Finite Group Databasebeta

← C2×C7×#3557 #13239954

Subgroups — C2×C7×#3557 #13239954

Order 1792.

6554 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3557C2132yesmaximal, direct product factor
2C2×C7×#563C214yesmaximal, complemented
3C2×C7×#559C212yesmaximal, complemented
4C2×C7×#557C212yesmaximal, complemented
5C2×C7×#556C212yesmaximal, complemented
6C2×C7×#554C212yesmaximal, complemented
7C2×C7×#552C214yesmaximal, complemented
8C2×C7×#542C212yesmaximal, complemented
9C2×C7×#542C214yesmaximal, complemented
10C2×C7×#541C211yesmaximal, characteristic, complemented
11C2×C7×#540C211yesmaximal, characteristic
12C2×C7×#539C214yesmaximal, complemented
13C2×C7×#533C211yesmaximal, characteristic, complemented
14C2×C7×#529C212yesmaximal, complemented
15C7×#563C22164yescomplemented
16C7×#559C22132yescomplemented
17C7×#557C22132yescomplemented
18C7×#556C22132yescomplemented
19C7×#554C22132yescomplemented
20C7×#552C22164yescomplemented
21C7×#542C22132yescomplemented
22C7×#542C22164yescomplemented
23C7×#541C22116yescomplemented
24C7×#540C22116yes—
25C7×#539C22164yescomplemented
26C7×#533C22116yescomplemented
27C2×C7×C4⋊Q8C2212yes—
28C2×C7×C4⋊Q8C2211yescharacteristic
29C2×C7×C4⋊Q8C2212yes—
30C2×C7×C4⋊Q8C2214yes—
31C2×C7×#127C2211yescharacteristic
32C7×#529C22132yescomplemented
33C2×C7×#126C2214yes—
34C2×C7×#126C2214yes—
35C2×C7×#126C2214yes—
36C2×C7×#126C2214yes—
37C2×C7×#126C2214yes—
38C2×C7×#125C2212yes—
39C2×C7×#125C2212yes—
40C2×C7×#125C2214yes—
41C2×C7×#125C2214yes—
42C2×C7×#125C2211yescharacteristic
43C2×C7×#125C2214yes—
44C2×C7×#125C2211yescharacteristic
45C2×C7×#124C2212yes—
46C2×C7×#124C2214yes—
47C2×C7×#124C2212yes—
48C2×C7×#124C2214yes—
49C2×C7×#123C2214yes—
50C2×C7×#123C2214yes—
51C2×C7×#123C2214yes—
52C2×C7×#123C2214yes—
53C2×C7×#123C2214yes—
54C2×C7×C22⋊Q8C2212yes—
55C2×C7×C22⋊Q8C2212yes—
56C2×C7×C22⋊Q8C2212yes—
57C2×C7×C22⋊Q8C2214yes—
58C2×C7×C22⋊Q8C2214yes—
59C2×C7×C22⋊Q8C2214yes—
60C2×C7×C22⋊Q8C2214yes—
61C2×C7×C22⋊Q8C2214yes—
62C2×C7×#121C2212yes—
63C2×C7×#121C2214yes—
64C2×C4×C7×Q8C2212yes—
65C2×C4×C7×Q8C2212yes—
66C2×C4×C7×Q8C2212yes—
67C2×C4×C7×Q8C2212yes—
68C2×C4×C7×Q8C2214yes—
69C2×C4×C7×Q8C2212yes—
70C2×C4×C7×D4C2214yes—
71C2×C4×C7×D4C2212yes—
72C2×C4×C7×D4C2214yes—
73C2×C4×C7×D4C2212yes—
74C2×C4×C7×D4C2212yes—
75C2×C7×#117C2214yes—
76C2×C7×#117C2211yescharacteristic
77C2×C7×#117C2211yescharacteristic
78C2×C7×#117C2214yes—
79C22×C7×C4⋊C4C2214yes—
80C22×C42×C7C2211yescharacteristic
