Finite Group Databasebeta

← C7×#15133 #13192349

Subgroups — C7×#15133 #13192349

Order 1792.

1454 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#398C212yesmaximal
2C2×C7×#389C211yesmaximal, characteristic
3C2×C7×#389C211yesmaximal, characteristic
4C2×C7×#384C211yesmaximal, characteristic
5C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
6C7×#1441C212yesmaximal
7C7×#1441C212yesmaximal
8C7×#1441C212yesmaximal
9C7×C4⋊#95C211yesmaximal, characteristic
10C7×C4⋊#95C211yesmaximal, characteristic
11C7×C4⋊#95C211yesmaximal, characteristic
12C22×C7×C4⋊C4C2212yes—
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2211yescharacteristic
24C22×C42×C7C2211yescharacteristic
25C7×#398—28no—
26C7×#389—24no—
27C7×#389—24no—
28C7×#384—24no—
29C4×C7×C4⋊C4—24no—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40#15133C711yesmaximal, characteristic, direct product factor, Sylow
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2312yes—
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C2×C7×C4⋊C4—22no—
53C2×C7×C4⋊C4—22no—
54C2×C7×C4⋊C4—22no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—22no—
57C2×C7×C4⋊C4—22no—
58C2×C7×C4⋊C4—22no—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—24no—
61C2×C7×C4⋊C4—24no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—24no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—42no—
76C2×C7×C4⋊C4—42no—
77C2×C7×C4⋊C4—42no—
78C2×C7×C4⋊C4D414yes—
79C2×C7×C4⋊C4D414yes—
80C2×C7×C4⋊C4Q814yes—
81C2×C7×C4⋊C4Q814yes—
82C2×C42×C7—22no—
83C2×C42×C7—22no—
84C2×C42×C7—22no—
85C2×C42×C7—22no—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—22no—
89C2×C42×C7D414yes—
90C2×C42×C7Q814yes—
91C7×#95—22no—
92C7×#95—22no—
93C7×#95—24no—
94C7×#95—24no—
95C7×#95—24no—
96C7×#95—24no—
97C7×#95—24no—
98C7×#95—42no—
99C7×#95—42no—
100C7×#95—42no—
101C2×#398C2×C712yes—
102C2×#389C2×C711yescharacteristic
103C2×#389C2×C711yescharacteristic
104C2×#384C2×C711yescharacteristic
105C2×C4×C4⋊C4C2×C711yescharacteristic
106#1441C2×C712yes—
107#1441C2×C712yes—
108#1441C2×C712yes—
109C4⋊#95C2×C711yescharacteristic
110C4⋊#95C2×C711yescharacteristic
111C4⋊#95C2×C711yescharacteristic
112C24×C7C2411yescharacteristic
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—21no—
117C22×C4×C7—21no—
118C22×C4×C7—21no—
119C22×C4×C7—21no—
120C22×C4×C7—21no—
121C22×C4×C7—21no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—22no—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—22no—
131C22×C4×C7—22no—
132C22×C4×C7—21no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—22no—
139C22×C4×C7—22no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—22no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D414yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×D412yes—
173C22×C4×C7C2×D412yes—
174C22×C4×C7C2×D412yes—
175C22×C4×C7C2×D412yes—
176C22×C4×C7C2×D412yes—
177C22×C4×C7C2×Q812yes—
178C22×C4×C7C2×Q814yes—
179C22×C4×C7C2×Q812yes—
180C22×C4×C7C2×Q812yes—
181C22×C4×C7C2×Q812yes—
182C22×C4×C7C2×Q812yes—
183C22×C4×C7C2×Q812yes—
184C22×C4×C7C2×Q812yes—
185C22×C4×C7#4112yes—
186C22×C4×C7#4112yes—
