Finite Group Databasebeta

← C7×#10595278 #72246848

Subgroups — C7×#10595278 #72246848

Order 4032.

2884 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#63983C212yesmaximal, complemented
2C7×#63977C212yesmaximal, complemented
3C7×#63923C212yesmaximal, complemented
4C3×C7×#937C212yesmaximal, complemented
5C7×#63974C211yesmaximal, characteristic, complemented
6C7×#63921C212yesmaximal, complemented
7C23×D32×C7C211yesmaximal, characteristic, complemented
8C2×C7×#3811C212yesmaximal, complemented
9C2×C7×D4×C3⋊D3C211yesmaximal, characteristic, complemented
10D3×C7×#120—32nomaximal
11C23×C7×C3⋊D3C2211yescharacteristic
12C23×C7×C3⋊D3C2211yescharacteristic, complemented
13C23×C3×D3×C7C2212yescomplemented
14C22×D32×C7—24no—
15C22×D32×C7—28no—
16C22×D32×C7C2212yes—
17C22×D32×C7C2212yescomplemented
18C2×C32×C7×D4C2211yescharacteristic, complemented
19C2×C7×#638C2211yescharacteristic, complemented
20C2×C7×#638C2211yescharacteristic, complemented
21C7×D4×C3⋊D3—24no—
22C2×C7×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C4×C7×C3⋊D3C2211yescharacteristic, complemented
24C2×C3×C7×#67C2214yescomplemented
25C7×#3811—28no—
26C2×C7×#626C2214yescomplemented
27C2×C7×#624C2212yescomplemented
28C3×C7×#217C2212yescomplemented
29C3×C7×(C2×D3)⋊C4C2214yescomplemented
30C7×#3722C2212yescomplemented
31C7×(C2×D3)⋊Dic3C2214yescomplemented
32C24×D3×C7—32no—
33C2×D3×C7×D4—32no—
34C2×D3×C7×D4—34no—
35C2×D3×C7×D4—61no—
36C3×C7×#120—32no—
37C7×#953—32no—
38C7×#937—34no—
39C7×#937D312yescomplemented
40C7×#882—32no—
41C7×#882—34no—
42D3×C7×C22⋊C4—32no—
43D3×C7×C22⋊C4—34no—
44#10595278C711yesmaximal, characteristic, direct product factor, Hall
45C23×C32×C7C2311yescharacteristic
46C23×C32×C7C2311yescharacteristic, complemented
47C22×C7×C3⋊D3—24no—
48C22×C7×C3⋊D3—22no—
49C22×C7×C3⋊D3—24no—
50C22×C7×C3⋊D3D414yescomplemented
51C22×C7×C3⋊D3C2311yescharacteristic
52C22×C7×C3⋊D3C2311yescharacteristic
53C22×C7×C3⋊D3C2311yescharacteristic, complemented
54C22×C3×D3×C7—24no—
55C22×C3×D3×C7—28no—
56C22×C3×D3×C7C2314yes—
57C2×D32×C7—232no—
58C2×D32×C7—24no—
59C2×D32×C7—24no—
60C2×D32×C7—24no—
61C2×D32×C7—28no—
62C2×D32×C7D418yescomplemented
63C32×C7×D4—22no—
64C2×C32×C4×C7C2311yescharacteristic, complemented
65C7×#638—22no—
66C7×#638—22no—
67C2×C7×C3⋊Dic3C2311yescharacteristic, complemented
68C7×C4⋊(C3⋊D3)—22no—
69C4×C7×C3⋊D3—22no—
70C3×C7×#67—28no—
71C2×C3×C7×Dic3C2314yescomplemented
72C7×#626—28no—
73C7×#624—24no—
74C2×C7×#120—91noHall
75C24×C3×C7—32no—
76C23×D3×C7—32no—
77C23×D3×C7—34no—
78C23×D3×C7—32no—
79C23×D3×C7—34no—
80C23×D3×C7—61no—
81C23×D3×C7—61no—
82C23×D3×C7—68no—
83C23×D3×C7—616no—
84C23×D3×C7C2×D312yescomplemented
85C2×C3×C7×D4—21no—
86C2×C3×C7×D4—34no—
87C2×C3×C7×D4C2×D312yescomplemented
