Finite Group Databasebeta

← C7×#15131 #13192347

Subgroups — C7×#15131 #13192347

Order 1792.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#396C212yesmaximal
2C2×C7×#389C211yesmaximal, characteristic, complemented
3C2×C7×#389C211yesmaximal, characteristic, complemented
4C2×C7×#384C211yesmaximal, characteristic, complemented
5C2×C7×#380C211yesmaximal, characteristic
6C2×C7×#380C211yesmaximal, characteristic
7C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
8C7×#1441C212yesmaximal, complemented
9C7×#1441C212yesmaximal, complemented
10C7×#1439C212yesmaximal
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C7C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2212yes—
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2212yes—
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C7×#396—28no—
28C7×#389—24no—
29C7×#389—24no—
30C7×#384—24no—
31C7×#380—24no—
32C7×#380—24no—
33C4×C7×C22⋊C4—24no—
34C2×C7×#95C2212yes—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42#15131C711yesmaximal, characteristic, direct product factor, Sylow
43C25×C7C2311yescharacteristic
44C23×C4×C7—22no—
45C23×C4×C7—22no—
46C23×C4×C7—22no—
47C23×C4×C7—22no—
48C23×C4×C7—22no—
49C23×C4×C7—22no—
50C23×C4×C7Q814yes—
51C23×C4×C7C2312yes—
52C23×C4×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2312yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—24no—
71C2×C7×C4⋊C4—24no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—24no—
74C2×C7×C4⋊C4—24no—
75C2×C7×C4⋊C4—24no—
76C2×C7×C4⋊C4—24no—
77C2×C7×C4⋊C4—24no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—42no—
81C2×C7×C4⋊C4—42no—
82C2×C7×C4⋊C4—42no—
83C2×C7×C4⋊C4D414yes—
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—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—42no—
94C2×C7×C22⋊C4—42no—
95C2×C7×C22⋊C4D414yes—
96C2×C7×C22⋊C4Q814yes—
97C2×C42×C7—22no—
98C2×C42×C7—22no—
99C2×C42×C7—22no—
100C2×C42×C7—22no—
101C2×C42×C7—22no—
102C2×C42×C7D414yes—
103C7×#95—22no—
104C7×#95—22no—
105C7×#95—24no—
106C7×#95—24no—
107C7×#95—24no—
108C7×#95—24no—
109C7×#95—24no—
110C7×#95—42no—
111C2×#396C2×C712yes—
112C2×#389C2×C711yescharacteristic, complemented
113C2×#389C2×C711yescharacteristic, complemented
114C2×#384C2×C711yescharacteristic, complemented
115C2×#380C2×C711yescharacteristic
116C2×#380C2×C711yescharacteristic
117C2×C4×C22⋊C4C2×C711yescharacteristic
118#1441C2×C712yescomplemented
119#1441C2×C712yescomplemented
120#1439C2×C712yes—
121C4⋊#95C2×C711yescharacteristic, complemented
122C24×C7—21no—
123C24×C7—21no—
124C24×C7—21no—
125C24×C7—21no—
126C24×C7—21no—
127C24×C7—21no—
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—21no—
131C24×C7—21no—
132C24×C7—21no—
133C24×C7—21no—
134C24×C7C2×D412yes—
135C24×C7C2×Q812yes—
136C24×C7C2×Q812yes—
137C24×C7C2411yescharacteristic
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—21no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—21no—
176C22×C4×C7—28no—
177C22×C4×C7—28no—
178C22×C4×C7—28no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—44no—
194C22×C4×C7—44no—
195C22×C4×C7—44no—
196C22×C4×C7—44no—
197C22×C4×C7C2×D414yes—
198C22×C4×C7C2×D412yes—
199C22×C4×C7C2×D414yes—
200C22×C4×C7C2×D412yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D412yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D412yes—
206C22×C4×C7C2×Q812yes—
207C22×C4×C7C2×Q812yes—
208C22×C4×C7C2×Q812yes—
