Finite Group Databasebeta

← C7×#14053 #13191269

Subgroups — C7×#14053 #13191269

Order 1792.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C4⋊Q8C211yesmaximal, characteristic
2C2×C7×#391C212yesmaximal
3C2×C7×#389C211yesmaximal, characteristic
4C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
5C7×#1446C212yesmaximal
6C7×#1441C212yesmaximal
7C7×#1436C212yesmaximal
8C7×C4⋊#95C211yesmaximal, characteristic
9C7×C4⋊#95C211yesmaximal, characteristic
10C7×C4⋊#95C211yesmaximal, characteristic
11C4×C7×#95C211yesmaximal, characteristic
12C23×C7×Q8C2212yes—
13C2×C7×C4⋊Q8—24no—
14C2×C7×C4⋊Q8—24no—
15C2×C7×C4⋊Q8C418yescomplemented
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2212yes—
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C42×C7C2211yescharacteristic
23C22×C42×C7C2212yes—
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C7×#391—28no—
27C7×#389—24no—
28C4×C7×C4⋊C4—24no—
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41#14053C711yesmaximal, characteristic, direct product factor, Sylow
42C22×C7×Q8—24no—
43C22×C7×Q8—24no—
44C22×C7×Q8—24no—
45C22×C7×Q8—24no—
46C22×C7×Q8—42no—
47C22×C7×Q8—42no—
48C22×C7×Q8C2×C418yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2312yes—
55C23×C4×C7C2312yes—
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C7×C4⋊Q8—232no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—24no—
63C2×C7×C4⋊C4—24no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—24no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—42no—
73C2×C7×C4⋊C4C2×C414yes—
74C2×C7×C4⋊C4C2×C418yes—
75C2×C7×C4⋊C4C2×C414yes—
76C2×C7×C4⋊C4D414yes—
77C2×C7×C4⋊C4D414yes—
78C2×C7×C4⋊C4Q814yescomplemented
79C2×C42×C7—22no—
80C2×C42×C7—22no—
81C2×C42×C7—22no—
82C2×C42×C7—22no—
83C2×C42×C7—24no—
84C2×C42×C7—22no—
85C2×C42×C7—24no—
86C2×C42×C7—22no—
87C2×C42×C7—22no—
88C2×C42×C7—42no—
89C2×C42×C7C2×C414yes—
90C2×C42×C7Q814yescomplemented
91C7×#95—24no—
92C7×#95—24no—
93C7×#95—24no—
94C7×#95—24no—
95C7×#95—24no—
96C7×#95—22no—
97C7×#95—22no—
98C7×#95—24no—
99C7×#95—42no—
100C7×#95—42no—
101C7×#95D414yes—
102C7×#95Q814yescomplemented
103C22×C4⋊Q8C2×C711yescharacteristic
104C2×#391C2×C712yes—
105C2×#389C2×C711yescharacteristic
106C2×C4×C4⋊C4C2×C711yescharacteristic
107#1446C2×C712yes—
108#1441C2×C712yes—
109#1436C2×C712yes—
110C4⋊#95C2×C711yescharacteristic
111C4⋊#95C2×C711yescharacteristic
112C4⋊#95C2×C711yescharacteristic
113C4×#95C2×C711yescharacteristic
114C24×C7C2411yescharacteristic
115C2×C7×Q8—216no—
116C2×C7×Q8—216no—
117C2×C7×Q8—48no—
118C2×C7×Q8—48no—
119C2×C7×Q8—48no—
120C2×C7×Q8—48no—
121C2×C7×Q8—48no—
122C22×C4×C7—21no—
123C22×C4×C7—21no—
124C22×C4×C7—21no—
125C22×C4×C7—22no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7—22no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—21no—
