Finite Group Databasebeta

← C7×#14099 #13191315

Subgroups — C7×#14099 #13191315

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic
2C2×C7×#391C211yesmaximal, characteristic, complemented
3C2×C7×#387C211yesmaximal, characteristic, complemented
4C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
6C7×#1446C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1439C211yesmaximal, characteristic
9C7×#1439C211yesmaximal, characteristic
10C7×#1437C211yesmaximal, characteristic
11C7×#1437C211yesmaximal, characteristic
12C7×#1436C211yesmaximal, characteristic, complemented
13C7×#1436C211yesmaximal, characteristic, complemented
14C7×#1436C211yesmaximal, characteristic, complemented
15C7×C22⋊#95C211yesmaximal, characteristic
16C23×C7×Q8C2211yescharacteristic
17C24×C4×C7C2211yescharacteristic
18C2×C7×C22⋊Q8—24no—
19C2×C7×C22⋊Q8—24no—
20C2×C7×C22⋊Q8C418yescomplemented
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C7×C22⋊C4C2211yescharacteristic
29C22×C7×C22⋊C4C2211yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31C22×C7×C22⋊C4C2211yescharacteristic
32C22×C42×C7C2211yescharacteristic
33C22×C42×C7C2211yescharacteristic
34C22×C42×C7C2211yescharacteristic
35C22×C42×C7C2211yescharacteristic
36C7×#391—24no—
37C7×#387—24no—
38C4×C7×C4⋊C4—24no—
39C4×C7×C22⋊C4—24no—
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48C2×C7×#95C2211yescharacteristic
49C2×C7×#95C2211yescharacteristic
50C2×C7×#95C2211yescharacteristic
51C2×C7×#95C2211yescharacteristic
52C2×C7×#95C2211yescharacteristic
53C2×C7×#95C2211yescharacteristic
54C2×C7×#95C2211yescharacteristic
55C2×C7×#95C2211yescharacteristic
56C2×C7×#95C2211yescharacteristic
57C2×C7×#95C2211yescharacteristic
58#14099C711yesmaximal, characteristic, direct product factor, Sylow
59C25×C7C2311yescharacteristic
60C22×C7×Q8—22no—
61C22×C7×Q8—22no—
62C22×C7×Q8—22no—
63C22×C7×Q8—22no—
64C22×C7×Q8—41no—
65C22×C7×Q8—41no—
66C22×C7×Q8C2×C414yes—
67C23×C4×C7—22no—
68C23×C4×C7—22no—
69C23×C4×C7—22no—
70C23×C4×C7—22no—
71C23×C4×C7—41no—
72C23×C4×C7—41no—
73C23×C4×C7C2×C414yes—
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C7×C22⋊Q8—232no—
89C2×C7×C4⋊C4—22no—
90C2×C7×C4⋊C4—22no—
91C2×C7×C4⋊C4—22no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4C2×C414yes—
100C2×C7×C4⋊C4C2×C414yes—
101C2×C7×C4⋊C4C2×C414yes—
102C2×C7×C4⋊C4D414yes—
103C2×C7×C4⋊C4D414yes—
104C2×C7×C22⋊C4—22no—
105C2×C7×C22⋊C4—22no—
106C2×C7×C22⋊C4—22no—
107C2×C7×C22⋊C4—22no—
108C2×C7×C22⋊C4—22no—
109C2×C7×C22⋊C4—22no—
110C2×C7×C22⋊C4—22no—
111C2×C7×C22⋊C4—22no—
112C2×C7×C22⋊C4—22no—
113C2×C7×C22⋊C4—22no—
114C2×C7×C22⋊C4—22no—
115C2×C7×C22⋊C4—22no—
116C2×C7×C22⋊C4—22no—
117C2×C7×C22⋊C4—41no—
118C2×C7×C22⋊C4—41no—
119C2×C7×C22⋊C4C2×C414yes—
120C2×C7×C22⋊C4C2×C414yes—
121C2×C7×C22⋊C4Q814yescomplemented
122C2×C42×C7—22no—
123C2×C42×C7—22no—
124C2×C42×C7—22no—