88C2×C7×#67—32no—
89C2×C7×#67—32no—
90C2×C7×#67—34no—
91C2×C7×#67—61no—
92C2×C7×#67—61no—
93C2×C7×#67C2×D314yescomplemented
94D3×C7×D4—616no—
95D3×C7×D4—68no—
96D3×C7×D4—64no—
97D3×C7×D4—64no—
98C2×C7×D12—34no—
99C2×C7×D12—32no—
100C2×C7×D12—61no—
101C2×C4×D3×C7—32no—
102C2×C4×D3×C7—34no—
103C2×C4×D3×C7—61no—
104C3×C7×C22⋊C4—32no—
105C3×C7×C22⋊C4—34no—
106C7×#217—34no—
107C7×#217C2×D312yescomplemented
108C7×(C2×D3)⋊C4—34no—
109C7×(C2×D3)⋊C4—34no—
110C7×(C2×D3)⋊C4C2×D314yescomplemented
111C23×D32C2×C711yescharacteristic, complemented
112C2×D4×C3⋊D3C2×C711yescharacteristic, complemented
113C2×#3811C2×C712yescomplemented
114C3×#937C2×C712yescomplemented
115#63983C2×C712yescomplemented
116#63977C2×C712yescomplemented
117#63974C2×C711yescharacteristic, complemented
118#63923C2×C712yescomplemented
119#63921C2×C712yescomplemented
120C22×C32×C7—22no—
121C22×C32×C7—21no—
122C22×C32×C7—22no—
123C22×C32×C7C2×D412yescomplemented
124C22×C32×C7C2411yescharacteristic
125C2×C7×C3⋊D3—22no—
126C2×C7×C3⋊D3—28no—
127C2×C7×C3⋊D3—21no—
128C2×C7×C3⋊D3—22no—
129C2×C7×C3⋊D3—44no—
130C2×C7×C3⋊D3C2×D414yes—
131C2×C7×C3⋊D3C2×D412yes—
132C2×C7×C3⋊D3C2×D412yescomplemented
133C2×C3×D3×C7—216no—
134C2×C3×D3×C7—24no—
135C2×C3×D3×C7—24no—
136C2×C3×D3×C7C2×D418yescomplemented
137D32×C7—216no—
138D32×C7—216no—
139C32×C4×C7—21no—
140C7×C3⋊Dic3—21no—
141C3×C7×Dic3—24no—
142C25×C7—91no—
143C22×C7×D4—92no—
144C22×C7×D4—91no—
145C7×#120—32no—
146C7×#120—92no—
147C7×#120—92no—
148C7×#120—92no—
149C2×C7×C22⋊C4—91no—
150C2×C7×C22⋊C4—92no—
151D3×#120—32no—
152C23×C3×C7—21no—
153C23×C3×C7—21no—
154C23×C3×C7—34no—
155C23×C3×C7—68no—
156C23×C3×C7—64no—
157C23×C3×C7C22×D312yes—
158C23×C3×C7C22×D312yescomplemented
159C22×D3×C7—24no—
160C22×D3×C7—28no—
161C22×D3×C7—32no—
162C22×D3×C7—38no—
163C22×D3×C7—32no—
164C22×D3×C7—316no—
165C22×D3×C7—32no—
166C22×D3×C7—61no—
167C22×D3×C7—64no—
168C22×D3×C7—61no—
169C22×D3×C7—61no—
170C22×D3×C7—68no—
171C22×D3×C7—68no—
172C22×D3×C7—68no—
173C22×D3×C7—68no—
174C22×D3×C7—664no—
175C22×D3×C7—68no—
176C22×D3×C7—64no—
177C22×D3×C7—68no—
178C22×D3×C7—68no—
179C22×D3×C7—62no—
180C22×D3×C7—62no—
181C22×D3×C7—124no—
182C22×D3×C7—124no—
183C22×D3×C7C22×D314yes—
184C3×C7×D4—22no—
185C3×C7×D4—22no—
186C3×C7×D4—24no—
187C3×C7×D4—68no—
188C2×C3×C4×C7—21no—
189C2×C3×C4×C7—34no—
190C2×C3×C4×C7C22×D312yescomplemented
191C7×#67—28no—
192C7×#67—68no—
193C7×#67—64no—
194C7×#67—62no—
195C7×#67—62no—
196C7×#67—62no—
197C7×#67—62no—
198C7×#67—64no—
199C2×C7×Dic3—32no—
200C2×C7×Dic3—61no—
201C2×C7×Dic3C22×D314yescomplemented
202C7×D12—64no—
203C7×D12—62no—
204C7×D12—62no—
205C7×D12—68no—
206C4×D3×C7—68no—
207C4×D3×C7—64no—
208C4×D3×C7—62no—
209C4×D3×C7—62no—
210C23×C3⋊D3C22×C711yescharacteristic