187C22×C4×C7#4112yes—
188C22×C4×C7#4112yes—
189C22×C4×C7#4112yes—
190C7×C4⋊C4—28no—
191C7×C4⋊C4—28no—
192C7×C4⋊C4—28no—
193C7×C4⋊C4—28no—
194C7×C4⋊C4—48no—
195C7×C4⋊C4—48no—
196C7×C4⋊C4—48no—
197C7×C4⋊C4—48no—
198C7×C4⋊C4—44no—
199C7×C4⋊C4—44no—
200C42×C7—28no—
201C42×C7—28no—
202C42×C7—44no—
203C22×C4⋊C4C22×C712yes—
204C22×C4⋊C4C22×C711yescharacteristic
205C22×C4⋊C4C22×C711yescharacteristic
206C22×C4⋊C4C22×C712yes—
207C22×C4⋊C4C22×C712yes—
208C22×C4⋊C4C22×C712yes—
209C22×C4⋊C4C22×C711yescharacteristic
210C22×C4⋊C4C22×C711yescharacteristic
211C22×C4⋊C4C22×C711yescharacteristic
212C22×C4⋊C4C22×C711yescharacteristic
213C22×C42C22×C711yescharacteristic
214C22×C42C22×C711yescharacteristic
215C22×C42C22×C711yescharacteristic
216#398—28no—
217#389—24no—
218#389—24no—
219#384—24no—
220C4×C4⋊C4—24no—
221C2×#95C22×C712yes—
222C2×#95C22×C712yes—
223C2×#95C22×C712yes—
224C2×#95C22×C711yescharacteristic
225C2×#95C22×C711yescharacteristic
226C2×#95C22×C712yes—
227C2×#95C22×C712yes—
228C2×#95C22×C712yes—
229C2×#95C22×C712yes—
230C2×#95C22×C712yes—
231C23×C7C22×D411yescharacteristic
232C23×C7C22×D411yescharacteristic
233C23×C7C22×D411yescharacteristic
234C23×C7C22×Q811yescharacteristic
235C23×C7C22×Q811yescharacteristic
236C23×C7C22×Q811yescharacteristic
237C23×C7C2×#4111yescharacteristic
238C23×C7C2×#4111yescharacteristic
239C23×C7C2×#4111yescharacteristic
240C23×C7C2×#4111yescharacteristic
241C23×C7C2×#4111yescharacteristic
242C23×C7H(5,𝔽2)11yescharacteristic
243C23×C7H(5,𝔽2)11yescharacteristic
244C23×C72−1+411yescharacteristic
245C23×C72−1+411yescharacteristic
246C2×C4×C7—22no—
247C2×C4×C7—22no—
248C2×C4×C7—22no—
249C2×C4×C7—22no—
250C2×C4×C7—22no—
251C2×C4×C7—22no—
252C2×C4×C7—22no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—22no—
264C2×C4×C7—22no—
265C2×C4×C7—22no—
266C2×C4×C7—22no—
267C2×C4×C7—24no—
268C2×C4×C7—24no—
269C2×C4×C7—22no—
270C2×C4×C7—22no—
271C2×C4×C7—22no—
272C2×C4×C7—24no—
273C2×C4×C7—24no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—24no—
277C2×C4×C7—22no—
278C2×C4×C7—24no—
279C2×C4×C7—41no—
280C2×C4×C7—41no—
281C2×C4×C7—42no—
282C2×C4×C7—42no—
283C2×C4×C7—41no—
284C2×C4×C7—41no—
285C2×C4×C7—41no—
286C2×C4×C7—41no—
287C2×C4×C7—42no—
288C2×C4×C7—41no—
289C2×C4×C7—42no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—42no—
294C2×C4×C7—42no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—42no—
298C2×C4×C7—42no—
299C2×C4×C7—42no—
300C2×C4×C7—42no—
301C2×C4×C7—42no—
302C2×C4×C7—42no—
303C2×C4×C7—42no—
304C2×C4×C7—42no—
305C2×C4×C7—42no—
306C2×C4×C7—42no—
307C2×C4×C7—42no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—42no—
312C2×C4×C7—42no—
313C2×C4×C7#12114yes—
314C2×C4×C7#12114yes—
315C2×C4×C7C22⋊Q814yes—
316C2×C4×C7C22⋊Q814yes—
317C2×C4×C7C22⋊Q814yes—
318C2×C4×C7#12314yes—
319C2×C4×C7#12514yes—
320C2×C4×C7#12514yes—
321C2×C4×C7C4⋊Q814yes—
322C2×C4×C7C4⋊Q814yes—
323C23×C4C23×C712yes—
324C23×C4C23×C712yes—
325C23×C4C23×C712yes—
326C23×C4C23×C711yescharacteristic
327C23×C4C23×C712yes—
328C23×C4C23×C711yescharacteristic
329C23×C4C23×C711yescharacteristic