209C22×C4×C7C2×Q812yes—
210C22×C4×C7#4112yes—
211C22×C4×C7#4112yes—
212C22×C4×C7#4112yes—
213C22×C4×C7#4112yes—
214C22×C4×C7#4112yes—
215C7×C4⋊C4—28no—
216C7×C4⋊C4—28no—
217C7×C4⋊C4—48no—
218C7×C4⋊C4—48no—
219C7×C4⋊C4—48no—
220C7×C4⋊C4—48no—
221C7×C4⋊C4—44no—
222C7×C4⋊C4—44no—
223C7×C22⋊C4—28no—
224C7×C22⋊C4—28no—
225C7×C22⋊C4—48no—
226C7×C22⋊C4—48no—
227C42×C7—28no—
228C42×C7—44no—
229C24×C4C22×C711yescharacteristic
230C22×C4⋊C4C22×C712yes—
231C22×C4⋊C4C22×C711yescharacteristic
232C22×C4⋊C4C22×C711yescharacteristic
233C22×C4⋊C4C22×C712yes—
234C22×C4⋊C4C22×C712yes—
235C22×C4⋊C4C22×C712yes—
236C22×C4⋊C4C22×C711yescharacteristic
237C22×C4⋊C4C22×C711yescharacteristic
238C22×C22⋊C4C22×C712yes—
239C22×C22⋊C4C22×C712yes—
240C22×C22⋊C4C22×C711yescharacteristic
241C22×C22⋊C4C22×C711yescharacteristic
242C22×C42C22×C711yescharacteristic
243C22×C42C22×C711yescharacteristic
244#396—28no—
245#389—24no—
246#389—24no—
247#384—24no—
248#380—24no—
249#380—24no—
250C4×C22⋊C4—24no—
251C2×#95C22×C712yes—
252C2×#95C22×C712yes—
253C2×#95C22×C712yes—
254C2×#95C22×C711yescharacteristic
255C2×#95C22×C711yescharacteristic
256C2×#95C22×C712yes—
257C2×#95C22×C712yes—
258C2×#95C22×C712yes—
259C23×C7—22no—
260C23×C7—22no—
261C23×C7—22no—
262C23×C7—22no—
263C23×C7—22no—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—22no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—22no—
273C23×C7—22no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—41no—
278C23×C7—41no—
279C23×C7—41no—
280C23×C7—41no—
281C23×C7—41no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7—41no—
289C23×C7—41no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7C4⋊Q814yes—
294C23×C7C22×D411yescharacteristic
295C23×C7C22×D411yescharacteristic
296C23×C7C22×D411yescharacteristic
297C23×C7C22×D411yescharacteristic
298C23×C7C22×Q811yescharacteristic
299C23×C7C22×Q811yescharacteristic
300C23×C7C2×#4111yescharacteristic
301C23×C7C2×#4111yescharacteristic
302C23×C7C2×#4111yescharacteristic
303C23×C7C2×#4111yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C23×C7H(5,𝔽2)11yescharacteristic
306C23×C7H(5,𝔽2)11yescharacteristic
307C23×C72−1+411yescharacteristic
308C23×C72−1+411yescharacteristic
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—24no—
323C2×C4×C7—24no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—24no—
329C2×C4×C7—24no—
330C2×C4×C7—22no—
331C2×C4×C7—24no—
332C2×C4×C7—24no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—42no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—42no—
344C2×C4×C7—41no—
345C2×C4×C7—42no—
346C2×C4×C7—41no—
347C2×C4×C7—42no—
348C2×C4×C7—42no—
349C2×C4×C7—41no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—42no—
355C2×C4×C7—41no—
356C2×C4×C7—416no—
357C2×C4×C7—42no—
358C2×C4×C7—42no—
359C2×C4×C7—42no—
360C2×C4×C7—42no—
361C2×C4×C7—42no—
362C2×C4×C7—42no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7#12114yes—
372C2×C4×C7#12114yes—
373C2×C4×C7#12114yes—
374C2×C4×C7#12114yes—
375C2×C4×C7C22⋊Q814yes—
376C2×C4×C7C22⋊Q814yes—
377C2×C4×C7C22⋊Q814yes—
378C2×C4×C7C22⋊Q814yes—
379C2×C4×C7#12614yes—
380C25C23×C711yescharacteristic
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4C7×Q814yes—
388C23×C4C23×C712yes—
389C23×C4C23×C712yes—
390C23×C4C23×C712yes—
391C23×C4C23×C712yes—
392C23×C4C23×C711yescharacteristic
393C23×C4C23×C711yescharacteristic
394C23×C4C23×C711yescharacteristic