125C2×C42×C7—22no—
126C2×C42×C7—22no—
127C2×C42×C7—22no—
128C2×C42×C7—22no—
129C2×C42×C7—22no—
130C2×C42×C7—22no—
131C2×C42×C7—41no—
132C2×C42×C7—41no—
133C2×C42×C7—41no—
134C7×#95—22no—
135C7×#95—22no—
136C7×#95—22no—
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—22no—
140C7×#95—22no—
141C7×#95—22no—
142C7×#95—22no—
143C7×#95—22no—
144C7×#95—22no—
145C7×#95—22no—
146C7×#95—22no—
147C7×#95—22no—
148C7×#95—22no—
149C7×#95—41no—
150C7×#95—41no—
151C7×#95D414yes—
152C22×C22⋊Q8C2×C711yescharacteristic
153C2×#391C2×C711yescharacteristic, complemented
154C2×#387C2×C711yescharacteristic, complemented
155C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
156C2×C4×C22⋊C4C2×C711yescharacteristic
157#1446C2×C711yescharacteristic, complemented
158#1441C2×C711yescharacteristic, complemented
159#1439C2×C711yescharacteristic
160#1439C2×C711yescharacteristic
161#1437C2×C711yescharacteristic
162#1437C2×C711yescharacteristic
163#1436C2×C711yescharacteristic, complemented
164#1436C2×C711yescharacteristic, complemented
165#1436C2×C711yescharacteristic, complemented
166C22⋊#95C2×C711yescharacteristic
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7—21no—
179C24×C7C22×C412yes—
180C24×C7C2×Q812yes—
181C24×C7#4112yes—
182C24×C7C2411yescharacteristic
183C2×C7×Q8—28no—
184C2×C7×Q8—28no—
185C2×C7×Q8—44no—
186C2×C7×Q8—44no—
187C2×C7×Q8—44no—
188C2×C7×Q8—44no—
189C2×C7×Q8—44no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—21no—
238C22×C4×C7—21no—
239C22×C4×C7—21no—
240C22×C4×C7—21no—
241C22×C4×C7—21no—
242C22×C4×C7—21no—
243C22×C4×C7—21no—
244C22×C4×C7—21no—
245C22×C4×C7—21no—
246C22×C4×C7—21no—
247C22×C4×C7—21no—
248C22×C4×C7—21no—
249C22×C4×C7—21no—
250C22×C4×C7—21no—
251C22×C4×C7—21no—
252C22×C4×C7—28no—
253C22×C4×C7—28no—
254C22×C4×C7—21no—
255C22×C4×C7—21no—
256C22×C4×C7—21no—
257C22×C4×C7—21no—
258C22×C4×C7—21no—
259C22×C4×C7—21no—
260C22×C4×C7—21no—
261C22×C4×C7—21no—
262C22×C4×C7—21no—
263C22×C4×C7—21no—
264C22×C4×C7—21no—
265C22×C4×C7—21no—
266C22×C4×C7—21no—
267C22×C4×C7—21no—
268C22×C4×C7—44no—
269C22×C4×C7—44no—
270C22×C4×C7—44no—
271C22×C4×C7—44no—
272C22×C4×C7—44no—
273C22×C4×C7C22×C412yes—
274C22×C4×C7C22×C412yes—
275C22×C4×C7C22×C412yes—
276C22×C4×C7C22×C412yes—
277C22×C4×C7C22×C412yes—
278C22×C4×C7C22×C412yes—
279C22×C4×C7C2×D412yes—
280C22×C4×C7C2×D412yes—
281C22×C4×C7C2×D412yes—
282C22×C4×C7C2×D412yes—
283C22×C4×C7C2×D412yes—
284C22×C4×C7C2×D412yes—
285C22×C4×C7C2×D412yes—
286C22×C4×C7C2×D412yes—
287C22×C4×C7C2×D412yes—
288C22×C4×C7C2×Q812yes—
289C22×C4×C7C2×Q812yes—
290C22×C4×C7#4112yes—
291C22×C4×C7#4112yes—
292C22×C4×C7#4112yes—
293C22×C4×C7#4112yes—
294C22×C4×C7#4112yes—
295C7×C4⋊C4—28no—
296C7×C4⋊C4—28no—
297C7×C4⋊C4—28no—
298C7×C4⋊C4—44no—
299C7×C4⋊C4C22⋊C4116yescomplemented
300C7×C22⋊C4—28no—
301C7×C22⋊C4—28no—
302C7×C22⋊C4—28no—
303C7×C22⋊C4—28no—
