24C24×C711yescharacteristic
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—44no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
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×C4C22×C4×C712yes—
653C22×C4C22×C4×C712yes—
654C22×C4C22×C4×C712yes—
655C22×C4C22×C4×C712yes—
656C22×C4C22×C4×C712yes—
657C22×C4C22×C4×C712yes—
658C22×C4C22×C4×C712yes—
659C22×C4C2×C7×D412yes—
660C22×C4C2×C7×D412yes—
661C22×C4C2×C7×D412yes—
662C22×C4C2×C7×D412yes—
663C22×C4C2×C7×D412yes—
664C22×C4C2×C7×D412yes—
665C22×C4C2×C7×Q812yes—
666C22×C4C2×C7×Q812yes—
667C22×C4C2×C7×Q812yes—
668C22×C4C7×#4112yes—
669C22×C4C7×#4112yes—
670C22×C4C7×#4112yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C42—44no—
679C42—44no—
680C42—44no—
681C2×C7#232311yescharacteristic
682C2×C7#232711yescharacteristic
683C2×C7#233111yescharacteristic
684C2×C7#235811yescharacteristic
685C2×C7#236011yescharacteristic
686C2×C7#236511yescharacteristic
687C2×C7#237811yescharacteristic
688C2×C7#267211yescharacteristic
689C2×C7#267711yescharacteristic
690C2×C7#269811yescharacteristic
691C2×C7#270011yescharacteristic
692C2×C7#270411yescharacteristic
693C2×C7#271311yescharacteristic
694C2×C7#275511yescharacteristic
695C2×C7#275811yescharacteristic
696C23C23×C4×C711yescharacteristic
697C23C22×C7×D411yescharacteristic
698C23C22×C7×D411yescharacteristic
699C23C22×C7×Q811yescharacteristic
700C23C2×C7×#4111yescharacteristic
701C23C2×C7×#4111yescharacteristic
702C23C2×C7×#4111yescharacteristic
703C23C7×H(5,𝔽2)11yescharacteristic
704C23C7×H(5,𝔽2)11yescharacteristic
705C23C7×H(5,𝔽2)11yescharacteristic
706C23C7×2−1+411yescharacteristic
707C23C7×2−1+411yescharacteristic
708C23C7×2−1+411yescharacteristic
709C23C7×2−1+411yescharacteristic
710C23C7×2−1+411yescharacteristic
711Q8—416no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4C4×C7×D414yes—
815C2×C4C4×C7×D414yes—
816C2×C4C4×C7×Q814yes—
817C7#1452411yescharacteristic, direct product factor, Sylow
818C22C2×C4×C7×D411yescharacteristic
819C22C2×C4×C7×D411yescharacteristic
820C22C2×C4×C7×Q811yescharacteristic
821C22C7×#51811yescharacteristic
822C22C7×#51911yescharacteristic
823C22C7×#51911yescharacteristic
824C22C7×#52011yescharacteristic
825C22C7×#53611yescharacteristic
826C22C7×#53611yescharacteristic
827C22C7×#53611yescharacteristic
828C22C7×#53711yescharacteristic
829C22C7×#54111yescharacteristic
830C22C7×#54111yescharacteristic
831C22C7×#54111yescharacteristic
832C22C7×#54211yescharacteristic
833C22C7×#54211yescharacteristic
834C22C7×#54211yescharacteristic
835C22C7×#54411yescharacteristic
836C22C7×#54411yescharacteristic
837C22C7×D4211yescharacteristic
838C22C7×#54611yescharacteristic
839C22C7×#54611yescharacteristic
840C22C7×#54611yescharacteristic
841C22C7×#54711yescharacteristic
842C22C7×D4×Q811yescharacteristic
843C22C7×D4×Q811yescharacteristic
844C22C7×#55111yescharacteristic
845C22C7×#55211yescharacteristic
846C22C7×#55411yescharacteristic
847C22C7×#55611yescharacteristic
848C22C7×#55711yescharacteristic
849C22C7×#56211yescharacteristic
850C22C7×#56211yescharacteristic
851C22C7×#56311yescharacteristic
852C22C7×#56311yescharacteristic
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—81no—
867C4—81no—
868C2C7×#232311yescharacteristic
869C2C7×#232711yescharacteristic
870C2C7×#233111yescharacteristic
871C2C7×#235811yescharacteristic
872C2C7×#236011yescharacteristic
873C2C7×#236511yescharacteristic
874C2C7×#237811yescharacteristic
875C2C7×#267211yescharacteristic
876C2C7×#267711yescharacteristic
877C2C7×#269811yescharacteristic
878C2C7×#270011yescharacteristic
879C2C7×#270411yescharacteristic
880C2C7×#271311yescharacteristic
881C2C7×#275511yescharacteristic
882C2C7×#275811yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
27. C7×#395C4semidirect
56. #14524C7direct (N × H)
132. C7×#95Q8semidirect
282. #395C4×C7semidirect
507. #95C7×Q8semidirect
817. C7#14524direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3952
C2×C7×#3912
C2×C7×#3892
C2×C7×#3872
C7×#14452
C7×#14422
C7×#14412
C7×#14362
C7×#14342
#145247