Finite Group Databasebeta

← C7×#14433 #13191649

Subgroups — C7×#14433 #13191649

Order 1792.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×C7×#387C211yesmaximal, characteristic, complemented
3C2×C7×#385C211yesmaximal, characteristic
4C7×#1443C211yesmaximal, characteristic, complemented
5C7×#1442C211yesmaximal, characteristic, complemented
6C7×#1442C211yesmaximal, characteristic, complemented
7C7×#1441C211yesmaximal, characteristic, complemented
8C7×#1440C211yesmaximal, characteristic
9C7×#1439C211yesmaximal, characteristic
10C7×#1437C211yesmaximal, characteristic
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C7×#1434C211yesmaximal, characteristic, complemented
13C7×#1434C211yesmaximal, characteristic, complemented
14C7×C22⋊#95C211yesmaximal, characteristic
15C7×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×C42×C7C2211yescharacteristic
29C7×#388C418yescomplemented
30C7×#387—24no—
31C7×#385—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39C2×C7×#95C2211yescharacteristic
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
54#14433C711yesmaximal, characteristic, direct product factor, Sylow
55C25×C7C2311yescharacteristic
56C23×C4×C7—22no—
57C23×C4×C7—22no—
58C23×C4×C7—22no—
59C23×C4×C7—41no—
60C23×C4×C7—41no—
61C23×C4×C7—41no—
62C23×C4×C7—41no—
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—41no—
85C2×C7×C4⋊C4—41no—
86C2×C7×C4⋊C4—41no—
87C2×C7×C4⋊C4—41no—
88C2×C7×C4⋊C4C2×C414yescomplemented
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—22no—
91C2×C7×C22⋊C4—22no—
92C2×C7×C22⋊C4—22no—
93C2×C7×C22⋊C4—22no—
94C2×C7×C22⋊C4—22no—
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—41no—
99C2×C7×C22⋊C4—41no—
100C2×C7×C22⋊C4—41no—
101C2×C7×C22⋊C4—41no—
102C2×C7×C22⋊C4—41no—
103C2×C7×C22⋊C4—41no—
104C2×C7×C22⋊C4C2×C414yes—
105C2×C7×C22⋊C4C2×C414yes—
106C2×C7×C22⋊C4C2×C414yes—
107C2×C42×C7—22no—
108C2×C42×C7—22no—
109C2×C42×C7—41no—
110C2×C42×C7—41no—
111C2×C42×C7—41no—
112C2×C42×C7C2×C414yescomplemented
113C7×#95—22no—
114C7×#95—22no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—22no—
119C7×#95—41no—
120C7×#95—41no—
121C7×#95—41no—
122C7×#95—41no—
123C7×#95—41no—
124C7×#95—41no—
125C7×#95—41no—
126C7×#95—41no—
127C7×#95—41no—
128C7×#95—41no—
129C7×#95—41no—
130C7×#95—41no—
131C7×#95—41no—
132C7×#95C2×C414yescomplemented
133C7×#95C2×C414yescomplemented
134C7×#95D414yes—
135C2×#388C2×C711yescharacteristic
136C2×#387C2×C711yescharacteristic, complemented
137C2×#385C2×C711yescharacteristic
138#1443C2×C711yescharacteristic, complemented
139#1442C2×C711yescharacteristic, complemented
140#1442C2×C711yescharacteristic, complemented
141#1441C2×C711yescharacteristic, complemented
142#1440C2×C711yescharacteristic
143#1439C2×C711yescharacteristic
144#1437C2×C711yescharacteristic
145C4⋊#95C2×C711yescharacteristic, complemented
146#1434C2×C711yescharacteristic, complemented
147#1434C2×C711yescharacteristic, complemented
148C22⋊#95C2×C711yescharacteristic
149C22⋊#95C2×C711yescharacteristic
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—21no—
153C24×C7—21no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—21no—
157C24×C7—21no—
158C24×C7—21no—
159C24×C7—21no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7C22×C412yes—
163C24×C7#4112yes—
164C24×C7#4112yes—
165C24×C7C2411yescharacteristic
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
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—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
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—44no—
253C22×C4×C7—44no—
254C22×C4×C7—44no—
