Finite Group Databasebeta

← C7×#14041 #13191257

Subgroups — C7×#14041 #13191257

Order 1792.

1386 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#389C211yesmaximal, characteristic
2C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
3C2×C4×C7×C4⋊C4C211yesmaximal, characteristic
4C7×#1445C212yesmaximal
5C7×#1442C212yesmaximal
6C7×#1436C212yesmaximal
7C7×#1436C212yesmaximal
8C7×C4⋊#95C211yesmaximal, characteristic
9C7×C4⋊#95C211yesmaximal, characteristic
10C7×C4⋊#95C211yesmaximal, characteristic
11C7×C4⋊#95C211yesmaximal, characteristic
12C22×C7×C4⋊C4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2212yes—
19C22×C42×C7C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C42×C7C2212yes—
23C7×#389C418yescomplemented
24C4×C7×C4⋊C4—24no—
25C4×C7×C4⋊C4—24no—
26C2×C7×#95C2211yescharacteristic
27C2×C7×#95C2212yes—
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2212yes—
30C2×C7×#95C2212yes—
31C2×C7×#95C2212yes—
32C2×C7×#95C2212yes—
33C2×C7×#95C2212yes—
34C2×C7×#95C2212yes—
35C2×C7×#95C2212yes—
36C2×C7×#95C2212yes—
37C2×C7×#95C2212yes—
38#14041C711yesmaximal, characteristic, direct product factor, Sylow
39C23×C4×C7C2312yes—
40C23×C4×C7C2311yescharacteristic
41C23×C4×C7C2312yes—
42C23×C4×C7C2312yes—
43C23×C4×C7C2311yescharacteristic
44C23×C4×C7C2312yes—
45C23×C4×C7C2311yescharacteristic
46C23×C4×C7C2311yescharacteristic
47C23×C4×C7C2311yescharacteristic
48C23×C4×C7C2311yescharacteristic
49C23×C4×C7C2311yescharacteristic
50C2×C7×C4⋊C4—22no—
51C2×C7×C4⋊C4—22no—
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—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—42no—
65C2×C7×C4⋊C4—42no—
66C2×C7×C4⋊C4C2×C414yes—
67C2×C7×C4⋊C4C2×C414yes—
68C2×C7×C4⋊C4C2×C418yes—
69C2×C7×C4⋊C4Q814yes—
70C2×C7×C4⋊C4Q814yes—
71C2×C42×C7—22no—
72C2×C42×C7—22no—
73C2×C42×C7—22no—
74C2×C42×C7—22no—
75C2×C42×C7—24no—
76C2×C42×C7—22no—
77C2×C42×C7—22no—
78C2×C42×C7—22no—
79C2×C42×C7—42no—
80C2×C42×C7—42no—
81C2×C42×C7C2×C414yes—
82C2×C42×C7D414yes—
83C7×#95—22no—
84C7×#95—22no—
85C7×#95—24no—
86C7×#95—24no—
87C7×#95—24no—
88C7×#95—24no—
89C7×#95—42no—
90C7×#95—42no—
91C7×#95—42no—
92C7×#95—42no—
93C7×#95—42no—
94C7×#95C2×C418yes—
95C2×#389C2×C711yescharacteristic
96C2×C4×C4⋊C4C2×C711yescharacteristic
97C2×C4×C4⋊C4C2×C711yescharacteristic
98#1445C2×C712yes—
99#1442C2×C712yes—
100#1436C2×C712yes—
101#1436C2×C712yes—
102C4⋊#95C2×C711yescharacteristic
103C4⋊#95C2×C711yescharacteristic
104C4⋊#95C2×C711yescharacteristic
105C4⋊#95C2×C711yescharacteristic
106C24×C7C2411yescharacteristic
107C22×C4×C7—21no—
108C22×C4×C7—21no—
109C22×C4×C7—21no—
110C22×C4×C7—21no—
111C22×C4×C7—21no—
112C22×C4×C7—21no—
113C22×C4×C7—21no—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—22no—
117C22×C4×C7—21no—
118C22×C4×C7—22no—
119C22×C4×C7—21no—
120C22×C4×C7—22no—
121C22×C4×C7—22no—
122C22×C4×C7—22no—
123C22×C4×C7—22no—
124C22×C4×C7—21no—
125C22×C4×C7—21no—
126C22×C4×C7—21no—
127C22×C4×C7—21no—
128C22×C4×C7—21no—
129C22×C4×C7—21no—
130C22×C4×C7—21no—
131C22×C4×C7—22no—
132C22×C4×C7—22no—
133C22×C4×C7—22no—
134C22×C4×C7—21no—
135C22×C4×C7—22no—
136C22×C4×C7—21no—
137C22×C4×C7—21no—
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—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—22no—