81C2×#3557C711yesmaximal, characteristic, direct product factor, Sylow
82C22×C7×Q8C2312yes—
83C22×C7×Q8C2312yes—
84C22×C7×Q8C2314yes—
85C22×C7×Q8C2312yes—
86C22×C7×D4C2312yes—
87C22×C7×D4C2314yes—
88C22×C7×D4C2314yes—
89C23×C4×C7C2311yescharacteristic
90C23×C4×C7C2312yes—
91C23×C4×C7C2314yes—
92C23×C4×C7C2314yes—
93C23×C4×C7C2314yes—
94C7×C4⋊Q8C23116yes—
95C7×C4⋊Q8C2318yes—
96C7×C4⋊Q8C23116yes—
97C7×C4⋊Q8C23132yes—
98C7×#127C2318yes—
99C7×#126C23132yes—
100C7×#126C23132yes—
101C7×#126C23132yes—
102C7×#126C23132yes—
103C7×#126C23132yes—
104C7×#125C23116yes—
105C7×#125C23116yes—
106C7×#125C23132yes—
107C7×#125C23132yes—
108C7×#125C2318yes—
109C7×#125C23132yes—
110C7×#125C2318yes—
111C7×#124C23116yes—
112C7×#124C23132yes—
113C7×#124C23116yes—
114C7×#124C23132yes—
115C7×#123C23132yes—
116C7×#123C23132yes—
117C7×#123C23132yes—
118C7×#123C23132yes—
119C7×#123C23132yes—
120C7×C22⋊Q8C23116yes—
121C7×C22⋊Q8C23116yes—
122C7×C22⋊Q8C23116yes—
123C7×C22⋊Q8C23132yes—
124C7×C22⋊Q8C23132yes—
125C7×C22⋊Q8C23132yes—
126C7×C22⋊Q8C23132yes—
127C7×C22⋊Q8C23132yes—
128C7×#121C23116yes—
129C7×#121C23132yes—
130C4×C7×Q8C23116yes—
131C4×C7×Q8C23116yes—
132C4×C7×Q8C23116yes—
133C4×C7×Q8C23116yes—
134C4×C7×Q8C23132yes—
135C4×C7×Q8C23116yes—
136C4×C7×D4C23132yes—
137C4×C7×D4C23116yes—
138C4×C7×D4C23132yes—
139C4×C7×D4C23116yes—
140C4×C7×D4C23116yes—
141C7×#117C23132yes—
142C7×#117C2318yes—
143C7×#117C2318yes—
144C7×#117C23132yes—
145C2×C7×C4⋊C4C2312yes—
146C2×C7×C4⋊C4C2314yes—
147C2×C7×C4⋊C4C2314yes—
148C2×C7×C4⋊C4C2314yes—
149C2×C7×C4⋊C4C23132yes—
150C2×C7×C4⋊C4C2312yes—
151C2×C7×C4⋊C4C2314yes—
152C2×C7×C4⋊C4C2312yes—
153C2×C7×C4⋊C4C2314yes—
154C2×C7×C4⋊C4C2312yes—
155C2×C7×C4⋊C4C2312yes—
156C2×C7×C4⋊C4C2312yes—
157C2×C7×C4⋊C4C2312yes—
158C2×C7×C4⋊C4C2314yes—
159C2×C7×C4⋊C4C2312yes—
160C2×C7×C4⋊C4C2314yes—
161C2×C7×C4⋊C4C2312yes—
162C2×C7×C4⋊C4C2314yes—
163C2×C7×C4⋊C4C2312yes—
164C2×C7×C4⋊C4C2314yes—
165C2×C7×C4⋊C4C2314yes—
166C2×C7×C22⋊C4C2314yes—
167C2×C7×C22⋊C4C2312yes—
168C2×C7×C22⋊C4C2314yes—
169C2×C7×C22⋊C4C2311yescharacteristic
170C2×C7×C22⋊C4C2311yescharacteristic
171C2×C7×C22⋊C4C2314yes—
172C2×C7×C22⋊C4C2314yes—
173C2×C7×C22⋊C4C2314yes—
174C2×C7×C22⋊C4C2314yes—
175C2×C7×C22⋊C4C2314yes—
176C2×C7×C22⋊C4C2314yes—
177C2×C7×C22⋊C4C2314yes—
178C2×C42×C7C2311yescharacteristic
179C2×C42×C7C2312yes—
180C2×C42×C7C2311yescharacteristic
181C2×C42×C7C2318yes—
182C2×C42×C7C2314yes—
183C2×C42×C7C2311yescharacteristic
184C2×C42×C7C2312yes—
185C2×C42×C7C2311yescharacteristic
186C2×C42×C7C2314yes—