255C22×C4×C7—44no—
256C22×C4×C7—44no—
257C22×C4×C7—44no—
258C22×C4×C7—44no—
259C22×C4×C7C22×C412yes—
260C22×C4×C7C22×C412yes—
261C22×C4×C7C22×C412yes—
262C22×C4×C7C22×C412yes—
263C22×C4×C7C22×C412yes—
264C22×C4×C7C22×C412yes—
265C22×C4×C7C2×D412yes—
266C22×C4×C7C2×D412yes—
267C22×C4×C7C2×D412yes—
268C22×C4×C7#4112yes—
269C22×C4×C7#4112yes—
270C22×C4×C7#4112yes—
271C7×C4⋊C4—28no—
272C7×C4⋊C4—44no—
273C7×C4⋊C4—44no—
274C7×C4⋊C4—44no—
275C7×C22⋊C4—28no—
276C7×C22⋊C4—28no—
277C7×C22⋊C4—44no—
278C7×C22⋊C4—44no—
279C7×C22⋊C4—44no—
280C7×C22⋊C4—44no—
281C42×C7—44no—
282C42×C7—44no—
283C24×C4C22×C711yescharacteristic
284C22×C4⋊C4C22×C711yescharacteristic
285C22×C4⋊C4C22×C711yescharacteristic
286C22×C4⋊C4C22×C711yescharacteristic
287C22×C4⋊C4C22×C711yescharacteristic
288C22×C22⋊C4C22×C711yescharacteristic
289C22×C22⋊C4C22×C711yescharacteristic
290C22×C22⋊C4C22×C711yescharacteristic
291C22×C22⋊C4C22×C711yescharacteristic
292C22×C22⋊C4C22×C711yescharacteristic
293C22×C22⋊C4C22×C711yescharacteristic
294C22×C42C22×C711yescharacteristic
295C22×C42C22×C711yescharacteristic
296#388C4×C718yescomplemented
297#387—24no—
298#385—24no—
299C2×#95C22×C711yescharacteristic
300C2×#95C22×C711yescharacteristic
301C2×#95C22×C711yescharacteristic
302C2×#95C22×C711yescharacteristic
303C2×#95C22×C711yescharacteristic
304C2×#95C22×C711yescharacteristic
305C2×#95C22×C711yescharacteristic
306C2×#95C22×C711yescharacteristic
307C2×#95C22×C711yescharacteristic
308C2×#95C22×C711yescharacteristic
309C2×#95C22×C711yescharacteristic
310C2×#95C22×C711yescharacteristic
311C2×#95C22×C711yescharacteristic
312C2×#95C22×C711yescharacteristic
313C2×#95C22×C711yescharacteristic
314C2×#95C22×C711yescharacteristic
315C2×#95C22×C711yescharacteristic
316C2×#95C22×C711yescharacteristic
317C2×#95C22×C711yescharacteristic
318C2×#95C22×C711yescharacteristic
319C2×#95C22×C711yescharacteristic
320C2×#95C22×C711yescharacteristic
321C23×C7—22no—
322C23×C7—22no—
323C23×C7—22no—
324C23×C7—22no—
325C23×C7—22no—
326C23×C7—22no—
327C23×C7—22no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—41no—
340C23×C7—41no—
341C23×C7—41no—
342C23×C7—41no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—41no—
346C23×C7—41no—
347C23×C7—41no—
348C23×C7—41no—
349C23×C7—41no—
350C23×C7—41no—
351C23×C7—41no—
352C23×C7—41no—
353C23×C7—41no—
354C23×C7—41no—
355C23×C7#11714yes—
356C23×C7C23×C411yescharacteristic
357C23×C7C22×D411yescharacteristic
358C23×C7C2×#4111yescharacteristic
359C23×C7C2×#4111yescharacteristic
360C23×C7C2×#4111yescharacteristic
361C23×C7C2×#4111yescharacteristic
362C23×C7C2×#4111yescharacteristic
363C23×C7H(5,𝔽2)11yescharacteristic
364C23×C7H(5,𝔽2)11yescharacteristic
365C23×C7H(5,𝔽2)11yescharacteristic
366C23×C7H(5,𝔽2)11yescharacteristic
367C23×C7H(5,𝔽2)11yescharacteristic
368C23×C72−1+411yescharacteristic
369C23×C72−1+411yescharacteristic
370C23×C72−1+411yescharacteristic
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
403C2×C4×C7—22no—
404C2×C4×C7—416no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
411C2×C4×C7—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
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×C7C4×D414yes—
470C25C23×C711yescharacteristic
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—41no—
475C23×C4—41no—
476C23×C4—41no—
477C23×C4—41no—
478C23×C4C23×C711yescharacteristic
479C23×C4C23×C711yescharacteristic
480C23×C4C23×C711yescharacteristic
481C23×C4C23×C711yescharacteristic
482C23×C4C23×C711yescharacteristic
483C23×C4C23×C711yescharacteristic
484C23×C4C23×C711yescharacteristic
485C23×C4C23×C711yescharacteristic