211C23×C3⋊D3C22×C711yescharacteristic, complemented
212C23×C3×D3C22×C712yescomplemented
213C22×D32—24no—
214C22×D32—28no—
215C22×D32C22×C712yes—
216C22×D32C22×C712yescomplemented
217C2×C32×D4C22×C711yescharacteristic, complemented
218C2×#638C22×C711yescharacteristic, complemented
219C2×#638C22×C711yescharacteristic, complemented
220D4×C3⋊D3—24no—
221C2×C4⋊(C3⋊D3)C22×C711yescharacteristic, complemented
222C2×C4×C3⋊D3C22×C711yescharacteristic, complemented
223C2×C3×#67C22×C714yescomplemented
224#3811—28no—
225C2×#626C22×C714yescomplemented
226C2×#624C22×C712yescomplemented
227C3×#217C22×C712yescomplemented
228C3×(C2×D3)⋊C4C22×C714yescomplemented
229#3722C22×C712yescomplemented
230(C2×D3)⋊Dic3C22×C714yescomplemented
231C2×C32×C7—22no—
232C2×C32×C7—41no—
233C2×C32×C7C22×D412yes—
234C2×C32×C7C22×D411yescharacteristic
235C7×C3⋊D3—22no—
236C7×C3⋊D3—41no—
237C7×C3⋊D3#12014yescomplemented
238C3×D3×C7—28no—
239C24×C7—32no—
240C24×C7—92no—
241C24×C7—92no—
242C24×C7—91no—
243C24×C7—91no—
244C24×C7—188no—
245C24×C7—184no—
246C2×C7×D4—34no—
247C2×C7×D4—94no—
248C2×C7×D4—91no—
249C2×C7×D4—91no—
250C2×C7×D4—91no—
251C2×C7×D4—184no—
252C2×C7×D4—188no—
253C2×C7×D4D3211yescharacteristic, complemented
254C22×C4×C7—92no—
255C22×C4×C7—91no—
256C7×C22⋊C4—32no—
257C7×C22⋊C4—34no—
258C7×C22⋊C4—92no—
259C7×C22⋊C4—94no—
260C24×D3—32no—
261C2×D3×D4—32no—
262C2×D3×D4—34no—
263C2×D3×D4—61no—
264C3×#120—32no—
265#953—32no—
266#937—34no—
267#937D3×C712yescomplemented
268#882—32no—
269#882—34no—
270D3×C22⋊C4—32no—
271D3×C22⋊C4—34no—
272C22×C3×C7—24no—
273C22×C3×C7—21no—
274C22×C3×C7—21no—
275C22×C3×C7—24no—
276C22×C3×C7—22no—
277C22×C3×C7—21no—
278C22×C3×C7—22no—
279C22×C3×C7—38no—
280C22×C3×C7—42no—
281C22×C3×C7—42no—
282C22×C3×C7—616no—
283C22×C3×C7—64no—
284C22×C3×C7—64no—
285C22×C3×C7D3×D414yescomplemented
286C22×C3×C7C23×D312yes—
287C2×D3×C7—216no—
288C2×D3×C7—24no—
289C2×D3×C7—24no—
290C2×D3×C7—38no—
291C2×D3×C7—34no—
292C2×D3×C7—34no—
293C2×D3×C7—62no—
294C2×D3×C7—64no—
295C2×D3×C7—62no—
296C2×D3×C7—632no—
297C2×D3×C7—632no—
298C2×D3×C7—616no—
299C2×D3×C7—64no—
300C2×D3×C7—61no—
301C2×D3×C7—61no—
302C2×D3×C7—64no—
303C2×D3×C7—62no—
304C2×D3×C7—128no—
305C2×D3×C7—122no—
306C2×D3×C7—122no—
307C2×D3×C7—128no—
308C2×D3×C7—124no—
309C2×D3×C7—124no—
310C2×D3×C7D3×D418yescomplemented
311C3×C4×C7—21no—
312C3×C4×C7—21no—
313C3×C4×C7—22no—
314C3×C4×C7—64no—
315C7×Dic3—24no—
316C7×Dic3—61no—
317C7×Dic3—61no—
318C7×Dic3—62no—
319C23×C32C23×C711yescharacteristic
320C23×C32C23×C711yescharacteristic, complemented
321C22×C3⋊D3—22no—
322C22×C3⋊D3—24no—
323C22×C3⋊D3—24no—
324C22×C3⋊D3C7×D414yescomplemented
325C22×C3⋊D3C23×C711yescharacteristic
326C22×C3⋊D3C23×C711yescharacteristic