149C22×C4×C7—22no—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—22no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
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×C7C22×C414yes—
165C22×C4×C7C22×C414yes—
166C22×C4×C7C22×C412yes—
167C22×C4×C7C22×C412yes—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C2×D412yes—
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2×D412yes—
172C22×C4×C7C2×Q814yes—
173C22×C4×C7C2×Q812yes—
174C22×C4×C7C2×Q812yes—
175C22×C4×C7C2×Q812yes—
176C22×C4×C7C2×Q812yes—
177C22×C4×C7#4112yes—
178C22×C4×C7#4112yes—
179C22×C4×C7#4112yes—
180C22×C4×C7#4112yes—
181C22×C4×C7#4112yes—
182C22×C4×C7#4112yes—
183C22×C4×C7#4112yes—
184C7×C4⋊C4—28no—
185C7×C4⋊C4—28no—
186C7×C4⋊C4—28no—
187C7×C4⋊C4—28no—
188C7×C4⋊C4—28no—
189C7×C4⋊C4—48no—
190C7×C4⋊C4—44no—
191C42×C7—28no—
192C42×C7—28no—
193C42×C7—48no—
194C42×C7—44no—
195C22×C4⋊C4C22×C711yescharacteristic
196C22×C4⋊C4C22×C711yescharacteristic
197C22×C4⋊C4C22×C711yescharacteristic
198C22×C4⋊C4C22×C711yescharacteristic
199C22×C4⋊C4C22×C711yescharacteristic
200C22×C4⋊C4C22×C711yescharacteristic
201C22×C4⋊C4C22×C712yes—
202C22×C42C22×C711yescharacteristic
203C22×C42C22×C711yescharacteristic
204C22×C42C22×C711yescharacteristic
205C22×C42C22×C712yes—
206#389C4×C718yescomplemented
207C4×C4⋊C4—24no—
208C4×C4⋊C4—24no—
209C2×#95C22×C712yes—
210C2×#95C22×C712yes—
211C2×#95C22×C712yes—
212C2×#95C22×C711yescharacteristic
213C2×#95C22×C712yes—
214C2×#95C22×C711yescharacteristic
215C2×#95C22×C712yes—
216C2×#95C22×C712yes—
217C2×#95C22×C712yes—
218C2×#95C22×C712yes—
219C2×#95C22×C712yes—
220C2×#95C22×C712yes—
221C23×C7C23×C411yescharacteristic
222C23×C7C22×D411yescharacteristic
223C23×C7C22×Q811yescharacteristic
224C23×C7C22×Q811yescharacteristic
225C23×C7C2×#4111yescharacteristic
226C23×C7C2×#4111yescharacteristic
227C23×C7C2×#4111yescharacteristic
228C23×C7C2×#4111yescharacteristic
229C23×C7C2×#4111yescharacteristic
230C23×C7C2×#4111yescharacteristic
231C23×C7C2×#4111yescharacteristic
232C23×C7H(5,𝔽2)11yescharacteristic
233C23×C7H(5,𝔽2)11yescharacteristic
234C23×C7H(5,𝔽2)11yescharacteristic
235C23×C72−1+411yescharacteristic
236C2×C4×C7—22no—
237C2×C4×C7—22no—
238C2×C4×C7—22no—
239C2×C4×C7—22no—
240C2×C4×C7—22no—
241C2×C4×C7—22no—
242C2×C4×C7—22no—
243C2×C4×C7—22no—
244C2×C4×C7—22no—
245C2×C4×C7—22no—
246C2×C4×C7—22no—
247C2×C4×C7—22no—
248C2×C4×C7—24no—
249C2×C4×C7—22no—
250C2×C4×C7—24no—
251C2×C4×C7—24no—
252C2×C4×C7—22no—
253C2×C4×C7—24no—
254C2×C4×C7—24no—
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—22no—
264C2×C4×C7—22no—
265C2×C4×C7—24no—
266C2×C4×C7—24no—
267C2×C4×C7—22no—
268C2×C4×C7—22no—
269C2×C4×C7—41no—
270C2×C4×C7—41no—
271C2×C4×C7—42no—
272C2×C4×C7—42no—
273C2×C4×C7—42no—
274C2×C4×C7—41no—
275C2×C4×C7—41no—
276C2×C4×C7—41no—
277C2×C4×C7—42no—
278C2×C4×C7—41no—
279C2×C4×C7—41no—
280C2×C4×C7—42no—
281C2×C4×C7—41no—
282C2×C4×C7—42no—
283C2×C4×C7—41no—
284C2×C4×C7—42no—
285C2×C4×C7—42no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7—41no—
289C2×C4×C7—41no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—42no—
294C2×C4×C7—42no—
295C2×C4×C7—42no—
296C2×C4×C7—42no—
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#11714yes—
305C2×C4×C7C4×D414yes—
306C2×C4×C7C4×Q814yes—
307C2×C4×C7C4×Q814yes—
308C2×C4×C7C22⋊Q814yes—
309C2×C4×C7C22⋊Q814yes—
310C2×C4×C7#12314yes—