395C23×C4C23×C711yescharacteristic
396C23×C4C23×C711yescharacteristic
397C23×C4C23×C711yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4C7×D414yes—
421C2×C4⋊C4C7×D414yes—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4C7×D414yes—
433C2×C22⋊C4C7×Q814yes—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42C7×D414yes—
440#95—22no—
441#95—22no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—42no—
448C22×C7—24no—
449C22×C7—24no—
450C22×C7—24no—
451C22×C7—42no—
452C22×C7—42no—
453C22×C7—42no—
454C22×C7—42no—
455C22×C7—42no—
456C22×C7—42no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—42no—
461C22×C7—42no—
462C22×C7—42no—
463C22×C7C2×#12111yescharacteristic
464C22×C7C2×#12111yescharacteristic
465C22×C7C2×#12111yescharacteristic
466C22×C7C2×#12111yescharacteristic
467C22×C7C2×C22⋊Q811yescharacteristic
468C22×C7C2×C22⋊Q811yescharacteristic
469C22×C7C2×C22⋊Q811yescharacteristic
470C22×C7C2×C22⋊Q811yescharacteristic
471C22×C7C2×#12611yescharacteristic
472C22×C7C2×C4⋊Q811yescharacteristic
473C22×C7#53211yescharacteristic
474C22×C7#53311yescharacteristic
475C22×C7#53311yescharacteristic
476C22×C7#53711yescharacteristic
477C22×C7#53711yescharacteristic
478C22×C7#54011yescharacteristic
479C22×C7#54111yescharacteristic
480C22×C7#54411yescharacteristic
481C22×C7#54411yescharacteristic
482C22×C7D4211yescharacteristic
483C22×C7D4211yescharacteristic
484C22×C7#54611yescharacteristic
485C22×C7#54711yescharacteristic
486C22×C7#54711yescharacteristic
487C22×C7#54711yescharacteristic
488C22×C7#54811yescharacteristic
489C22×C7D4×Q811yescharacteristic
490C22×C7D4×Q811yescharacteristic
491C22×C7#55011yescharacteristic
492C22×C7#55211yescharacteristic
493C22×C7#55311yescharacteristic
494C22×C7#55411yescharacteristic
495C22×C7#55411yescharacteristic
496C22×C7#55511yescharacteristic
497C22×C7#55611yescharacteristic
498C4×C7—24no—
499C4×C7—24no—
500C4×C7—42no—
501C4×C7—44no—
502C4×C7—42no—
503C4×C7—44no—
504C4×C7—42no—
505C4×C7—82no—
506C4×C7—82no—
507C4×C7#39618yescomplemented
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24C2×C7×D412yes—
521C24C2×C7×Q812yes—
522C24C2×C7×Q812yes—
523C24C24×C711yescharacteristic
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4C2×C7×D414yes—
584C22×C4C2×C7×D412yes—
585C22×C4C2×C7×D414yes—
586C22×C4C2×C7×D412yes—
587C22×C4C2×C7×D412yes—
588C22×C4C2×C7×D412yes—
589C22×C4C2×C7×D412yes—
590C22×C4C2×C7×D412yes—
591C22×C4C2×C7×D412yes—
592C22×C4C2×C7×Q812yes—
593C22×C4C2×C7×Q812yes—
594C22×C4C2×C7×Q812yes—
595C22×C4C2×C7×Q812yes—
596C22×C4C7×#4112yes—
597C22×C4C7×#4112yes—
598C22×C4C7×#4112yes—
599C22×C4C7×#4112yes—
600C22×C4C7×#4112yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C42—28no—
614C42—44no—
615C2×C7—44no—
616C2×C7C2×#39611yescharacteristic
617C2×C7#241611yescharacteristic
618C2×C7#241711yescharacteristic
619C2×C7#242811yescharacteristic
620C2×C7#242911yescharacteristic
621C2×C7#243911yescharacteristic
622C2×C7#244011yescharacteristic
623C2×C7#244011yescharacteristic
624C2×C7#244111yescharacteristic
625C2×C7#249611yescharacteristic
626C2×C7#249711yescharacteristic
627C2×C7#253711yescharacteristic
628C2×C7#253811yescharacteristic
629C2×C7#262911yescharacteristic
630C2×C7#285711yescharacteristic
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23C7×C4⋊Q814yes—
666C23C22×C7×D411yescharacteristic
667C23C22×C7×D411yescharacteristic