134C22×C4×C7—21no—
135C22×C4×C7—21no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—22no—
141C22×C4×C7—22no—
142C22×C4×C7—22no—
143C22×C4×C7—21no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—22no—
161C22×C4×C7—22no—
162C22×C4×C7—22no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—21no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7C22×C414yes—
176C22×C4×C7C22×C414yes—
177C22×C4×C7C22×C412yes—
178C22×C4×C7C22×C412yes—
179C22×C4×C7C22×C412yes—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×D414yes—
182C22×C4×C7C2×D414yes—
183C22×C4×C7C2×D412yes—
184C22×C4×C7C2×D412yes—
185C22×C4×C7C2×D412yes—
186C22×C4×C7C2×D412yes—
187C22×C4×C7C2×Q812yes—
188C22×C4×C7C2×Q812yes—
189C22×C4×C7C2×Q814yes—
190C22×C4×C7C2×Q812yes—
191C22×C4×C7C2×Q812yes—
192C22×C4×C7C2×Q812yes—
193C22×C4×C7C2×Q812yes—
194C22×C4×C7C2×Q812yes—
195C22×C4×C7#4112yes—
196C22×C4×C7#4112yes—
197C22×C4×C7#4112yes—
198C22×C4×C7#4112yes—
199C7×C4⋊C4—216no—
200C7×C4⋊C4—28no—
201C7×C4⋊C4—28no—
202C7×C4⋊C4—48no—
203C7×C4⋊C4—44no—
204C7×C4⋊C4C22⋊C4116yes—
205C42×C7—28no—
206C42×C7—28no—
207C42×C7—48no—
208C42×C7—44no—
209C23×Q8C22×C712yes—
210C2×C4⋊Q8—24no—
211C2×C4⋊Q8—24no—
212C2×C4⋊Q8C4×C718yescomplemented
213C22×C4⋊C4C22×C711yescharacteristic
214C22×C4⋊C4C22×C712yes—
215C22×C4⋊C4C22×C711yescharacteristic
216C22×C4⋊C4C22×C712yes—
217C22×C4⋊C4C22×C711yescharacteristic
218C22×C4⋊C4C22×C711yescharacteristic
219C22×C42C22×C711yescharacteristic
220C22×C42C22×C712yes—
221C22×C42C22×C711yescharacteristic
222C22×C42C22×C711yescharacteristic
223#391—28no—
224#389—24no—
225C4×C4⋊C4—24no—
226C2×#95C22×C711yescharacteristic
227C2×#95C22×C711yescharacteristic
228C2×#95C22×C712yes—
229C2×#95C22×C712yes—
230C2×#95C22×C712yes—
231C2×#95C22×C712yes—
232C2×#95C22×C712yes—
233C2×#95C22×C712yes—
234C2×#95C22×C712yes—
235C2×#95C22×C712yes—
236C2×#95C22×C711yescharacteristic
237C2×#95C22×C711yescharacteristic
238C23×C7C23×C411yescharacteristic
239C23×C7C22×D411yescharacteristic
240C23×C7C22×D411yescharacteristic
241C23×C7C22×D411yescharacteristic
242C23×C7C22×Q811yescharacteristic
243C23×C7C22×Q811yescharacteristic
244C23×C7C22×Q811yescharacteristic
245C23×C7C2×#4111yescharacteristic
246C23×C7C2×#4111yescharacteristic
247C23×C7C2×#4111yescharacteristic
248C23×C7C2×#4111yescharacteristic
249C23×C7H(5,𝔽2)11yescharacteristic
250C23×C7H(5,𝔽2)11yescharacteristic
251C23×C72−1+411yescharacteristic
252C23×C72−1+411yescharacteristic
253C7×Q8—432no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—24no—
257C2×C4×C7—24no—
258C2×C4×C7—22no—
259C2×C4×C7—22no—
260C2×C4×C7—22no—
261C2×C4×C7—22no—
262C2×C4×C7—22no—
263C2×C4×C7—24no—
264C2×C4×C7—24no—
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—22no—