311C2×C4×C7#12514yes—
312C2×C4×C7#12614yes—
313C23×C4C23×C712yes—
314C23×C4C23×C712yes—
315C23×C4C23×C711yescharacteristic
316C23×C4C23×C712yes—
317C23×C4C23×C711yescharacteristic
318C23×C4C23×C712yes—
319C23×C4C23×C711yescharacteristic
320C23×C4C23×C711yescharacteristic
321C23×C4C23×C711yescharacteristic
322C23×C4C23×C711yescharacteristic
323C23×C4C23×C711yescharacteristic
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4C2×C4×C714yes—
341C2×C4⋊C4C2×C4×C714yes—
342C2×C4⋊C4C2×C4×C718yes—
343C2×C4⋊C4C7×Q814yes—
344C2×C4⋊C4C7×Q814yes—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42C2×C4×C714yes—
356C2×C42C7×D414yes—
357#95—22no—
358#95—22no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—42no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95C2×C4×C718yes—
369C22×C7C2×#11711yescharacteristic
370C22×C7C2×C4×D411yescharacteristic
371C22×C7C2×C4×Q811yescharacteristic
372C22×C7C2×C4×Q811yescharacteristic
373C22×C7C4×#4111yescharacteristic
374C22×C7#51811yescharacteristic
375C22×C7#52011yescharacteristic
376C22×C7C2×C22⋊Q811yescharacteristic
377C22×C7C2×C22⋊Q811yescharacteristic
378C22×C7C2×#12311yescharacteristic
379C22×C7#52511yescharacteristic
380C22×C7C2×#12511yescharacteristic
381C22×C7C2×#12611yescharacteristic
382C22×C7#52911yescharacteristic
383C22×C7#53311yescharacteristic
384C22×C7#53511yescharacteristic
385C22×C7#53711yescharacteristic
386C22×C7#54011yescharacteristic
387C22×C7#54211yescharacteristic
388C22×C7#55211yescharacteristic
389C22×C7#55311yescharacteristic
390C22×C7#55311yescharacteristic
391C22×C7#55311yescharacteristic
392C22×C7#55411yescharacteristic
393C22×C7#55411yescharacteristic
394C22×C7#55411yescharacteristic
395C22×C7#55411yescharacteristic
396C22×C7#55511yescharacteristic
397C22×C7#55611yescharacteristic
398C22×C7#55711yescharacteristic
399C22×C7#55711yescharacteristic
400C22×C7Q8211yescharacteristic
401C22×C7#55911yescharacteristic
402C22×C7#55911yescharacteristic
403C22×C7#55911yescharacteristic
404C4×C7—24no—
405C4×C7—24no—
406C4×C7—42no—
407C4×C7—44no—
408C4×C7—44no—
409C4×C7—44no—
410C4×C7—42no—
411C4×C7—42no—
412C4×C7—42no—
413C4×C7—82no—
414C4×C7#38718yes—
415C24C24×C711yescharacteristic
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
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—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4C22×C4×C714yes—
474C22×C4C22×C4×C714yes—
475C22×C4C22×C4×C712yes—
476C22×C4C22×C4×C712yes—
477C22×C4C22×C4×C712yes—
478C22×C4C2×C7×D412yes—
479C22×C4C2×C7×D412yes—
480C22×C4C2×C7×D412yes—
481C22×C4C2×C7×Q814yes—
482C22×C4C2×C7×Q812yes—
483C22×C4C2×C7×Q812yes—
484C22×C4C2×C7×Q812yes—
485C22×C4C2×C7×Q812yes—
486C22×C4C7×#4112yes—
487C22×C4C7×#4112yes—
488C22×C4C7×#4112yes—
489C22×C4C7×#4112yes—
490C22×C4C7×#4112yes—
491C22×C4C7×#4112yes—
492C22×C4C7×#4112yes—
493C4⋊C4—28no—
494C4⋊C4—28no—
495C4⋊C4—28no—
496C4⋊C4—28no—
497C4⋊C4—28no—
498C4⋊C4—48no—
499C4⋊C4—44no—
500C42—28no—
501C42—28no—
502C42—48no—
503C42—44no—
504C2×C7C2×#38711yescharacteristic
505C2×C7C4×C22⋊Q811yescharacteristic
506C2×C7#232411yescharacteristic
507C2×C7#235511yescharacteristic
508C2×C7#235711yescharacteristic
509C2×C7#236911yescharacteristic
510C2×C7#237011yescharacteristic
511C2×C7#248511yescharacteristic
512C2×C7#248711yescharacteristic