187C2×C42×C7C2314yes—
188#3557C2×C7132yesdirect product factor
189C2×#563C2×C714yescomplemented
190C2×#559C2×C712yescomplemented
191C2×#557C2×C712yescomplemented
192C2×#556C2×C712yescomplemented
193C2×#554C2×C712yescomplemented
194C2×#552C2×C714yescomplemented
195C2×#542C2×C712yescomplemented
196C2×#542C2×C714yescomplemented
197C2×#541C2×C711yescharacteristic, complemented
198C2×#540C2×C711yescharacteristic
199C2×#539C2×C714yescomplemented
200C2×#533C2×C711yescharacteristic, complemented
201C2×#529C2×C712yescomplemented
202C24×C7C2411yescharacteristic
203C24×C7C2414yes—
204C2×C7×Q8—28no—
205C2×C7×Q8—44no—
206C2×C7×Q8—48no—
207C2×C7×Q8—44no—
208C2×C7×Q8C2418yes—
209C2×C7×Q8C2418yes—
210C2×C7×Q8C24116yes—
211C2×C7×Q8C2418yes—
212C2×C7×D4—28no—
213C2×C7×D4—48no—
214C2×C7×D4—48no—
215C2×C7×D4C2418yes—
216C2×C7×D4C24116yes—
217C2×C7×D4C24116yes—
218C22×C4×C7—24no—
219C22×C4×C7—48no—
220C22×C4×C7—44no—
221C22×C4×C7—48no—
222C22×C4×C7—48no—
223C22×C4×C7C2414yes—
224C22×C4×C7C2412yes—
225C22×C4×C7C2414yes—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2411yescharacteristic
229C22×C4×C7C2412yes—
230C22×C4×C7C2414yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2412yes—
233C22×C4×C7C2414yes—
234C22×C4×C7C2418yes—
235C22×C4×C7C24116yes—
236C22×C4×C7C24116yes—
237C22×C4×C7C24116yes—
238C22×C4×C7C2411yescharacteristic
239C7×C4⋊C4C2418yes—
240C7×C4⋊C4C24116yes—
241C7×C4⋊C4C24116yes—
242C7×C4⋊C4C24116yes—
243C7×C4⋊C4C2418yes—
244C7×C4⋊C4C24116yes—
245C7×C4⋊C4C2418yes—
246C7×C4⋊C4C24116yes—
247C7×C4⋊C4C2418yes—
248C7×C4⋊C4C2418yes—
249C7×C4⋊C4C2418yes—
250C7×C4⋊C4C2418yes—
251C7×C4⋊C4C24116yes—
252C7×C4⋊C4C2418yes—
253C7×C4⋊C4C24116yes—
254C7×C4⋊C4C2418yes—
255C7×C4⋊C4C24116yes—
256C7×C4⋊C4C2418yes—
257C7×C4⋊C4C24116yes—
258C7×C4⋊C4C24116yes—
259C7×C22⋊C4C24116yes—
260C7×C22⋊C4C2418yes—
261C7×C22⋊C4C24116yes—
262C7×C22⋊C4C2414yes—
263C7×C22⋊C4C2414yes—
264C7×C22⋊C4C24116yes—
265C7×C22⋊C4C24116yes—
266C7×C22⋊C4C24116yes—
267C7×C22⋊C4C24116yes—
268C7×C22⋊C4C24116yes—
269C7×C22⋊C4C24116yes—
270C7×C22⋊C4C24116yes—
271C42×C7C2414yes—
272C42×C7C2418yes—
273C42×C7C2414yes—
274C42×C7C24116yes—
275C42×C7C2414yes—
276C42×C7C2418yes—
277C42×C7C2414yes—
278C42×C7C24116yes—
279C42×C7C24116yes—
280#563C22×C7164yescomplemented
281#559C22×C7132yescomplemented
282#557C22×C7132yescomplemented
283#556C22×C7132yescomplemented
284#554C22×C7132yescomplemented
285#552C22×C7164yescomplemented
286#542C22×C7132yescomplemented
287#542C22×C7164yescomplemented