273C2×C4×C7—22no—
274C2×C4×C7—22no—
275C2×C4×C7—22no—
276C2×C4×C7—22no—
277C2×C4×C7—22no—
278C2×C4×C7—24no—
279C2×C4×C7—24no—
280C2×C4×C7—24no—
281C2×C4×C7—22no—
282C2×C4×C7—24no—
283C2×C4×C7—22no—
284C2×C4×C7—22no—
285C2×C4×C7—22no—
286C2×C4×C7—22no—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—24no—
290C2×C4×C7—22no—
291C2×C4×C7—24no—
292C2×C4×C7—22no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7—42no—
296C2×C4×C7—42no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7—42no—
300C2×C4×C7—42no—
301C2×C4×C7—42no—
302C2×C4×C7—41no—
303C2×C4×C7—41no—
304C2×C4×C7—42no—
305C2×C4×C7—42no—
306C2×C4×C7—41no—
307C2×C4×C7—42no—
308C2×C4×C7—41no—
309C2×C4×C7—41no—
310C2×C4×C7—41no—
311C2×C4×C7—41no—
312C2×C4×C7—41no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7C2×C22⋊C418yes—
321C2×C4×C7C2×C22⋊C414yes—
322C2×C4×C7C4×D414yes—
323C2×C4×C7C4×Q814yes—
324C2×C4×C7C4×Q814yes—
325C2×C4×C7C4×Q814yes—
326C2×C4×C7C22⋊Q814yes—
327C2×C4×C7C22⋊Q814yes—
328C2×C4×C7#12414yes—
329C2×C4×C7C4⋊Q814yes—
330C2×C4×C7C4⋊Q814yescomplemented
331C22×Q8—24no—
332C22×Q8—24no—
333C22×Q8—24no—
334C22×Q8—24no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×Q8C2×C4×C718yes—
338C23×C4C23×C712yes—
339C23×C4C23×C712yes—
340C23×C4C23×C711yescharacteristic
341C23×C4C23×C712yes—
342C23×C4C23×C711yescharacteristic
343C23×C4C23×C711yescharacteristic
344C23×C4C23×C712yes—
345C23×C4C23×C711yescharacteristic
346C23×C4C23×C711yescharacteristic
347C23×C4C23×C711yescharacteristic
348C23×C4C23×C711yescharacteristic
349C4⋊Q8—232no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4C2×C4×C714yes—
363C2×C4⋊C4C2×C4×C718yes—
364C2×C4⋊C4C2×C4×C714yes—
365C2×C4⋊C4C7×D414yes—
366C2×C4⋊C4C7×D414yes—
367C2×C4⋊C4C7×Q814yescomplemented
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—42no—
378C2×C42C2×C4×C714yes—
379C2×C42C7×Q814yescomplemented
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—22no—
386#95—22no—
387#95—24no—
388#95—42no—
389#95—42no—
390#95C7×D414yes—
391#95C7×Q814yescomplemented
392C22×C7C22×C22⋊C411yescharacteristic
393C22×C7C2×C4×D411yescharacteristic
394C22×C7C2×C4×Q811yescharacteristic
395C22×C7C2×C4×Q811yescharacteristic
396C22×C7C2×C4×Q811yescharacteristic
397C22×C7#51811yescharacteristic
398C22×C7#51911yescharacteristic
399C22×C7C2×C22⋊Q811yescharacteristic
400C22×C7C2×C22⋊Q811yescharacteristic
401C22×C7C2×#12411yescharacteristic
402C22×C7C2×C4⋊Q811yescharacteristic
403C22×C7C2×C4⋊Q811yescharacteristic
404C22×C7#53211yescharacteristic
405C22×C7#53311yescharacteristic
406C22×C7#53311yescharacteristic
407C22×C7#54211yescharacteristic
408C22×C7#54211yescharacteristic
409C22×C7#54411yescharacteristic
410C22×C7#54411yescharacteristic
411C22×C7D4211yescharacteristic
412C22×C7D4211yescharacteristic