513C2×C7#250711yescharacteristic
514C2×C7#250911yescharacteristic
515C2×C7#251111yescharacteristic
516C2×C7#251311yescharacteristic
517C2×C7#258011yescharacteristic
518C2×C7#258211yescharacteristic
519C23C23×C4×C711yescharacteristic
520C23C22×C7×D411yescharacteristic
521C23C22×C7×Q811yescharacteristic
522C23C22×C7×Q811yescharacteristic
523C23C2×C7×#4111yescharacteristic
524C23C2×C7×#4111yescharacteristic
525C23C2×C7×#4111yescharacteristic
526C23C2×C7×#4111yescharacteristic
527C23C2×C7×#4111yescharacteristic
528C23C2×C7×#4111yescharacteristic
529C23C2×C7×#4111yescharacteristic
530C23C7×H(5,𝔽2)11yescharacteristic
531C23C7×H(5,𝔽2)11yescharacteristic
532C23C7×H(5,𝔽2)11yescharacteristic
533C23C7×2−1+411yescharacteristic
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
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—24no—
566C2×C4—24no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4C7×#11714yes—
603C2×C4C4×C7×D414yes—
604C2×C4C4×C7×Q814yes—
605C2×C4C4×C7×Q814yes—
606C2×C4C7×C22⋊Q814yes—
607C2×C4C7×C22⋊Q814yes—
608C2×C4C7×#12314yes—
609C2×C4C7×#12514yes—
610C2×C4C7×#12614yes—
611C7#1404111yescharacteristic, direct product factor, Sylow
612C22C2×C7×#11711yescharacteristic
613C22C2×C4×C7×D411yescharacteristic
614C22C2×C4×C7×Q811yescharacteristic
615C22C2×C4×C7×Q811yescharacteristic
616C22C4×C7×#4111yescharacteristic
617C22C7×#51811yescharacteristic
618C22C7×#52011yescharacteristic
619C22C2×C7×C22⋊Q811yescharacteristic
620C22C2×C7×C22⋊Q811yescharacteristic
621C22C2×C7×#12311yescharacteristic
622C22C7×#52511yescharacteristic
623C22C2×C7×#12511yescharacteristic
624C22C2×C7×#12611yescharacteristic
625C22C7×#52911yescharacteristic
626C22C7×#53311yescharacteristic
627C22C7×#53511yescharacteristic
628C22C7×#53711yescharacteristic
629C22C7×#54011yescharacteristic
630C22C7×#54211yescharacteristic
631C22C7×#55211yescharacteristic
632C22C7×#55311yescharacteristic
633C22C7×#55311yescharacteristic
634C22C7×#55311yescharacteristic
635C22C7×#55411yescharacteristic
636C22C7×#55411yescharacteristic
637C22C7×#55411yescharacteristic
638C22C7×#55411yescharacteristic
639C22C7×#55511yescharacteristic
640C22C7×#55611yescharacteristic
641C22C7×#55711yescharacteristic
642C22C7×#55711yescharacteristic
643C22C7×Q8211yescharacteristic
644C22C7×#55911yescharacteristic
645C22C7×#55911yescharacteristic
646C22C7×#55911yescharacteristic
647C4—24no—
648C4—24no—
649C4—42no—
650C4—42no—
651C4—42no—
652C4—42no—
653C4—44no—
654C4—44no—
655C4—44no—
656C4—82no—
657C4C7×#38718yes—
658C2C2×C7×#38711yescharacteristic
659C2C4×C7×C22⋊Q811yescharacteristic
660C2C7×#232411yescharacteristic
661C2C7×#235511yescharacteristic
662C2C7×#235711yescharacteristic
663C2C7×#236911yescharacteristic
664C2C7×#237011yescharacteristic
665C2C7×#248511yescharacteristic
666C2C7×#248711yescharacteristic
667C2C7×#250711yescharacteristic
668C2C7×#250911yescharacteristic
669C2C7×#251111yescharacteristic
670C2C7×#251311yescharacteristic
671C2C7×#258011yescharacteristic
672C2C7×#258211yescharacteristic
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
23. C7×#389C4semidirect
38. #14041C7direct (N × H)
206. #389C4×C7semidirect
611. C7#14041direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3892
C2×C4×C7×C4⋊C42
C7×#14452
C7×#14422
C7×#14362
C7×C4⋊#952
#140417