288#541C22×C7116yescomplemented
289#540C22×C7116yes—
290#539C22×C7164yescomplemented
291#533C22×C7116yescomplemented
292C2×C4⋊Q8C22×C712yes—
293C2×C4⋊Q8C22×C711yescharacteristic
294C2×C4⋊Q8C22×C712yes—
295C2×C4⋊Q8C22×C714yes—
296C2×#127C22×C711yescharacteristic
297#529C22×C7132yescomplemented
298C2×#126C22×C714yes—
299C2×#126C22×C714yes—
300C2×#126C22×C714yes—
301C2×#126C22×C714yes—
302C2×#126C22×C714yes—
303C2×#125C22×C712yes—
304C2×#125C22×C712yes—
305C2×#125C22×C714yes—
306C2×#125C22×C714yes—
307C2×#125C22×C711yescharacteristic
308C2×#125C22×C714yes—
309C2×#125C22×C711yescharacteristic
310C2×#124C22×C712yes—
311C2×#124C22×C714yes—
312C2×#124C22×C712yes—
313C2×#124C22×C714yes—
314C2×#123C22×C714yes—
315C2×#123C22×C714yes—
316C2×#123C22×C714yes—
317C2×#123C22×C714yes—
318C2×#123C22×C714yes—
319C2×C22⋊Q8C22×C712yes—
320C2×C22⋊Q8C22×C712yes—
321C2×C22⋊Q8C22×C712yes—
322C2×C22⋊Q8C22×C714yes—
323C2×C22⋊Q8C22×C714yes—
324C2×C22⋊Q8C22×C714yes—
325C2×C22⋊Q8C22×C714yes—
326C2×C22⋊Q8C22×C714yes—
327C2×#121C22×C712yes—
328C2×#121C22×C714yes—
329C2×C4×Q8C22×C712yes—
330C2×C4×Q8C22×C712yes—
331C2×C4×Q8C22×C712yes—
332C2×C4×Q8C22×C712yes—
333C2×C4×Q8C22×C714yes—
334C2×C4×Q8C22×C712yes—
335C2×C4×D4C22×C714yes—
336C2×C4×D4C22×C712yes—
337C2×C4×D4C22×C714yes—
338C2×C4×D4C22×C712yes—
339C2×C4×D4C22×C712yes—
340C2×#117C22×C714yes—
341C2×#117C22×C711yescharacteristic
342C2×#117C22×C711yescharacteristic
343C2×#117C22×C714yes—
344C22×C4⋊C4C22×C714yes—
345C22×C42C22×C711yescharacteristic
346C23×C7—22no—
347C23×C7—28no—
348C23×C7—28no—
349C23×C7—24no—
350C23×C7—28no—
351C23×C7C2512yes—
352C23×C7C2518yes—
353C23×C7C2511yescharacteristic
354C7×Q8—216no—
355C7×Q8—48no—
356C7×Q8—416no—
357C7×Q8—48no—
358C7×D4—216no—
359C7×D4—416no—
360C7×D4—416no—
361C2×C4×C7—22no—
362C2×C4×C7—28no—
363C2×C4×C7—24no—
364C2×C4×C7—28no—
365C2×C4×C7—24no—
366C2×C4×C7—24no—
367C2×C4×C7—28no—
368C2×C4×C7—24no—
369C2×C4×C7—24no—
370C2×C4×C7—24no—
371C2×C4×C7—28no—
372C2×C4×C7—416no—
373C2×C4×C7—48no—
374C2×C4×C7—416no—
375C2×C4×C7—416no—
376C2×C4×C72−1+414yes—
377C2×C4×C7C2514yes—
378C2×C4×C7C2518yes—
379C2×C4×C7C2514yes—
380C2×C4×C7C2514yes—
381C2×C4×C7C2512yes—
382C2×C4×C7C2514yes—
383C2×C4×C7C2518yes—
384C2×C4×C7C2514yes—
385C2×C4×C7C2514yes—
386C2×C4×C7C2518yes—
387C2×C4×C7C2512yes—
388C22×Q8C23×C712yes—
389C22×Q8C23×C712yes—
390C22×Q8C23×C714yes—
391C22×Q8C23×C712yes—
392C22×D4C23×C712yes—
393C22×D4C23×C714yes—
394C22×D4C23×C714yes—
395C23×C4C23×C711yescharacteristic
396C23×C4C23×C714yes—