413C22×C7#54611yescharacteristic
414C22×C7#54611yescharacteristic
415C22×C7#54711yescharacteristic
416C22×C7#54811yescharacteristic
417C22×C7#54811yescharacteristic
418C22×C7D4×Q811yescharacteristic
419C22×C7D4×Q811yescharacteristic
420C22×C7D4×Q811yescharacteristic
421C22×C7#55411yescharacteristic
422C22×C7#55411yescharacteristic
423C22×C7#55511yescharacteristic
424C22×C7#55611yescharacteristic
425C22×C7#55711yescharacteristic
426C22×C7Q8211yescharacteristic
427C4×C7—28no—
428C4×C7—24no—
429C4×C7—24no—
430C4×C7—24no—
431C4×C7—44no—
432C4×C7—42no—
433C4×C7—44no—
434C4×C7—42no—
435C4×C7—42no—
436C4×C7—82no—
437C4×C7#39118yescomplemented
438C24C24×C711yescharacteristic
439C2×Q8—216no—
440C2×Q8—216no—
441C2×Q8—48no—
442C2×Q8—48no—
443C2×Q8—48no—
444C2×Q8—48no—
445C2×Q8—48no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4C22×C4×C714yes—
500C22×C4C22×C4×C714yes—
501C22×C4C22×C4×C712yes—
502C22×C4C22×C4×C712yes—
503C22×C4C22×C4×C712yes—
504C22×C4C2×C7×D412yes—
505C22×C4C2×C7×D414yes—
506C22×C4C2×C7×D414yes—
507C22×C4C2×C7×D412yes—
508C22×C4C2×C7×D412yes—
509C22×C4C2×C7×D412yes—
510C22×C4C2×C7×D412yes—
511C22×C4C2×C7×Q812yes—
512C22×C4C2×C7×Q812yes—
513C22×C4C2×C7×Q814yes—
514C22×C4C2×C7×Q812yes—
515C22×C4C2×C7×Q812yes—
516C22×C4C2×C7×Q812yes—
517C22×C4C2×C7×Q812yes—
518C22×C4C2×C7×Q812yes—
519C22×C4C7×#4112yes—
520C22×C4C7×#4112yes—
521C22×C4C7×#4112yes—
522C22×C4C7×#4112yes—
523C4⋊C4—216no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—48no—
527C4⋊C4—44no—
528C4⋊C4C7×C22⋊C4116yes—
529C42—28no—
530C42—28no—
531C42—48no—
532C42—44no—
533C2×C7C2×#39111yescharacteristic
534C2×C7C4×C4⋊Q811yescharacteristic
535C2×C7#233111yescharacteristic
536C2×C7D4×C22⋊C411yescharacteristic
537C2×C7Q8×C22⋊C411yescharacteristic
538C2×C7#236511yescharacteristic
539C2×C7#236911yescharacteristic
540C2×C7#243911yescharacteristic
541C2×C7#244011yescharacteristic
542C2×C7#245111yescharacteristic
543C2×C7#245211yescharacteristic
544C2×C7#249111yescharacteristic
545C2×C7#249211yescharacteristic
546C2×C7#255011yescharacteristic
547C2×C7#255111yescharacteristic
548C23C23×C4×C711yescharacteristic
549C23C22×C7×D411yescharacteristic
550C23C22×C7×D411yescharacteristic
551C23C22×C7×D411yescharacteristic
552C23C22×C7×Q811yescharacteristic
553C23C22×C7×Q811yescharacteristic
554C23C22×C7×Q811yescharacteristic
555C23C2×C7×#4111yescharacteristic
556C23C2×C7×#4111yescharacteristic
557C23C2×C7×#4111yescharacteristic
558C23C2×C7×#4111yescharacteristic
559C23C7×H(5,𝔽2)11yescharacteristic
560C23C7×H(5,𝔽2)11yescharacteristic
561C23C7×2−1+411yescharacteristic
562C23C7×2−1+411yescharacteristic
563Q8—432no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4C2×C7×C22⋊C418yes—
631C2×C4C2×C7×C22⋊C414yes—
632C2×C4C4×C7×D414yes—