330C23×C4C23×C711yescharacteristic
331C23×C4C23×C711yescharacteristic
332C23×C4C23×C711yescharacteristic
333C23×C4C23×C711yescharacteristic
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4C7×D414yes—
361C2×C4⋊C4C7×D414yes—
362C2×C4⋊C4C7×Q814yes—
363C2×C4⋊C4C7×Q814yes—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42C7×D414yes—
372C2×C42C7×Q814yes—
373#95—22no—
374#95—22no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—42no—
381#95—42no—
382#95—42no—
383C22×C7C2×#12111yescharacteristic
384C22×C7C2×#12111yescharacteristic
385C22×C7C2×C22⋊Q811yescharacteristic
386C22×C7C2×C22⋊Q811yescharacteristic
387C22×C7C2×C22⋊Q811yescharacteristic
388C22×C7C2×#12311yescharacteristic
389C22×C7C2×#12511yescharacteristic
390C22×C7C2×#12511yescharacteristic
391C22×C7C2×C4⋊Q811yescharacteristic
392C22×C7C2×C4⋊Q811yescharacteristic
393C22×C7#53211yescharacteristic
394C22×C7#53311yescharacteristic
395C22×C7#53311yescharacteristic
396C22×C7#53711yescharacteristic
397C22×C7#53711yescharacteristic
398C22×C7#54011yescharacteristic
399C22×C7#54111yescharacteristic
400C22×C7#54411yescharacteristic
401C22×C7#54411yescharacteristic
402C22×C7D4211yescharacteristic
403C22×C7#54611yescharacteristic
404C22×C7#54711yescharacteristic
405C22×C7#54811yescharacteristic
406C22×C7D4×Q811yescharacteristic
407C22×C7D4×Q811yescharacteristic
408C22×C7#55011yescharacteristic
409C22×C7#55211yescharacteristic
410C22×C7#55311yescharacteristic
411C22×C7#55411yescharacteristic
412C22×C7#55411yescharacteristic
413C22×C7#55611yescharacteristic
414C22×C7#55711yescharacteristic
415C22×C7#55711yescharacteristic
416C22×C7Q8211yescharacteristic
417C22×C7#55911yescharacteristic
418C4×C7—24no—
419C4×C7—24no—
420C4×C7—24no—
421C4×C7—42no—
422C4×C7—42no—
423C4×C7—42no—
424C4×C7—44no—
425C4×C7—44no—
426C4×C7—82no—
427C4×C7—82no—
428C4×C7#39818yescomplemented
429C24C24×C711yescharacteristic
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4C2×C7×D412yes—
487C22×C4C2×C7×D414yes—
488C22×C4C2×C7×D412yes—
489C22×C4C2×C7×D412yes—
490C22×C4C2×C7×D412yes—
491C22×C4C2×C7×D412yes—
492C22×C4C2×C7×D412yes—
493C22×C4C2×C7×D412yes—
494C22×C4C2×C7×Q812yes—
495C22×C4C2×C7×Q814yes—
496C22×C4C2×C7×Q812yes—
497C22×C4C2×C7×Q812yes—
498C22×C4C2×C7×Q812yes—
499C22×C4C2×C7×Q812yes—
500C22×C4C2×C7×Q812yes—
501C22×C4C2×C7×Q812yes—
502C22×C4C7×#4112yes—
503C22×C4C7×#4112yes—
504C22×C4C7×#4112yes—
505C22×C4C7×#4112yes—
506C22×C4C7×#4112yes—
507C4⋊C4—28no—
508C4⋊C4—28no—
509C4⋊C4—28no—
510C4⋊C4—28no—
511C4⋊C4—48no—
512C4⋊C4—48no—
513C4⋊C4—48no—
514C4⋊C4—48no—
515C4⋊C4—44no—
516C4⋊C4—44no—
517C42—28no—
518C42—28no—
519C42—44no—
520C2×C7C2×#39811yescharacteristic
521C2×C7#241611yescharacteristic
522C2×C7#241711yescharacteristic
523C2×C7#244511yescharacteristic
524C2×C7#244611yescharacteristic
525C2×C7#250611yescharacteristic
526C2×C7#250711yescharacteristic
527C2×C7#253811yescharacteristic
528C2×C7#255011yescharacteristic
529C2×C7#255111yescharacteristic
530C2×C7#255211yescharacteristic
531C2×C7#257011yescharacteristic
532C2×C7#258211yescharacteristic
533C2×C7#262911yescharacteristic
