Finite Group Databasebeta

← C7×#13969 #13191185

Subgroups — C7×#13969 #13191185

Order 1792.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic
2C22×C4×C7×Q8C211yesmaximal, characteristic, complemented
3C2×C7×#391C211yesmaximal, characteristic, complemented
4C2×C7×#380C211yesmaximal, characteristic
5C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
6C7×#1441C212yesmaximal, complemented
7C7×#1439C212yesmaximal
8C7×#1437C212yesmaximal
9C7×#1436C212yesmaximal, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×Q8C2211yescharacteristic
13C24×C4×C7C2211yescharacteristic
14C2×C7×C22⋊Q8—24no—
15C2×C7×C22⋊Q8—24no—
16C2×C7×C22⋊Q8C418yescomplemented
17C2×C4×C7×Q8—24no—
18C2×C4×C7×Q8—24no—
19C2×C4×C7×Q8—24no—
20C22×C7×C4⋊C4C2212yes—
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2212yes—
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C42×C7C2212yes—
30C22×C42×C7C2211yescharacteristic
31C22×C42×C7C2211yescharacteristic
32C7×#391—24no—
33C7×#380—24no—
34C4×C7×C22⋊C4—24no—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43C2×C7×#95C2212yes—
44#13969C711yesmaximal, characteristic, direct product factor, Sylow
45C25×C7C2311yescharacteristic
46C22×C7×Q8—22no—
47C22×C7×Q8—22no—
48C22×C7×Q8—22no—
49C22×C7×Q8—22no—
50C22×C7×Q8C2×C414yes—
51C22×C7×Q8D414yes—
52C22×C7×Q8D414yes—
53C23×C4×C7—22no—
54C23×C4×C7—22no—
55C23×C4×C7—22no—
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7C2×C414yes—
60C23×C4×C7C2312yes—
61C23×C4×C7C2312yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2312yes—
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2312yes—
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C7×C22⋊Q8—232no—
71C4×C7×Q8—232no—
72C2×C7×C4⋊C4—24no—
73C2×C7×C4⋊C4—24no—
74C2×C7×C4⋊C4—24no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—24no—
80C2×C7×C4⋊C4—24no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4C2×C414yes—
85C2×C7×C4⋊C4C2×C418yes—
86C2×C7×C4⋊C4D414yes—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—42no—
97C2×C7×C22⋊C4C2×C418yes—
98C2×C7×C22⋊C4Q814yescomplemented
99C2×C42×C7—24no—
100C2×C42×C7—24no—
101C2×C42×C7—24no—
102C2×C42×C7—22no—
103C2×C42×C7—22no—
104C2×C42×C7—22no—
105C2×C42×C7—22no—
106C2×C42×C7—22no—
107C2×C42×C7D414yes—
108C7×#95—22no—
109C7×#95—22no—
110C7×#95—24no—
111C7×#95—24no—
112C7×#95—24no—
113C7×#95—24no—
114C7×#95—24no—
115C7×#95—42no—
116C7×#95—42no—
117C22×C22⋊Q8C2×C711yescharacteristic
118C22×C4×Q8C2×C711yescharacteristic, complemented
119C2×#391C2×C711yescharacteristic, complemented
120C2×#380C2×C711yescharacteristic
121C2×C4×C22⋊C4C2×C711yescharacteristic
122#1441C2×C712yescomplemented
123#1439C2×C712yes—
124#1437C2×C712yes—
125#1436C2×C712yescomplemented
126C4⋊#95C2×C711yescharacteristic, complemented
127C4⋊#95C2×C711yescharacteristic, complemented
128C24×C7—21no—
129C24×C7—21no—
130C24×C7—21no—
131C24×C7—21no—
132C24×C7—21no—
133C24×C7—21no—
134C24×C7—21no—
135C24×C7—21no—
136C24×C7—21no—
137C24×C7—21no—
138C24×C7—21no—
139C24×C7—21no—
140C24×C7C22×C412yes—
141C24×C7C2×Q812yes—