304C7×C22⋊C4—44no—
305C7×C22⋊C4—44no—
306C42×C7—28no—
307C42×C7—44no—
308C42×C7—44no—
309C42×C7—44no—
310C23×Q8C22×C711yescharacteristic
311C24×C4C22×C711yescharacteristic
312C2×C22⋊Q8—24no—
313C2×C22⋊Q8—24no—
314C2×C22⋊Q8C4×C718yescomplemented
315C22×C4⋊C4C22×C711yescharacteristic
316C22×C4⋊C4C22×C711yescharacteristic
317C22×C4⋊C4C22×C711yescharacteristic
318C22×C4⋊C4C22×C711yescharacteristic
319C22×C4⋊C4C22×C711yescharacteristic
320C22×C22⋊C4C22×C711yescharacteristic
321C22×C22⋊C4C22×C711yescharacteristic
322C22×C22⋊C4C22×C711yescharacteristic
323C22×C22⋊C4C22×C711yescharacteristic
324C22×C22⋊C4C22×C711yescharacteristic
325C22×C22⋊C4C22×C711yescharacteristic
326C22×C42C22×C711yescharacteristic
327C22×C42C22×C711yescharacteristic
328C22×C42C22×C711yescharacteristic
329C22×C42C22×C711yescharacteristic
330#391—24no—
331#387—24no—
332C4×C4⋊C4—24no—
333C4×C22⋊C4—24no—
334C2×#95C22×C711yescharacteristic
335C2×#95C22×C711yescharacteristic
336C2×#95C22×C711yescharacteristic
337C2×#95C22×C711yescharacteristic
338C2×#95C22×C711yescharacteristic
339C2×#95C22×C711yescharacteristic
340C2×#95C22×C711yescharacteristic
341C2×#95C22×C711yescharacteristic
342C2×#95C22×C711yescharacteristic
343C2×#95C22×C711yescharacteristic
344C2×#95C22×C711yescharacteristic
345C2×#95C22×C711yescharacteristic
346C2×#95C22×C711yescharacteristic
347C2×#95C22×C711yescharacteristic
348C2×#95C22×C711yescharacteristic
349C2×#95C22×C711yescharacteristic
350C2×#95C22×C711yescharacteristic
351C2×#95C22×C711yescharacteristic
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—41no—
373C23×C7—41no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7—41no—
377C23×C7—41no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7—41no—
382C23×C7—41no—
383C23×C7—41no—
384C23×C7—41no—
385C23×C7—41no—
386C23×C7C4×Q814yes—
387C23×C7C23×C411yescharacteristic
388C23×C7C22×D411yescharacteristic
389C23×C7C22×D411yescharacteristic
390C23×C7C22×D411yescharacteristic
391C23×C7C22×Q811yescharacteristic
392C23×C7C2×#4111yescharacteristic
393C23×C7C2×#4111yescharacteristic
394C23×C7C2×#4111yescharacteristic
395C23×C7C2×#4111yescharacteristic
396C23×C7C2×#4111yescharacteristic
397C23×C7C2×#4111yescharacteristic
398C23×C7H(5,𝔽2)11yescharacteristic
399C23×C7H(5,𝔽2)11yescharacteristic
400C23×C72−1+411yescharacteristic
401C23×C72−1+411yescharacteristic
402C7×Q8—416no—
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
435C2×C4×C7—22no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—22no—
441C2×C4×C7—22no—
442C2×C4×C7—22no—
443C2×C4×C7—22no—
444C2×C4×C7—22no—
445C2×C4×C7—22no—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—22no—
450C2×C4×C7—22no—
451C2×C4×C7—22no—
452C2×C4×C7—22no—
453C2×C4×C7—22no—
454C2×C4×C7—416no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7—41no—
459C2×C4×C7—41no—
460C2×C4×C7—41no—
461C2×C4×C7—41no—