534C2×C7#285711yescharacteristic
535C23C22×C7×D411yescharacteristic
536C23C22×C7×D411yescharacteristic
537C23C22×C7×D411yescharacteristic
538C23C22×C7×Q811yescharacteristic
539C23C22×C7×Q811yescharacteristic
540C23C22×C7×Q811yescharacteristic
541C23C2×C7×#4111yescharacteristic
542C23C2×C7×#4111yescharacteristic
543C23C2×C7×#4111yescharacteristic
544C23C2×C7×#4111yescharacteristic
545C23C2×C7×#4111yescharacteristic
546C23C7×H(5,𝔽2)11yescharacteristic
547C23C7×H(5,𝔽2)11yescharacteristic
548C23C7×2−1+411yescharacteristic
549C23C7×2−1+411yescharacteristic
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4C7×#12114yes—
618C2×C4C7×#12114yes—
619C2×C4C7×C22⋊Q814yes—
620C2×C4C7×C22⋊Q814yes—
621C2×C4C7×C22⋊Q814yes—
622C2×C4C7×#12314yes—
623C2×C4C7×#12514yes—
624C2×C4C7×#12514yes—
625C2×C4C7×C4⋊Q814yes—
626C2×C4C7×C4⋊Q814yes—
627C7#1513311yescharacteristic, direct product factor, Sylow
628C22C2×C7×#12111yescharacteristic
629C22C2×C7×#12111yescharacteristic
630C22C2×C7×C22⋊Q811yescharacteristic
631C22C2×C7×C22⋊Q811yescharacteristic
632C22C2×C7×C22⋊Q811yescharacteristic
633C22C2×C7×#12311yescharacteristic
634C22C2×C7×#12511yescharacteristic
635C22C2×C7×#12511yescharacteristic
636C22C2×C7×C4⋊Q811yescharacteristic
637C22C2×C7×C4⋊Q811yescharacteristic
638C22C7×#53211yescharacteristic
639C22C7×#53311yescharacteristic
640C22C7×#53311yescharacteristic
641C22C7×#53711yescharacteristic
642C22C7×#53711yescharacteristic
643C22C7×#54011yescharacteristic
644C22C7×#54111yescharacteristic
645C22C7×#54411yescharacteristic
646C22C7×#54411yescharacteristic
647C22C7×D4211yescharacteristic
648C22C7×#54611yescharacteristic
649C22C7×#54711yescharacteristic
650C22C7×#54811yescharacteristic
651C22C7×D4×Q811yescharacteristic
652C22C7×D4×Q811yescharacteristic
653C22C7×#55011yescharacteristic
654C22C7×#55211yescharacteristic
655C22C7×#55311yescharacteristic
656C22C7×#55411yescharacteristic
657C22C7×#55411yescharacteristic
658C22C7×#55611yescharacteristic
659C22C7×#55711yescharacteristic
660C22C7×#55711yescharacteristic
661C22C7×Q8211yescharacteristic
662C22C7×#55911yescharacteristic
663C4—24no—
664C4—24no—
665C4—24no—
666C4—42no—
667C4—42no—
668C4—44no—
669C4—44no—
670C4—42no—
671C4—82no—
672C4—82no—
673C4C7×#39818yescomplemented
674C2C2×C7×#39811yescharacteristic
675C2C7×#241611yescharacteristic
676C2C7×#241711yescharacteristic
677C2C7×#244511yescharacteristic
678C2C7×#244611yescharacteristic
679C2C7×#250611yescharacteristic
680C2C7×#250711yescharacteristic
681C2C7×#253811yescharacteristic
682C2C7×#255011yescharacteristic
683C2C7×#255111yescharacteristic
684C2C7×#255211yescharacteristic
685C2C7×#257011yescharacteristic
686C2C7×#258211yescharacteristic
687C2C7×#262911yescharacteristic
688C2C7×#285711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C7C24
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
40. #15133C7direct (N × H)
428. C4×C7#398semidirect
627. C7#15133direct (N × H)
673. C4C7×#398semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3982
C2×C7×#3892
C2×C7×#3842
C2×C4×C7×C4⋊C42
C7×#14412
C7×C4⋊#952
#151337