397C23×C4C23×C714yes—
398C23×C4C23×C714yes—
399C23×C4C23×C712yes—
400C4⋊Q8C23×C7116yes—
401C4⋊Q8C23×C718yes—
402C4⋊Q8C23×C7116yes—
403C4⋊Q8C23×C7132yes—
404#127C23×C718yes—
405#126C23×C7132yes—
406#126C23×C7132yes—
407#126C23×C7132yes—
408#126C23×C7132yes—
409#126C23×C7132yes—
410#125C23×C7116yes—
411#125C23×C7116yes—
412#125C23×C7132yes—
413#125C23×C7132yes—
414#125C23×C718yes—
415#125C23×C7132yes—
416#125C23×C718yes—
417#124C23×C7116yes—
418#124C23×C7132yes—
419#124C23×C7116yes—
420#124C23×C7132yes—
421#123C23×C7132yes—
422#123C23×C7132yes—
423#123C23×C7132yes—
424#123C23×C7132yes—
425#123C23×C7132yes—
426C22⋊Q8C23×C7116yes—
427C22⋊Q8C23×C7116yes—
428C22⋊Q8C23×C7116yes—
429C22⋊Q8C23×C7132yes—
430C22⋊Q8C23×C7132yes—
431C22⋊Q8C23×C7132yes—
432C22⋊Q8C23×C7132yes—
433C22⋊Q8C23×C7132yes—
434#121C23×C7116yes—
435#121C23×C7132yes—
436C4×Q8C23×C7116yes—
437C4×Q8C23×C7116yes—
438C4×Q8C23×C7116yes—
439C4×Q8C23×C7116yes—
440C4×Q8C23×C7132yes—
441C4×Q8C23×C7116yes—
442C4×D4C23×C7132yes—
443C4×D4C23×C7116yes—
444C4×D4C23×C7132yes—
445C4×D4C23×C7116yes—
446C4×D4C23×C7116yes—
447#117C23×C7132yes—
448#117C23×C718yes—
449#117C23×C718yes—
450#117C23×C7132yes—
451C2×C4⋊C4C23×C712yes—
452C2×C4⋊C4C23×C714yes—
453C2×C4⋊C4C23×C714yes—
454C2×C4⋊C4C23×C714yes—
455C2×C4⋊C4C23×C7132yes—
456C2×C4⋊C4C23×C712yes—
457C2×C4⋊C4C23×C714yes—
458C2×C4⋊C4C23×C712yes—
459C2×C4⋊C4C23×C714yes—
460C2×C4⋊C4C23×C712yes—
461C2×C4⋊C4C23×C712yes—
462C2×C4⋊C4C23×C712yes—
463C2×C4⋊C4C23×C712yes—
464C2×C4⋊C4C23×C714yes—
465C2×C4⋊C4C23×C712yes—
466C2×C4⋊C4C23×C714yes—
467C2×C4⋊C4C23×C712yes—
468C2×C4⋊C4C23×C714yes—
469C2×C4⋊C4C23×C712yes—
470C2×C4⋊C4C23×C714yes—
471C2×C4⋊C4C23×C714yes—
472C2×C22⋊C4C23×C714yes—
473C2×C22⋊C4C23×C712yes—
474C2×C22⋊C4C23×C714yes—
475C2×C22⋊C4C23×C711yescharacteristic
476C2×C22⋊C4C23×C711yescharacteristic
477C2×C22⋊C4C23×C714yes—
478C2×C22⋊C4C23×C714yes—
479C2×C22⋊C4C23×C714yes—
480C2×C22⋊C4C23×C714yes—
481C2×C22⋊C4C23×C714yes—
482C2×C22⋊C4C23×C714yes—
483C2×C22⋊C4C23×C714yes—
484C2×C42C23×C711yescharacteristic
485C2×C42C23×C714yes—
486C2×C42C23×C711yescharacteristic
487C2×C42C23×C712yes—
488C2×C42C23×C711yescharacteristic
489C2×C42C23×C714yes—
490C2×C42C23×C712yes—
491C2×C42C23×C714yes—
492C2×C42C23×C711yescharacteristic
493C2×C42C23×C718yes—
494C22×C7—22no—
495C22×C7—28no—
496C22×C7—28no—
497C22×C7—24no—
498C22×C7—28no—
499C22×C7—44no—
500C22×C7—416no—
501C22×C7C2×2−1+412yes—
502C22×C7#58514yes—
503C22×C7C2611yescharacteristic
504C4×C7—22no—