327C22×C3⋊D3C23×C711yescharacteristic, complemented
328C22×C3×D3—24no—
329C22×C3×D3—28no—
330C22×C3×D3C23×C714yes—
331C2×D32—232no—
332C2×D32—24no—
333C2×D32—24no—
334C2×D32—24no—
335C2×D32—28no—
336C2×D32C7×D418yescomplemented
337C32×D4—22no—
338C2×C32×C4C23×C711yescharacteristic, complemented
339#638—22no—
340#638—22no—
341C2×C3⋊Dic3C23×C711yescharacteristic, complemented
342C4⋊(C3⋊D3)—22no—
343C4×C3⋊D3—22no—
344C3×#67—28no—
345C2×C3×Dic3C23×C714yescomplemented
346#626—28no—
347#624—24no—
348C2×#120—91noSylow
349C32×C7C2×#12011yescharacteristic, complemented, Hall
350C23×C7—34no—
351C23×C7—68no—
352C23×C7—64no—
353C23×C7—98no—
354C23×C7—91no—
355C23×C7—91no—
356C23×C7—94no—
357C23×C7—91no—
358C23×C7—184no—
359C23×C7—182no—
360C23×C7—184no—
361C23×C7—188no—
362C23×C7—184no—
363C23×C7—184no—
364C23×C7—184no—
365C23×C7—1832no—
366C23×C7C2×D3211yescharacteristic
367C23×C7C2×D3211yescharacteristic, complemented
368C7×D4—22no—
369C7×D4—68no—
370C7×D4—182no—
371C7×D4—188no—
372C7×D4—182no—
373C7×D4—182no—
374C2×C4×C7—34no—
375C2×C4×C7—91no—
376C2×C4×C7—182no—
377C2×C4×C7—184no—
378C2×C4×C7C2×D3211yescharacteristic, complemented
379C24×C3—32no—
380C23×D3—32no—
381C23×D3—34no—
382C23×D3—32no—
383C23×D3—34no—
384C23×D3—61no—
385C23×D3—61no—
386C23×D3—68no—
387C23×D3—616no—
388C23×D3C2×D3×C712yescomplemented
389C2×C3×D4—21no—
390C2×C3×D4—34no—
391C2×C3×D4C2×D3×C712yescomplemented
392C2×#67—32no—
393C2×#67—32no—
394C2×#67—34no—
395C2×#67—61no—
396C2×#67—61no—
397C2×#67C2×D3×C714yescomplemented
398D3×D4—616no—
399D3×D4—68no—
400D3×D4—64no—
401D3×D4—64no—
402C2×D12—34no—
403C2×D12—32no—
404C2×D12—61no—
405C2×C4×D3—32no—
406C2×C4×D3—34no—
407C2×C4×D3—61no—
408C3×C22⋊C4—32no—
409C3×C22⋊C4—34no—
410#217—34no—
411#217C2×D3×C712yescomplemented
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4C2×D3×C714yescomplemented
415C2×C3×C7—24no—
416C2×C3×C7—22no—
417C2×C3×C7—21no—
418C2×C3×C7—42no—
419C2×C3×C7—41no—
420C2×C3×C7—41no—
421C2×C3×C7—42no—
422C2×C3×C7—68no—
423C2×C3×C7C2×D3×D414yes—
424C2×C3×C7C2×D3×D412yes—
425D3×C7—28no—
426D3×C7—38no—
427D3×C7—64no—
428D3×C7—64no—
429D3×C7—122no—
430D3×C7—121no—
431D3×C7—121no—
432D3×C7—122no—
433C22×C32—21no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32C2×C7×D412yescomplemented
437C22×C32C24×C711yescharacteristic
438C2×C3⋊D3—21no—
439C2×C3⋊D3—22no—
440C2×C3⋊D3—28no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—44no—
443C2×C3⋊D3C2×C7×D414yes—
444C2×C3⋊D3C2×C7×D412yes—
445C2×C3⋊D3C2×C7×D412yescomplemented
446C2×C3×D3—216no—
447C2×C3×D3—24no—
448C2×C3×D3—24no—
449C2×C3×D3C2×C7×D418yescomplemented
450D32—216no—
451D32—216no—
452C32×C4—21no—
453C3⋊Dic3—21no—
454C3×Dic3—24no—
455C25—91no—
456C22×D4—92no—
457C22×D4—91no—
458#120—32no—