486C23×C4C23×C711yescharacteristic
487C23×C4C23×C711yescharacteristic
488C23×C4C23×C711yescharacteristic
489C23×C4C23×C711yescharacteristic
490C23×C4C23×C711yescharacteristic
491C23×C4C23×C711yescharacteristic
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4C2×C4×C714yescomplemented
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4C2×C4×C714yes—
520C2×C22⋊C4C2×C4×C714yes—
521C2×C22⋊C4C2×C4×C714yes—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—41no—
525C2×C42—41no—
526C2×C42—41no—
527C2×C42C2×C4×C714yescomplemented
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—41no—
535#95—41no—
536#95—41no—
537#95—41no—
538#95—41no—
539#95—41no—
540#95—41no—
541#95—41no—
542#95—41no—
543#95—41no—
544#95—41no—
545#95—41no—
546#95—41no—
547#95C2×C4×C714yescomplemented
548#95C2×C4×C714yescomplemented
549#95C7×D414yes—
550C22×C7—24no—
551C22×C7—24no—
552C22×C7—24no—
553C22×C7—42no—
554C22×C7—42no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7C2×#11711yescharacteristic
566C22×C7C2×C4×D411yescharacteristic
567C22×C7C4×#4111yescharacteristic
568C22×C7#51811yescharacteristic
569C22×C7#52011yescharacteristic
570C22×C7#52011yescharacteristic
571C22×C7#52011yescharacteristic
572C22×C7#53511yescharacteristic
573C22×C7#53611yescharacteristic
574C22×C7#53811yescharacteristic
575C22×C7#53811yescharacteristic
576C22×C7#53811yescharacteristic
577C22×C7#53911yescharacteristic
578C22×C7#53911yescharacteristic
579C22×C7#53911yescharacteristic
580C22×C7#54111yescharacteristic
581C22×C7#54211yescharacteristic
582C22×C7#54211yescharacteristic
583C22×C7#54211yescharacteristic
584C22×C7#54611yescharacteristic
585C22×C7#54611yescharacteristic
586C22×C7#54611yescharacteristic
587C22×C7#54811yescharacteristic
588C22×C7#55111yescharacteristic
589C22×C7#55111yescharacteristic
590C22×C7#55211yescharacteristic
591C22×C7#55211yescharacteristic
592C22×C7#55211yescharacteristic
593C22×C7#55311yescharacteristic
594C22×C7#55311yescharacteristic
595C22×C7#55311yescharacteristic
596C22×C7#56011yescharacteristic
597C22×C7#56211yescharacteristic
598C22×C7#56211yescharacteristic
599C22×C7#56311yescharacteristic
600C4×C7—24no—
601C4×C7—42no—
602C4×C7—42no—
603C4×C7—42no—
604C4×C7—42no—
605C4×C7—42no—
606C4×C7—42no—
607C4×C7—42no—
608C4×C7—42no—
609C4×C7—42no—
610C4×C7—81no—
611C4×C7—81no—
612C4×C7—81no—
613C4×C7—81no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C22×C4×C712yes—
627C24C7×#4112yes—
628C24C7×#4112yes—
629C24C24×C711yescharacteristic
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
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—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4C22×C4×C712yes—
724C22×C4C22×C4×C712yes—
725C22×C4C22×C4×C712yes—
726C22×C4C22×C4×C712yes—
727C22×C4C22×C4×C712yes—
728C22×C4C22×C4×C712yes—
729C22×C4C2×C7×D412yes—
730C22×C4C2×C7×D412yes—
731C22×C4C2×C7×D412yes—
732C22×C4C7×#4112yes—
733C22×C4C7×#4112yes—
734C22×C4C7×#4112yes—
735C4⋊C4—28no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C22⋊C4—28no—
740C22⋊C4—28no—
741C22⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C42—44no—
746C42—44no—
747C2×C7—44no—
748C2×C7#231811yescharacteristic
749C2×C7#232611yescharacteristic
750C2×C7#233411yescharacteristic
751C2×C7#234311yescharacteristic
752C2×C7#235211yescharacteristic
753C2×C7#236411yescharacteristic
754C2×C7#237611yescharacteristic
755C2×C7#268511yescharacteristic
756C2×C7#268711yescharacteristic
757C2×C7#269011yescharacteristic
758C2×C7#269611yescharacteristic
759C2×C7#273911yescharacteristic
760C2×C7#275711yescharacteristic