505C4×C7—28no—
506C4×C7—24no—
507C4×C7—28no—
508C4×C7—24no—
509C4×C7—24no—
510C4×C7—28no—
511C4×C7—24no—
512C4×C7—24no—
513C4×C7—24no—
514C4×C7C2×2−1+414yes—
515C24C24×C711yescharacteristic
516C24C24×C714yes—
517C2×Q8—28no—
518C2×Q8—44no—
519C2×Q8—48no—
520C2×Q8—44no—
521C2×Q8C24×C718yes—
522C2×Q8C24×C718yes—
523C2×Q8C24×C7116yes—
524C2×Q8C24×C718yes—
525C2×D4—28no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4C24×C718yes—
529C2×D4C24×C7116yes—
530C2×D4C24×C7116yes—
531C22×C4—24no—
532C22×C4—48no—
533C22×C4—44no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4C24×C712yes—
537C22×C4C24×C714yes—
538C22×C4C24×C712yes—
539C22×C4C24×C712yes—
540C22×C4C24×C711yescharacteristic
541C22×C4C24×C712yes—
542C22×C4C24×C714yes—
543C22×C4C24×C714yes—
544C22×C4C24×C712yes—
545C22×C4C24×C712yes—
546C22×C4C24×C714yes—
547C22×C4C24×C718yes—
548C22×C4C24×C7116yes—
549C22×C4C24×C7116yes—
550C22×C4C24×C7116yes—
551C22×C4C24×C711yescharacteristic
552C4⋊C4C24×C718yes—
553C4⋊C4C24×C7116yes—
554C4⋊C4C24×C7116yes—
555C4⋊C4C24×C7116yes—
556C4⋊C4C24×C718yes—
557C4⋊C4C24×C7116yes—
558C4⋊C4C24×C718yes—
559C4⋊C4C24×C7116yes—
560C4⋊C4C24×C718yes—
561C4⋊C4C24×C718yes—
562C4⋊C4C24×C718yes—
563C4⋊C4C24×C718yes—
564C4⋊C4C24×C7116yes—
565C4⋊C4C24×C718yes—
566C4⋊C4C24×C7116yes—
567C4⋊C4C24×C718yes—
568C4⋊C4C24×C7116yes—
569C4⋊C4C24×C718yes—
570C4⋊C4C24×C7116yes—
571C4⋊C4C24×C7116yes—
572C22⋊C4C24×C7116yes—
573C22⋊C4C24×C718yes—
574C22⋊C4C24×C7116yes—
575C22⋊C4C24×C714yes—
576C22⋊C4C24×C714yes—
577C22⋊C4C24×C7116yes—
578C22⋊C4C24×C7116yes—
579C22⋊C4C24×C7116yes—
580C22⋊C4C24×C7116yes—
581C22⋊C4C24×C7116yes—
582C22⋊C4C24×C7116yes—
583C22⋊C4C24×C7116yes—
584C42C24×C714yes—
585C42C24×C718yes—
586C42C24×C714yes—
587C42C24×C7116yes—
588C42C24×C714yes—
589C42C24×C718yes—
590C42C24×C714yes—
591C42C24×C7116yes—
592C42C24×C7116yes—
593C2×C7—42no—
594C2×C7—48no—
595C2×C7#355714yesdirect product factor
596C2×C7C22×2−1+411yescharacteristic
597C2×C7C2×#58512yes—
598C23—22no—
599C23—28no—
600C23—28no—
601C23—24no—
602C23—28no—
603C23C25×C712yes—
604C23C25×C718yes—
605C23C25×C711yescharacteristic
606Q8—216no—
607Q8—48no—
608Q8—416no—
609Q8—48no—
610D4—216no—
611D4—416no—
612D4—416no—
613C2×C4—22no—
614C2×C4—28no—
615C2×C4—24no—
616C2×C4—28no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—28no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—28no—
624C2×C4—416no—
625C2×C4—48no—
626C2×C4—416no—
627C2×C4—416no—
628C2×C4C7×2−1+414yes—
629C2×C4C25×C714yes—
630C2×C4C25×C718yes—