462C2×C4×C7—41no—
463C2×C4×C7—41no—
464C2×C4×C7—41no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—41no—
469C2×C4×C7—41no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—41no—
489C2×C4×C7—41no—
490C2×C4×C7—41no—
491C2×C4×C7—41no—
492C2×C4×C7—41no—
493C2×C4×C7—41no—
494C2×C4×C7—41no—
495C2×C4×C7—41no—
496C2×C4×C7—41no—
497C2×C4×C7C2×C22⋊C414yes—
498C2×C4×C7C2×C22⋊C414yes—
499C2×C4×C7C2×C22⋊C414yes—
500C2×C4×C7C4×D414yes—
501C2×C4×C7C22⋊Q814yescomplemented
502C25C23×C711yescharacteristic
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8C2×C4×C714yes—
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4C2×C4×C714yes—
517C23×C4C23×C711yescharacteristic
518C23×C4C23×C711yescharacteristic
519C23×C4C23×C711yescharacteristic
520C23×C4C23×C711yescharacteristic
521C23×C4C23×C711yescharacteristic
522C23×C4C23×C711yescharacteristic
523C23×C4C23×C711yescharacteristic
524C23×C4C23×C711yescharacteristic
525C23×C4C23×C711yescharacteristic
526C23×C4C23×C711yescharacteristic
527C23×C4C23×C711yescharacteristic
528C23×C4C23×C711yescharacteristic
529C23×C4C23×C711yescharacteristic
530C23×C4C23×C711yescharacteristic
531C22⋊Q8—232no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4C2×C4×C714yes—
543C2×C4⋊C4C2×C4×C714yes—
544C2×C4⋊C4C2×C4×C714yes—
545C2×C4⋊C4C7×D414yes—
546C2×C4⋊C4C7×D414yes—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4C2×C4×C714yes—
563C2×C22⋊C4C2×C4×C714yes—
564C2×C22⋊C4C7×Q814yescomplemented
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—41no—
575C2×C42—41no—
576C2×C42—41no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—41no—
593#95—41no—
594#95C7×D414yes—
595C22×C7—24no—
596C22×C7—24no—
597C22×C7—24no—
598C22×C7—42no—
599C22×C7—42no—
600C22×C7—42no—
601C22×C7—42no—
602C22×C7—42no—
603C22×C7—42no—
604C22×C7—42no—
605C22×C7—42no—
606C22×C7—42no—
607C22×C7—42no—
608C22×C7—42no—
609C22×C7—42no—
610C22×C7C22×C22⋊C411yescharacteristic
611C22×C7C2×C4×D411yescharacteristic
612C22×C7C2×C4×Q811yescharacteristic
613C22×C7C4×#4111yescharacteristic
614C22×C7C4×#4111yescharacteristic
615C22×C7#51811yescharacteristic
616C22×C7#51911yescharacteristic
617C22×C7C2×C22⋊Q811yescharacteristic
618C22×C7#52511yescharacteristic
619C22×C7#52511yescharacteristic
620C22×C7#52511yescharacteristic
621C22×C7#52911yescharacteristic
622C22×C7#53211yescharacteristic
623C22×C7#53211yescharacteristic
624C22×C7#53311yescharacteristic
625C22×C7#53911yescharacteristic
626C22×C7#53911yescharacteristic
627C22×C7#54211yescharacteristic
628C22×C7#54211yescharacteristic
629C22×C7D4211yescharacteristic
630C22×C7D4211yescharacteristic
631C22×C7#54611yescharacteristic
632C22×C7#54611yescharacteristic
633C22×C7#54711yescharacteristic
634C22×C7#54811yescharacteristic
635C22×C7#54811yescharacteristic
636C22×C7#54811yescharacteristic
637C22×C7D4×Q811yescharacteristic