633C2×C4C4×C7×Q814yes—
634C2×C4C4×C7×Q814yes—
635C2×C4C4×C7×Q814yes—
636C2×C4C7×C22⋊Q814yes—
637C2×C4C7×C22⋊Q814yes—
638C2×C4C7×#12414yes—
639C2×C4C7×C4⋊Q814yes—
640C2×C4C7×C4⋊Q814yescomplemented
641C7#1405311yescharacteristic, direct product factor, Sylow
642C22C22×C7×C22⋊C411yescharacteristic
643C22C2×C4×C7×D411yescharacteristic
644C22C2×C4×C7×Q811yescharacteristic
645C22C2×C4×C7×Q811yescharacteristic
646C22C2×C4×C7×Q811yescharacteristic
647C22C7×#51811yescharacteristic
648C22C7×#51911yescharacteristic
649C22C2×C7×C22⋊Q811yescharacteristic
650C22C2×C7×C22⋊Q811yescharacteristic
651C22C2×C7×#12411yescharacteristic
652C22C2×C7×C4⋊Q811yescharacteristic
653C22C2×C7×C4⋊Q811yescharacteristic
654C22C7×#53211yescharacteristic
655C22C7×#53311yescharacteristic
656C22C7×#53311yescharacteristic
657C22C7×#54211yescharacteristic
658C22C7×#54211yescharacteristic
659C22C7×#54411yescharacteristic
660C22C7×#54411yescharacteristic
661C22C7×D4211yescharacteristic
662C22C7×D4211yescharacteristic
663C22C7×#54611yescharacteristic
664C22C7×#54611yescharacteristic
665C22C7×#54711yescharacteristic
666C22C7×#54811yescharacteristic
667C22C7×#54811yescharacteristic
668C22C7×D4×Q811yescharacteristic
669C22C7×D4×Q811yescharacteristic
670C22C7×D4×Q811yescharacteristic
671C22C7×#55411yescharacteristic
672C22C7×#55411yescharacteristic
673C22C7×#55511yescharacteristic
674C22C7×#55611yescharacteristic
675C22C7×#55711yescharacteristic
676C22C7×Q8211yescharacteristic
677C4—24no—
678C4—28no—
679C4—24no—
680C4—24no—
681C4—42no—
682C4—44no—
683C4—42no—
684C4—42no—
685C4—44no—
686C4—82no—
687C4C7×#39118yescomplemented
688C2C2×C7×#39111yescharacteristic
689C2C4×C7×C4⋊Q811yescharacteristic
690C2C7×#233111yescharacteristic
691C2C7×D4×C22⋊C411yescharacteristic
692C2C7×Q8×C22⋊C411yescharacteristic
693C2C7×#236511yescharacteristic
694C2C7×#236911yescharacteristic
695C2C7×#243911yescharacteristic
696C2C7×#244011yescharacteristic
697C2C7×#245111yescharacteristic
698C2C7×#245211yescharacteristic
699C2C7×#249111yescharacteristic
700C2C7×#249211yescharacteristic
701C2C7×#255011yescharacteristic
702C2C7×#255111yescharacteristic
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
15. C2×C7×C4⋊Q8C4semidirect
41. #14053C7direct (N × H)
78. C2×C7×C4⋊C4Q8semidirect
90. C2×C42×C7Q8semidirect
102. C7×#95Q8semidirect
212. C2×C4⋊Q8C4×C7semidirect
330. C2×C4×C7C4⋊Q8semidirect
367. C2×C4⋊C4C7×Q8semidirect
379. C2×C42C7×Q8semidirect
391. #95C7×Q8semidirect
437. C4×C7#391semidirect
640. C2×C4C7×C4⋊Q8semidirect
641. C7#14053direct (N × H)
687. C4C7×#391semidirect

Maximal subgroups

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

subgroupindex
C22×C7×C4⋊Q82
C2×C7×#3912
C2×C7×#3892
C2×C4×C7×C4⋊C42
C7×#14462
C7×#14412
C7×#14362
C7×C4⋊#952
C4×C7×#952
#140537