459#120—92no—
460#120—92no—
461#120—92no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—92no—
464C22×C7—22no—
465C22×C7—22no—
466C22×C7—21no—
467C22×C7—38no—
468C22×C7—616no—
469C22×C7—64no—
470C22×C7—64no—
471C22×C7—94no—
472C22×C7—92no—
473C22×C7—92no—
474C22×C7—188no—
475C22×C7—1816no—
476C22×C7—1816no—
477C22×C7—182no—
478C22×C7—182no—
479C22×C7—181no—
480C22×C7—364no—
481C22×C7#381112yescomplemented
482C22×C7C22×D3211yescharacteristic
483C4×C7—21no—
484C4×C7—64no—
485C4×C7—181no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—34no—
489C23×C3—68no—
490C23×C3—64no—
491C23×C3C22×D3×C712yes—
492C23×C3C22×D3×C712yescomplemented
493C22×D3—24no—
494C22×D3—28no—
495C22×D3—32no—
496C22×D3—38no—
497C22×D3—32no—
498C22×D3—316no—
499C22×D3—32no—
500C22×D3—61no—
501C22×D3—64no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—68no—
505C22×D3—68no—
506C22×D3—68no—
507C22×D3—68no—
508C22×D3—664no—
509C22×D3—68no—
510C22×D3—64no—
511C22×D3—68no—
512C22×D3—68no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—124no—
516C22×D3—124no—
517C22×D3C22×D3×C714yes—
518C3×D4—22no—
519C3×D4—22no—
520C3×D4—24no—
521C3×D4—68no—
522C2×C3×C4—21no—
523C2×C3×C4—34no—
524C2×C3×C4C22×D3×C712yescomplemented
525#67—28no—
526#67—68no—
527#67—64no—
528#67—62no—
529#67—62no—
530#67—62no—
531#67—62no—
532#67—64no—
533C2×Dic3—32no—
534C2×Dic3—61no—
535C2×Dic3C22×D3×C714yescomplemented
536D12—64no—
537D12—62no—
538D12—62no—
539D12—68no—
540C4×D3—68no—
541C4×D3—64no—
542C4×D3—62no—
543C4×D3—62no—
544C3×C7—21no—
545C3×C7D3×#12012yescomplemented
546C2×C32—22no—
547C2×C32—41no—
548C2×C32C22×C7×D412yes—
549C2×C32C22×C7×D411yescharacteristic
550C3⋊D3—22no—
551C3⋊D3—41no—
552C3⋊D3C7×#12014yescomplemented
553C3×D3—28no—
554C24—32no—
555C24—92no—
556C24—92no—
557C24—91no—
558C24—91no—
559C24—188no—
560C24—184no—
561C2×D4—34no—
562C2×D4—94no—
563C2×D4—91no—
564C2×D4—91no—
565C2×D4—91no—
566C2×D4—184no—
567C2×D4—188no—
568C2×D4D32×C711yescharacteristic, complemented
569C22×C4—92no—
570C22×C4—91no—
571C22⋊C4—32no—
572C22⋊C4—34no—
573C22⋊C4—92no—
574C22⋊C4—94no—
575C2×C7—22no—
576C2×C7—41no—
577C2×C7—68no—
578C2×C7—94no—
579C2×C7—182no—
580C2×C7—361no—
581C2×C7D32×D412yes—
582C2×C7C2×#381111yescharacteristic
583C22×C3—24no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—24no—
587C22×C3—22no—
588C22×C3—21no—
589C22×C3—22no—
590C22×C3—38no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—616no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3D3×C7×D414yescomplemented
597C22×C3C23×D3×C712yes—
598C2×D3—216no—
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—38no—
602C2×D3—34no—
603C2×D3—34no—
604C2×D3—62no—
605C2×D3—64no—
606C2×D3—62no—
607C2×D3—632no—
608C2×D3—632no—