142C24×C7#4112yes—
143C24×C7C2411yescharacteristic
144C2×C7×Q8—28no—
145C2×C7×Q8—28no—
146C2×C7×Q8—28no—
147C2×C7×Q8—28no—
148C2×C7×Q8—28no—
149C2×C7×Q8—28no—
150C2×C7×Q8C22⋊C4116yescomplemented
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—22no—
154C22×C4×C7—22no—
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—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—22no—
166C22×C4×C7—21no—
167C22×C4×C7—22no—
168C22×C4×C7—21no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
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—22no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—22no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—21no—
191C22×C4×C7—22no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—28no—
196C22×C4×C7—28no—
197C22×C4×C7—28no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—44no—
206C22×C4×C7—44no—
207C22×C4×C7—44no—
208C22×C4×C7—44no—
209C22×C4×C7C22×C414yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C22×C414yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C2×D414yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×D414yes—
216C22×C4×C7C2×D414yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×Q812yes—
223C22×C4×C7C2×Q812yes—
224C22×C4×C7#4112yes—
225C22×C4×C7#4112yes—
226C22×C4×C7#4112yes—
227C22×C4×C7#4112yes—
228C7×C4⋊C4—216no—
229C7×C4⋊C4—28no—
230C7×C4⋊C4—216no—
231C7×C4⋊C4—28no—
232C7×C4⋊C4—44no—
233C7×C22⋊C4—28no—
234C7×C22⋊C4—216no—
235C7×C22⋊C4—28no—
236C7×C22⋊C4—48no—
237C42×C7—216no—
238C42×C7—28no—
239C42×C7—44no—
240C23×Q8C22×C711yescharacteristic
241C24×C4C22×C711yescharacteristic
242C2×C22⋊Q8—24no—
243C2×C22⋊Q8—24no—
244C2×C22⋊Q8C4×C718yescomplemented
245C2×C4×Q8—24no—
246C2×C4×Q8—24no—
247C2×C4×Q8—24no—
248C22×C4⋊C4C22×C712yes—
249C22×C4⋊C4C22×C711yescharacteristic
250C22×C4⋊C4C22×C711yescharacteristic
251C22×C4⋊C4C22×C712yes—
252C22×C4⋊C4C22×C711yescharacteristic
253C22×C22⋊C4C22×C711yescharacteristic
254C22×C22⋊C4C22×C712yes—
255C22×C22⋊C4C22×C712yes—
256C22×C22⋊C4C22×C711yescharacteristic
257C22×C42C22×C712yes—
258C22×C42C22×C711yescharacteristic
259C22×C42C22×C711yescharacteristic
260#391—24no—
261#380—24no—
262C4×C22⋊C4—24no—
263C2×#95C22×C712yes—
264C2×#95C22×C712yes—
265C2×#95C22×C711yescharacteristic
266C2×#95C22×C712yes—
267C2×#95C22×C712yes—
268C2×#95C22×C712yes—
269C2×#95C22×C711yescharacteristic
270C2×#95C22×C712yes—
271C2×#95C22×C712yes—
272C23×C7—22no—
273C23×C7—22no—
274C23×C7—22no—
275C23×C7—22no—
276C23×C7—22no—
277C23×C7—22no—
278C23×C7—22no—
279C23×C7—22no—
280C23×C7—22no—
281C23×C7—22no—
282C23×C7—22no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—22no—
287C23×C7—22no—
288C23×C7—22no—
289C23×C7—22no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—41no—
297C23×C7—41no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—41no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7C4×Q814yescomplemented
307C23×C7C23×C411yescharacteristic
308C23×C7C22×D411yescharacteristic
309C23×C7C22×D411yescharacteristic
310C23×C7C22×D411yescharacteristic