668C23C22×C7×D411yescharacteristic
669C23C22×C7×D411yescharacteristic
670C23C22×C7×Q811yescharacteristic
671C23C22×C7×Q811yescharacteristic
672C23C2×C7×#4111yescharacteristic
673C23C2×C7×#4111yescharacteristic
674C23C2×C7×#4111yescharacteristic
675C23C2×C7×#4111yescharacteristic
676C23C2×C7×#4111yescharacteristic
677C23C7×H(5,𝔽2)11yescharacteristic
678C23C7×H(5,𝔽2)11yescharacteristic
679C23C7×2−1+411yescharacteristic
680C23C7×2−1+411yescharacteristic
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—416no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4C7×#12114yes—
744C2×C4C7×#12114yes—
745C2×C4C7×#12114yes—
746C2×C4C7×#12114yes—
747C2×C4C7×C22⋊Q814yes—
748C2×C4C7×C22⋊Q814yes—
749C2×C4C7×C22⋊Q814yes—
750C2×C4C7×C22⋊Q814yes—
751C2×C4C7×#12614yes—
752C7#1513111yescharacteristic, direct product factor, Sylow
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22C2×C7×#12111yescharacteristic
769C22C2×C7×#12111yescharacteristic
770C22C2×C7×#12111yescharacteristic
771C22C2×C7×#12111yescharacteristic
772C22C2×C7×C22⋊Q811yescharacteristic
773C22C2×C7×C22⋊Q811yescharacteristic
774C22C2×C7×C22⋊Q811yescharacteristic
775C22C2×C7×C22⋊Q811yescharacteristic
776C22C2×C7×#12611yescharacteristic
777C22C2×C7×C4⋊Q811yescharacteristic
778C22C7×#53211yescharacteristic
779C22C7×#53311yescharacteristic
780C22C7×#53311yescharacteristic
781C22C7×#53711yescharacteristic
782C22C7×#53711yescharacteristic
783C22C7×#54011yescharacteristic
784C22C7×#54111yescharacteristic
785C22C7×#54411yescharacteristic
786C22C7×#54411yescharacteristic
787C22C7×D4211yescharacteristic
788C22C7×D4211yescharacteristic
789C22C7×#54611yescharacteristic
790C22C7×#54711yescharacteristic
791C22C7×#54711yescharacteristic
792C22C7×#54711yescharacteristic
793C22C7×#54811yescharacteristic
794C22C7×D4×Q811yescharacteristic
795C22C7×D4×Q811yescharacteristic
796C22C7×#55011yescharacteristic
797C22C7×#55211yescharacteristic
798C22C7×#55311yescharacteristic
799C22C7×#55411yescharacteristic
800C22C7×#55411yescharacteristic
801C22C7×#55511yescharacteristic
802C22C7×#55611yescharacteristic
803C4—24no—
804C4—24no—
805C4—42no—
806C4—44no—
807C4—42no—
808C4—44no—
809C4—42no—
810C4—82no—
811C4—82no—
812C4C7×#39618yescomplemented
813C2—44no—
814C2C2×C7×#39611yescharacteristic
815C2C7×#241611yescharacteristic
816C2C7×#241711yescharacteristic
817C2C7×#242811yescharacteristic
818C2C7×#242911yescharacteristic
819C2C7×#243911yescharacteristic
820C2C7×#244011yescharacteristic
821C2C7×#244011yescharacteristic
822C2C7×#244111yescharacteristic
823C2C7×#249611yescharacteristic
824C2C7×#249711yescharacteristic
825C2C7×#253711yescharacteristic
826C2C7×#253811yescharacteristic
827C2C7×#262911yescharacteristic
828C2C7×#285711yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC25×C7C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#389C2semidirect
3. C2×C7×#389C2semidirect
4. C2×C7×#384C2semidirect
8. C7×#1441C2semidirect
9. C7×#1441C2semidirect
11. C7×C4⋊#95C2semidirect
42. #15131C7direct (N × H)
112. C2×#389C2×C7semidirect
113. C2×#389C2×C7semidirect
114. C2×#384C2×C7semidirect
118. #1441C2×C7semidirect
119. #1441C2×C7semidirect
121. C4⋊#95C2×C7semidirect
507. C4×C7#396semidirect
752. C7#15131direct (N × H)
812. C4C7×#396semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3962
C2×C7×#3892
C2×C7×#3842
C2×C7×#3802
C2×C4×C7×C22⋊C42
C7×#14412
C7×#14392
C7×C4⋊#952
#151317