631C2×C4C25×C714yes—
632C2×C4C25×C714yes—
633C2×C4C25×C712yes—
634C2×C4C25×C714yes—
635C2×C4C25×C718yes—
636C2×C4C25×C714yes—
637C2×C4C25×C714yes—
638C2×C4C25×C718yes—
639C2×C4C25×C712yes—
640C7C2×#355711yescharacteristic, direct product factor, Sylow
641C22—22no—
642C22—28no—
643C22—28no—
644C22—24no—
645C22—28no—
646C22—44no—
647C22—416no—
648C22C2×C7×2−1+412yes—
649C22C7×#58514yes—
650C22C26×C711yescharacteristic
651C4—22no—
652C4—28no—
653C4—24no—
654C4—28no—
655C4—24no—
656C4—24no—
657C4—28no—
658C4—24no—
659C4—24no—
660C4—24no—
661C4C2×C7×2−1+414yes—
662C2—42no—
663C2—48no—
664C2C7×#355714yesdirect product factor
665C2C22×C7×2−1+411yescharacteristic
666C2C2×C7×#58512yes—
subgroupG/H
center, socleC23×C7C25
commutator, Frattini, cosocleC22C26×C7
prime radicalC2×C7×#540C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C7×#3557C2direct (N × H)
2. C2×C7×#563C2semidirect
3. C2×C7×#559C2semidirect
4. C2×C7×#557C2semidirect
5. C2×C7×#556C2semidirect
6. C2×C7×#554C2semidirect
7. C2×C7×#552C2semidirect
8. C2×C7×#542C2semidirect
9. C2×C7×#542C2semidirect
10. C2×C7×#541C2semidirect
12. C2×C7×#539C2semidirect
13. C2×C7×#533C2semidirect
14. C2×C7×#529C2semidirect
15. C7×#563C22semidirect
16. C7×#559C22semidirect
17. C7×#557C22semidirect
18. C7×#556C22semidirect
19. C7×#554C22semidirect
20. C7×#552C22semidirect
21. C7×#542C22semidirect
22. C7×#542C22semidirect
23. C7×#541C22semidirect
25. C7×#539C22semidirect
26. C7×#533C22semidirect
32. C7×#529C22semidirect
81. C2×#3557C7direct (N × H)
188. #3557C2×C7direct (N × H)
189. C2×#563C2×C7semidirect
190. C2×#559C2×C7semidirect
191. C2×#557C2×C7semidirect
192. C2×#556C2×C7semidirect
193. C2×#554C2×C7semidirect
194. C2×#552C2×C7semidirect
195. C2×#542C2×C7semidirect
196. C2×#542C2×C7semidirect
197. C2×#541C2×C7semidirect
199. C2×#539C2×C7semidirect
200. C2×#533C2×C7semidirect
201. C2×#529C2×C7semidirect
280. #563C22×C7semidirect
281. #559C22×C7semidirect
282. #557C22×C7semidirect
283. #556C22×C7semidirect
284. #554C22×C7semidirect
285. #552C22×C7semidirect
286. #542C22×C7semidirect
287. #542C22×C7semidirect
288. #541C22×C7semidirect
290. #539C22×C7semidirect
291. #533C22×C7semidirect
297. #529C22×C7semidirect
595. C2×C7#3557direct (N × H)
640. C7C2×#3557direct (N × H)
664. C2C7×#3557direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#35572
C2×C7×#5632
C2×C7×#5592
C2×C7×#5572
C2×C7×#5562
C2×C7×#5542
C2×C7×#5522
C2×C7×#5422
C2×C7×#5412
C2×C7×#5402
C2×C7×#5392
C2×C7×#5332
C2×C7×#5292
C2×#35577