311C23×C7C22×D411yescharacteristic
312C23×C7C22×Q811yescharacteristic
313C23×C7C2×#4111yescharacteristic
314C23×C7C2×#4111yescharacteristic
315C23×C7C2×#4111yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7H(5,𝔽2)11yescharacteristic
319C23×C72−1+411yescharacteristic
320C23×C72−1+411yescharacteristic
321C23×C72−1+411yescharacteristic
322C7×Q8—232no—
323C2×C4×C7—24no—
324C2×C4×C7—24no—
325C2×C4×C7—22no—
326C2×C4×C7—24no—
327C2×C4×C7—24no—
328C2×C4×C7—24no—
329C2×C4×C7—24no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—24no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—24no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—24no—
348C2×C4×C7—24no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—42no—
360C2×C4×C7—41no—
361C2×C4×C7—42no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—41no—
368C2×C4×C7—42no—
369C2×C4×C7—41no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—41no—
377C2×C4×C7—416no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7C2×C22⋊C418yes—
386C2×C4×C7C2×C22⋊C414yes—
387C2×C4×C7C4×D414yes—
388C2×C4×C7C4×D414yes—
389C2×C4×C7#12014yes—
390C2×C4×C7#12114yes—
391C2×C4×C7#12114yes—
392C2×C4×C7C22⋊Q814yescomplemented
393C2×C4×C7#12314yes—
394C25C23×C711yescharacteristic
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8C2×C4×C714yes—
400C22×Q8C7×D414yes—
401C22×Q8C7×D414yes—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4C2×C4×C714yes—
409C23×C4C23×C712yes—
410C23×C4C23×C712yes—
411C23×C4C23×C711yescharacteristic
412C23×C4C23×C712yes—
413C23×C4C23×C711yescharacteristic
414C23×C4C23×C711yescharacteristic
415C23×C4C23×C711yescharacteristic
416C23×C4C23×C712yes—
417C23×C4C23×C711yescharacteristic
418C23×C4C23×C711yescharacteristic
419C22⋊Q8—232no—
420C4×Q8—232no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4C2×C4×C714yes—
434C2×C4⋊C4C2×C4×C718yes—
435C2×C4⋊C4C7×D414yes—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—42no—
446C2×C22⋊C4C2×C4×C718yes—
447C2×C22⋊C4C7×Q814yescomplemented
448C2×C42—24no—
449C2×C42—24no—
450C2×C42—24no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42C7×D414yes—
457#95—22no—
458#95—22no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—42no—
465#95—42no—
466C22×C7—24no—
467C22×C7—24no—
468C22×C7—24no—
469C22×C7—42no—
470C22×C7—42no—
471C22×C7—42no—
472C22×C7—42no—
473C22×C7—42no—
474C22×C7—42no—
475C22×C7—42no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7C22×C22⋊C411yescharacteristic
482C22×C7C2×C4×D411yescharacteristic
483C22×C7C2×C4×D411yescharacteristic
484C22×C7C2×C4×Q811yescharacteristic
485C22×C7C4×#4111yescharacteristic
486C22×C7#51911yescharacteristic
487C22×C7#52011yescharacteristic
488C22×C7C2×#12011yescharacteristic
489C22×C7C2×#12111yescharacteristic
490C22×C7C2×#12111yescharacteristic
491C22×C7C2×C22⋊Q811yescharacteristic
492C22×C7C2×#12311yescharacteristic
493C22×C7#52511yescharacteristic
494C22×C7#52911yescharacteristic
495C22×C7#53311yescharacteristic
496C22×C7#53611yescharacteristic
497C22×C7#53711yescharacteristic