609C2×D3—616no—
610C2×D3—64no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—64no—
614C2×D3—62no—
615C2×D3—128no—
616C2×D3—122no—
617C2×D3—122no—
618C2×D3—128no—
619C2×D3—124no—
620C2×D3—124no—
621C2×D3D3×C7×D418yescomplemented
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—22no—
625C3×C4—64no—
626Dic3—24no—
627Dic3—61no—
628Dic3—61no—
629Dic3—62no—
630C32C2×C7×#12011yescharacteristic, complemented, Sylow
631C23—34no—
632C23—68no—
633C23—64no—
634C23—98no—
635C23—91no—
636C23—91no—
637C23—94no—
638C23—91no—
639C23—184no—
640C23—182no—
641C23—184no—
642C23—188no—
643C23—184no—
644C23—184no—
645C23—184no—
646C23—1832no—
647C23C2×D32×C711yescharacteristic
648C23C2×D32×C711yescharacteristic, complemented
649D4—22no—
650D4—68no—
651D4—182no—
652D4—188no—
653D4—182no—
654D4—182no—
655C2×C4—34no—
656C2×C4—91no—
657C2×C4—182no—
658C2×C4—184no—
659C2×C4C2×D32×C711yescharacteristic, complemented
660C7#1059527811yescharacteristic, direct product factor, Sylow
661C2×C3—24no—
662C2×C3—22no—
663C2×C3—21no—
664C2×C3—42no—
665C2×C3—41no—
666C2×C3—41no—
667C2×C3—42no—
668C2×C3—68no—
669C2×C3C2×D3×C7×D414yes—
670C2×C3C2×D3×C7×D412yes—
671D3—28no—
672D3—38no—
673D3—64no—
674D3—64no—
675D3—122no—
676D3—121no—
677D3—121no—
678D3—122no—
679C22—22no—
680C22—22no—
681C22—21no—
682C22—38no—
683C22—616no—
684C22—64no—
685C22—64no—
686C22—94no—
687C22—92no—
688C22—92no—
689C22—188no—
690C22—1816no—
691C22—1816no—
692C22—182no—
693C22—182no—
694C22—181no—
695C22—364no—
696C22C7×#381112yescomplemented
697C22C22×D32×C711yescharacteristic
698C4—21no—
699C4—64no—
700C4—181no—
701C3—21no—
702C3D3×C7×#12012yescomplemented
703C2—22no—
704C2—41no—
705C2—68no—
706C2—94no—
707C2—182no—
708C2—361no—
709C2C2×C7×#381111yescharacteristic
710C2D32×C7×D412yes—
subgroupG/H
centerC22×C7C22×D32
commutator, cosocleC22×C32C24×C7
FrattiniC22C22×D32×C7
FittingC2×C32×C7×D4C22
socleC22×C32×C7C24
hypercenterC2×C7×D4D32
hypocenterC32C2×C7×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C7 ◁ C2×C7×D4

Complements

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

NH ≅ G/Ntype
1. C7×#63983C2semidirect
2. C7×#63977C2semidirect
3. C7×#63923C2semidirect
4. C3×C7×#937C2semidirect
5. C7×#63974C2semidirect
6. C7×#63921C2semidirect
7. C23×D32×C7C2semidirect
8. C2×C7×#3811C2semidirect
9. C2×C7×D4×C3⋊D3C2semidirect
12. C23×C7×C3⋊D3C22semidirect
13. C23×C3×D3×C7C22semidirect
17. C22×D32×C7C22semidirect
18. C2×C32×C7×D4C22semidirect
19. C2×C7×#638C22semidirect
20. C2×C7×#638C22semidirect
22. C2×C7×C4⋊(C3⋊D3)C22semidirect
23. C2×C4×C7×C3⋊D3C22semidirect
24. C2×C3×C7×#67C22semidirect
26. C2×C7×#626C22semidirect
27. C2×C7×#624C22semidirect
28. C3×C7×#217C22semidirect
29. C3×C7×(C2×D3)⋊C4C22semidirect