761C2×C7#276511yescharacteristic
762C2×C7#277911yescharacteristic
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23C7×#11714yes—
798C23C23×C4×C711yescharacteristic
799C23C22×C7×D411yescharacteristic
800C23C2×C7×#4111yescharacteristic
801C23C2×C7×#4111yescharacteristic
802C23C2×C7×#4111yescharacteristic
803C23C2×C7×#4111yescharacteristic
804C23C2×C7×#4111yescharacteristic
805C23C7×H(5,𝔽2)11yescharacteristic
806C23C7×H(5,𝔽2)11yescharacteristic
807C23C7×H(5,𝔽2)11yescharacteristic
808C23C7×H(5,𝔽2)11yescharacteristic
809C23C7×H(5,𝔽2)11yescharacteristic
810C23C7×2−1+411yescharacteristic
811C23C7×2−1+411yescharacteristic
812C23C7×2−1+411yescharacteristic
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—416no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4C4×C7×D414yes—
912C7#1443311yescharacteristic, direct product factor, Sylow
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×C7×#11711yescharacteristic
929C22C2×C4×C7×D411yescharacteristic
930C22C4×C7×#4111yescharacteristic
931C22C7×#51811yescharacteristic
932C22C7×#52011yescharacteristic
933C22C7×#52011yescharacteristic
934C22C7×#52011yescharacteristic
935C22C7×#53511yescharacteristic
936C22C7×#53611yescharacteristic
937C22C7×#53811yescharacteristic
938C22C7×#53811yescharacteristic
939C22C7×#53811yescharacteristic
940C22C7×#53911yescharacteristic
941C22C7×#53911yescharacteristic
942C22C7×#53911yescharacteristic
943C22C7×#54111yescharacteristic
944C22C7×#54211yescharacteristic
945C22C7×#54211yescharacteristic
946C22C7×#54211yescharacteristic
947C22C7×#54611yescharacteristic
948C22C7×#54611yescharacteristic
949C22C7×#54611yescharacteristic
950C22C7×#54811yescharacteristic
951C22C7×#55111yescharacteristic
952C22C7×#55111yescharacteristic
953C22C7×#55211yescharacteristic
954C22C7×#55211yescharacteristic
955C22C7×#55211yescharacteristic
956C22C7×#55311yescharacteristic
957C22C7×#55311yescharacteristic
958C22C7×#55311yescharacteristic
959C22C7×#56011yescharacteristic
960C22C7×#56211yescharacteristic
961C22C7×#56211yescharacteristic
962C22C7×#56311yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—81no—
977C2—44no—
978C2C7×#231811yescharacteristic
979C2C7×#232611yescharacteristic
980C2C7×#233411yescharacteristic
981C2C7×#234311yescharacteristic
982C2C7×#235211yescharacteristic
983C2C7×#236411yescharacteristic
984C2C7×#237611yescharacteristic
985C2C7×#268511yescharacteristic
986C2C7×#268711yescharacteristic
987C2C7×#269011yescharacteristic
988C2C7×#269611yescharacteristic
989C2C7×#273911yescharacteristic
990C2C7×#275711yescharacteristic
991C2C7×#276511yescharacteristic
992C2C7×#277911yescharacteristic
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×#387C2semidirect
4. C7×#1443C2semidirect
5. C7×#1442C2semidirect
6. C7×#1442C2semidirect
7. C7×#1441C2semidirect
11. C7×C4⋊#95C2semidirect
12. C7×#1434C2semidirect
13. C7×#1434C2semidirect
29. C7×#388C4semidirect
54. #14433C7direct (N × H)
88. C2×C7×C4⋊C4C2×C4semidirect
112. C2×C42×C7C2×C4semidirect
132. C7×#95C2×C4semidirect
133. C7×#95C2×C4semidirect
136. C2×#387C2×C7semidirect
138. #1443C2×C7semidirect
139. #1442C2×C7semidirect
140. #1442C2×C7semidirect
141. #1441C2×C7semidirect
145. C4⋊#95C2×C7semidirect
146. #1434C2×C7semidirect
147. #1434C2×C7semidirect
296. #388C4×C7semidirect
503. C2×C4⋊C4C2×C4×C7semidirect
527. C2×C42C2×C4×C7semidirect
547. #95C2×C4×C7semidirect
548. #95C2×C4×C7semidirect
912. C7#14433direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C7×#3872
C2×C7×#3852
C7×#14432
C7×#14422
C7×#14412
C7×#14402
C7×#14392
C7×#14372
C7×C4⋊#952
C7×#14342
C7×C22⋊#952
#144337