638C22×C7D4×Q811yescharacteristic
639C22×C7#55111yescharacteristic
640C22×C7#55111yescharacteristic
641C22×C7#55211yescharacteristic
642C22×C7#55411yescharacteristic
643C22×C7#55411yescharacteristic
644C22×C7#55611yescharacteristic
645C4×C7—24no—
646C4×C7—24no—
647C4×C7—24no—
648C4×C7—24no—
649C4×C7—24no—
650C4×C7—42no—
651C4×C7—42no—
652C4×C7—42no—
653C4×C7—42no—
654C4×C7—42no—
655C4×C7—42no—
656C4×C7—42no—
657C4×C7—81no—
658C4×C7—81no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24C22×C4×C712yes—
672C24C2×C7×Q812yes—
673C24C7×#4112yes—
674C24C24×C711yescharacteristic
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4C22×C4×C712yes—
766C22×C4C22×C4×C712yes—
767C22×C4C22×C4×C712yes—
768C22×C4C22×C4×C712yes—
769C22×C4C22×C4×C712yes—
770C22×C4C22×C4×C712yes—
771C22×C4C2×C7×D412yes—
772C22×C4C2×C7×D412yes—
773C22×C4C2×C7×D412yes—
774C22×C4C2×C7×D412yes—
775C22×C4C2×C7×D412yes—
776C22×C4C2×C7×D412yes—
777C22×C4C2×C7×D412yes—
778C22×C4C2×C7×D412yes—
779C22×C4C2×C7×D412yes—
780C22×C4C2×C7×Q812yes—
781C22×C4C2×C7×Q812yes—
782C22×C4C7×#4112yes—
783C22×C4C7×#4112yes—
784C22×C4C7×#4112yes—
785C22×C4C7×#4112yes—
786C22×C4C7×#4112yes—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—44no—
791C4⋊C4C7×C22⋊C4116yescomplemented
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C42—28no—
799C42—44no—
800C42—44no—
801C42—44no—
802C2×C7—44no—
803C2×C7#229711yescharacteristic
804C2×C7C4×C22⋊Q811yescharacteristic
805C2×C7#233211yescharacteristic
806C2×C7D4×C22⋊C411yescharacteristic
807C2×C7Q8×C22⋊C411yescharacteristic
808C2×C7#236211yescharacteristic
809C2×C7#236811yescharacteristic
810C2×C7#244911yescharacteristic
811C2×C7#245211yescharacteristic
812C2×C7#246111yescharacteristic
813C2×C7#246311yescharacteristic
814C2×C7#246511yescharacteristic
815C2×C7#247711yescharacteristic
816C2×C7#255611yescharacteristic
817C2×C7#256011yescharacteristic
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23C4×C7×Q814yes—
853C23C23×C4×C711yescharacteristic
854C23C22×C7×D411yescharacteristic
855C23C22×C7×D411yescharacteristic
856C23C22×C7×D411yescharacteristic
857C23C22×C7×Q811yescharacteristic
858C23C2×C7×#4111yescharacteristic
859C23C2×C7×#4111yescharacteristic
860C23C2×C7×#4111yescharacteristic
861C23C2×C7×#4111yescharacteristic
862C23C2×C7×#4111yescharacteristic
863C23C2×C7×#4111yescharacteristic
864C23C7×H(5,𝔽2)11yescharacteristic
865C23C7×H(5,𝔽2)11yescharacteristic
866C23C7×2−1+411yescharacteristic
867C23C7×2−1+411yescharacteristic
868Q8—416no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—416no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C2×C7×C22⋊C414yes—
964C2×C4C2×C7×C22⋊C414yes—
965C2×C4C2×C7×C22⋊C414yes—
966C2×C4C4×C7×D414yes—
967C2×C4C7×C22⋊Q814yescomplemented
968C7#1409911yescharacteristic, direct product factor, Sylow