498C22×C7#54111yescharacteristic
499C22×C7#54211yescharacteristic
500C22×C7#54611yescharacteristic
501C22×C7#54711yescharacteristic
502C22×C7#54811yescharacteristic
503C22×C7#54811yescharacteristic
504C22×C7#54811yescharacteristic
505C22×C7#54811yescharacteristic
506C22×C7#54811yescharacteristic
507C22×C7D4×Q811yescharacteristic
508C22×C7D4×Q811yescharacteristic
509C22×C7D4×Q811yescharacteristic
510C22×C7#55011yescharacteristic
511C22×C7#55011yescharacteristic
512C22×C7#55211yescharacteristic
513C22×C7#55211yescharacteristic
514C22×C7#55411yescharacteristic
515C22×C7#55611yescharacteristic
516C4×C7—24no—
517C4×C7—28no—
518C4×C7—44no—
519C4×C7—42no—
520C4×C7—44no—
521C4×C7—42no—
522C4×C7—42no—
523C4×C7—42no—
524C4×C7—82no—
525C4×C7#38618yes—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24C22×C4×C712yes—
539C24C2×C7×Q812yes—
540C24C7×#4112yes—
541C24C24×C711yescharacteristic
542C2×Q8—28no—
543C2×Q8—28no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—28no—
547C2×Q8—28no—
548C2×Q8C7×C22⋊C4116yescomplemented
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4C22×C4×C714yes—
608C22×C4C22×C4×C712yes—
609C22×C4C22×C4×C714yes—
610C22×C4C22×C4×C712yes—
611C22×C4C2×C7×D414yes—
612C22×C4C2×C7×D412yes—
613C22×C4C2×C7×D414yes—
614C22×C4C2×C7×D414yes—
615C22×C4C2×C7×D412yes—
616C22×C4C2×C7×D412yes—
617C22×C4C2×C7×D412yes—
618C22×C4C2×C7×D412yes—
619C22×C4C2×C7×D412yes—
620C22×C4C2×C7×Q812yes—
621C22×C4C2×C7×Q812yes—
622C22×C4C7×#4112yes—
623C22×C4C7×#4112yes—
624C22×C4C7×#4112yes—
625C22×C4C7×#4112yes—
626C4⋊C4—216no—
627C4⋊C4—28no—
628C4⋊C4—216no—
629C4⋊C4—28no—
630C4⋊C4—44no—
631C22⋊C4—28no—
632C22⋊C4—216no—
633C22⋊C4—28no—
634C22⋊C4—48no—
635C42—216no—
636C42—28no—
637C42—44no—
638C2×C7—44no—
639C2×C7C2×#38611yescharacteristic
640C2×C7C4×C22⋊Q811yescharacteristic
641C2×C7#232311yescharacteristic
642C2×C7Q8×C22⋊C411yescharacteristic
643C2×C7#234111yescharacteristic
644C2×C7#236011yescharacteristic
645C2×C7#236211yescharacteristic
646C2×C7#240711yescharacteristic
647C2×C7#240911yescharacteristic
648C2×C7#242111yescharacteristic
649C2×C7#242311yescharacteristic
650C2×C7#242611yescharacteristic
651C2×C7#242911yescharacteristic
652C2×C7#253611yescharacteristic
653C2×C7#253811yescharacteristic
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23C4×C7×Q814yescomplemented
689C23C23×C4×C711yescharacteristic
690C23C22×C7×D411yescharacteristic
691C23C22×C7×D411yescharacteristic
692C23C22×C7×D411yescharacteristic
693C23C22×C7×D411yescharacteristic
694C23C22×C7×Q811yescharacteristic
695C23C2×C7×#4111yescharacteristic
696C23C2×C7×#4111yescharacteristic
697C23C2×C7×#4111yescharacteristic
698C23C2×C7×#4111yescharacteristic
699C23C2×C7×#4111yescharacteristic
700C23C7×H(5,𝔽2)11yescharacteristic
701C23C7×2−1+411yescharacteristic
702C23C7×2−1+411yescharacteristic
703C23C7×2−1+411yescharacteristic
704Q8—232no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—416no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4C2×C7×C22⋊C418yes—
768C2×C4C2×C7×C22⋊C414yes—