30. C7×#3722C22semidirect
31. C7×(C2×D3)⋊Dic3C22semidirect
39. C7×#937D3semidirect
44. #10595278C7direct (N × H)
46. C23×C32×C7C23semidirect
50. C22×C7×C3⋊D3D4semidirect
53. C22×C7×C3⋊D3C23semidirect
62. C2×D32×C7D4semidirect
64. C2×C32×C4×C7C23semidirect
67. C2×C7×C3⋊Dic3C23semidirect
71. C2×C3×C7×Dic3C23semidirect
84. C23×D3×C7C2×D3semidirect
87. C2×C3×C7×D4C2×D3semidirect
93. C2×C7×#67C2×D3semidirect
107. C7×#217C2×D3semidirect
110. C7×(C2×D3)⋊C4C2×D3semidirect
111. C23×D32C2×C7semidirect
112. C2×D4×C3⋊D3C2×C7semidirect
113. C2×#3811C2×C7semidirect
114. C3×#937C2×C7semidirect
115. #63983C2×C7semidirect
116. #63977C2×C7semidirect
117. #63974C2×C7semidirect
118. #63923C2×C7semidirect
119. #63921C2×C7semidirect
123. C22×C32×C7C2×D4semidirect
132. C2×C7×C3⋊D3C2×D4semidirect
136. C2×C3×D3×C7C2×D4semidirect
158. C23×C3×C7C22×D3semidirect
190. C2×C3×C4×C7C22×D3semidirect
201. C2×C7×Dic3C22×D3semidirect
211. C23×C3⋊D3C22×C7semidirect
212. C23×C3×D3C22×C7semidirect
216. C22×D32C22×C7semidirect
217. C2×C32×D4C22×C7semidirect
218. C2×#638C22×C7semidirect
219. C2×#638C22×C7semidirect
221. C2×C4⋊(C3⋊D3)C22×C7semidirect
222. C2×C4×C3⋊D3C22×C7semidirect
223. C2×C3×#67C22×C7semidirect
225. C2×#626C22×C7semidirect
226. C2×#624C22×C7semidirect
227. C3×#217C22×C7semidirect
228. C3×(C2×D3)⋊C4C22×C7semidirect
229. #3722C22×C7semidirect
230. (C2×D3)⋊Dic3C22×C7semidirect
237. C7×C3⋊D3#120semidirect
253. C2×C7×D4D32semidirect
267. #937D3×C7semidirect
285. C22×C3×C7D3×D4semidirect
310. C2×D3×C7D3×D4semidirect
320. C23×C32C23×C7semidirect
324. C22×C3⋊D3C7×D4semidirect
327. C22×C3⋊D3C23×C7semidirect
336. C2×D32C7×D4semidirect
338. C2×C32×C4C23×C7semidirect
341. C2×C3⋊Dic3C23×C7semidirect
345. C2×C3×Dic3C23×C7semidirect
349. C32×C7C2×#120semidirect
367. C23×C7C2×D32semidirect
378. C2×C4×C7C2×D32semidirect
388. C23×D3C2×D3×C7semidirect
391. C2×C3×D4C2×D3×C7semidirect
397. C2×#67C2×D3×C7semidirect
411. #217C2×D3×C7semidirect
414. (C2×D3)⋊C4C2×D3×C7semidirect
436. C22×C32C2×C7×D4semidirect
445. C2×C3⋊D3C2×C7×D4semidirect
449. C2×C3×D3C2×C7×D4semidirect
481. C22×C7#3811semidirect
492. C23×C3C22×D3×C7semidirect
524. C2×C3×C4C22×D3×C7semidirect
535. C2×Dic3C22×D3×C7semidirect
545. C3×C7D3×#120semidirect
552. C3⋊D3C7×#120semidirect
568. C2×D4D32×C7semidirect
596. C22×C3D3×C7×D4semidirect
621. C2×D3D3×C7×D4semidirect
630. C32C2×C7×#120semidirect
648. C23C2×D32×C7semidirect
659. C2×C4C2×D32×C7semidirect
660. C7#10595278direct (N × H)
696. C22C7×#3811semidirect
702. C3D3×C7×#120semidirect

Maximal subgroups

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

subgroupindex
C7×#639832
C7×#639772
C7×#639232
C3×C7×#9372
C7×#639742
C7×#639212
C23×D32×C72
C2×C7×#38112
C2×C7×D4×C3⋊D32
D3×C7×#1203
#105952787