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C22×C7×C22⋊C411yescharacteristic
985C22C2×C4×C7×D411yescharacteristic
986C22C2×C4×C7×Q811yescharacteristic
987C22C4×C7×#4111yescharacteristic
988C22C4×C7×#4111yescharacteristic
989C22C7×#51811yescharacteristic
990C22C7×#51911yescharacteristic
991C22C2×C7×C22⋊Q811yescharacteristic
992C22C7×#52511yescharacteristic
993C22C7×#52511yescharacteristic
994C22C7×#52511yescharacteristic
995C22C7×#52911yescharacteristic
996C22C7×#53211yescharacteristic
997C22C7×#53211yescharacteristic
998C22C7×#53311yescharacteristic
999C22C7×#53911yescharacteristic
1000C22C7×#53911yescharacteristic
1001C22C7×#54211yescharacteristic
1002C22C7×#54211yescharacteristic
1003C22C7×D4211yescharacteristic
1004C22C7×D4211yescharacteristic
1005C22C7×#54611yescharacteristic
1006C22C7×#54611yescharacteristic
1007C22C7×#54711yescharacteristic
1008C22C7×#54811yescharacteristic
1009C22C7×#54811yescharacteristic
1010C22C7×#54811yescharacteristic
1011C22C7×D4×Q811yescharacteristic
1012C22C7×D4×Q811yescharacteristic
1013C22C7×#55111yescharacteristic
1014C22C7×#55111yescharacteristic
1015C22C7×#55211yescharacteristic
1016C22C7×#55411yescharacteristic
1017C22C7×#55411yescharacteristic
1018C22C7×#55611yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—24no—
1022C4—24no—
1023C4—24no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—81no—
1032C4—81no—
1033C2—44no—
1034C2C7×#229711yescharacteristic
1035C2C4×C7×C22⋊Q811yescharacteristic
1036C2C7×#233211yescharacteristic
1037C2C7×D4×C22⋊C411yescharacteristic
1038C2C7×Q8×C22⋊C411yescharacteristic
1039C2C7×#236211yescharacteristic
1040C2C7×#236811yescharacteristic
1041C2C7×#244911yescharacteristic
1042C2C7×#245211yescharacteristic
1043C2C7×#246111yescharacteristic
1044C2C7×#246311yescharacteristic
1045C2C7×#246511yescharacteristic
1046C2C7×#247711yescharacteristic
1047C2C7×#255611yescharacteristic
1048C2C7×#256011yescharacteristic
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. C2×C7×#391C2semidirect
3. C2×C7×#387C2semidirect
4. C2×C4×C7×C4⋊C4C2semidirect
6. C7×#1446C2semidirect
7. C7×#1441C2semidirect
12. C7×#1436C2semidirect
13. C7×#1436C2semidirect
14. C7×#1436C2semidirect
20. C2×C7×C22⋊Q8C4semidirect
58. #14099C7direct (N × H)
121. C2×C7×C22⋊C4Q8semidirect
153. C2×#391C2×C7semidirect
154. C2×#387C2×C7semidirect
155. C2×C4×C4⋊C4C2×C7semidirect
157. #1446C2×C7semidirect
158. #1441C2×C7semidirect
163. #1436C2×C7semidirect
164. #1436C2×C7semidirect
165. #1436C2×C7semidirect
299. C7×C4⋊C4C22⋊C4semidirect
314. C2×C22⋊Q8C4×C7semidirect
501. C2×C4×C7C22⋊Q8semidirect
564. C2×C22⋊C4C7×Q8semidirect
791. C4⋊C4C7×C22⋊C4semidirect
967. C2×C4C7×C22⋊Q8semidirect
968. C7#14099direct (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
C2×C7×#3912
C2×C7×#3872
C2×C4×C7×C4⋊C42
C2×C4×C7×C22⋊C42
C7×#14462
C7×#14412
C7×#14392
C7×#14372
C7×#14362
C7×C22⋊#952
#140997