769C2×C4C4×C7×D414yes—
770C2×C4C4×C7×D414yes—
771C2×C4C7×#12014yes—
772C2×C4C7×#12114yes—
773C2×C4C7×#12114yes—
774C2×C4C7×C22⋊Q814yescomplemented
775C2×C4C7×#12314yes—
776C7#1396911yescharacteristic, direct product factor, Sylow
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C22×C7×C22⋊C411yescharacteristic
793C22C2×C4×C7×D411yescharacteristic
794C22C2×C4×C7×D411yescharacteristic
795C22C2×C4×C7×Q811yescharacteristic
796C22C4×C7×#4111yescharacteristic
797C22C7×#51911yescharacteristic
798C22C7×#52011yescharacteristic
799C22C2×C7×#12011yescharacteristic
800C22C2×C7×#12111yescharacteristic
801C22C2×C7×#12111yescharacteristic
802C22C2×C7×C22⋊Q811yescharacteristic
803C22C2×C7×#12311yescharacteristic
804C22C7×#52511yescharacteristic
805C22C7×#52911yescharacteristic
806C22C7×#53311yescharacteristic
807C22C7×#53611yescharacteristic
808C22C7×#53711yescharacteristic
809C22C7×#54111yescharacteristic
810C22C7×#54211yescharacteristic
811C22C7×#54611yescharacteristic
812C22C7×#54711yescharacteristic
813C22C7×#54811yescharacteristic
814C22C7×#54811yescharacteristic
815C22C7×#54811yescharacteristic
816C22C7×#54811yescharacteristic
817C22C7×#54811yescharacteristic
818C22C7×D4×Q811yescharacteristic
819C22C7×D4×Q811yescharacteristic
820C22C7×D4×Q811yescharacteristic
821C22C7×#55011yescharacteristic
822C22C7×#55011yescharacteristic
823C22C7×#55211yescharacteristic
824C22C7×#55211yescharacteristic
825C22C7×#55411yescharacteristic
826C22C7×#55611yescharacteristic
827C4—24no—
828C4—28no—
829C4—42no—
830C4—44no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—44no—
835C4—82no—
836C4C7×#38618yes—
837C2—44no—
838C2C2×C7×#38611yescharacteristic
839C2C4×C7×C22⋊Q811yescharacteristic
840C2C7×#232311yescharacteristic
841C2C7×Q8×C22⋊C411yescharacteristic
842C2C7×#234111yescharacteristic
843C2C7×#236011yescharacteristic
844C2C7×#236211yescharacteristic
845C2C7×#240711yescharacteristic
846C2C7×#240911yescharacteristic
847C2C7×#242111yescharacteristic
848C2C7×#242311yescharacteristic
849C2C7×#242611yescharacteristic
850C2C7×#242911yescharacteristic
851C2C7×#253611yescharacteristic
852C2C7×#253811yescharacteristic
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. C22×C4×C7×Q8C2semidirect
3. C2×C7×#391C2semidirect
6. C7×#1441C2semidirect
9. C7×#1436C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×C4⋊#95C2semidirect
16. C2×C7×C22⋊Q8C4semidirect
44. #13969C7direct (N × H)
98. C2×C7×C22⋊C4Q8semidirect
118. C22×C4×Q8C2×C7semidirect
119. C2×#391C2×C7semidirect
122. #1441C2×C7semidirect
125. #1436C2×C7semidirect
126. C4⋊#95C2×C7semidirect
127. C4⋊#95C2×C7semidirect
150. C2×C7×Q8C22⋊C4semidirect
244. C2×C22⋊Q8C4×C7semidirect
306. C23×C7C4×Q8semidirect
392. C2×C4×C7C22⋊Q8semidirect
447. C2×C22⋊C4C7×Q8semidirect
548. C2×Q8C7×C22⋊C4semidirect
688. C23C4×C7×Q8semidirect
774. C2×C4C7×C22⋊Q8semidirect
776. C7#13969direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C22×C4×C7×Q82
C2×C7×#3912
C2×C7×#3802
C2×C4×C7×C22⋊C42
C7×#14412
C7×#14392
C7×#14372
C7×#14362
C7×C4⋊#952
#139697