Finite Group Databasebeta

← C2×C7×#3124 #13237769

Subgroups — C2×C7×#3124 #13237769

Order 1792.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic, complemented
2C2×C7×#520C211yesmaximal, characteristic, complemented
3C7×#3124C2116yesmaximal, direct product factor
4C2×C7×#484C211yesmaximal, characteristic, complemented
5C2×C7×#480C211yesmaximal, characteristic, complemented
6C2×C7×#477C211yesmaximal, characteristic, complemented
7C2×C7×#474C211yesmaximal, characteristic, complemented
8C2×C7×#464C211yesmaximal, characteristic, complemented
9C2×C7×#463C211yesmaximal, characteristic, complemented
10C2×C7×#452C211yesmaximal, characteristic, complemented
11C2×C7×#449C211yesmaximal, characteristic
12C2×C7×#440C211yesmaximal, characteristic, complemented
13C2×C7×#440C211yesmaximal, characteristic, complemented
14C2×C4×C7×Q16C211yesmaximal, characteristic, complemented
15C2×C4×C7×D8C211yesmaximal, characteristic, complemented
16C2×C7×#433C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C22×C7×D8C2211yescharacteristic
22C7×#542—24no—
23C7×#542C2218yescomplemented
24C2×C7×C4⋊Q8C2211yescharacteristic
25C2×C7×#126—21no—
26C2×C7×#124—21no—
27C2×C7×#124C2211yescharacteristic
28C2×C7×#123—21no—
29C2×C7×C22⋊Q8—21no—
30C2×C7×C22⋊Q8C2211yescharacteristic
31C2×C7×#121C2211yescharacteristic
32C7×#520—24no—
33C7×#520C2218yescomplemented
34C2×C4×C7×Q8C2211yescharacteristic
35C2×C4×C7×Q8C2211yescharacteristic
36C2×C4×C7×Q8C2211yescharacteristic
37C2×C4×C7×D4—21no—
38C2×C4×C7×D4—21no—
39C2×C4×C7×D4C2211yescharacteristic
40C2×C4×C7×D4C2211yescharacteristic
41C2×C4×C7×D4C2211yescharacteristic
42C2×C7×#117—21no—
43C2×C7×#117C2211yescharacteristic
44C22×C7×C4⋊C4—21no—
45C22×C7×C4⋊C4C2211yescharacteristic
46C7×#484C2218yescomplemented
47C7×#480C2218yescomplemented
48C7×#477C2218yescomplemented
49C7×#474C2218yescomplemented
50C7×#464C2218yescomplemented
51C7×#463C2218yescomplemented
52C7×#452C2218yescomplemented
53C7×#449C2218yes—
54C7×#440C2218yescomplemented
55C7×#440C2218yescomplemented
56C4×C7×Q16C2218yescomplemented
57C4×C7×D8C2218yescomplemented
58C7×#433C2218yescomplemented
59C2×C7×#107C2211yescharacteristic
60C2×C7×#107C2211yescharacteristic
61C2×C7×#107C2211yescharacteristic
62C2×C7×#107C2211yescharacteristic
63C2×C7×C4⋊C8C2211yescharacteristic
64C2×C7×C4⋊C8C2211yescharacteristic
65C2×C7×#103C2211yescharacteristic
66C2×C7×#103C2211yescharacteristic
67C2×C7×#103C2211yescharacteristic
68C2×C7×#103C2211yescharacteristic
69C2×C7×#102C2211yescharacteristic
70C2×C7×#102C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×C22⋊C8C2211yescharacteristic
74C2×C7×C22⋊C8C2211yescharacteristic
75C2×C7×#97C2211yescharacteristic
76C2×C4×C7×C8C2211yescharacteristic
77C2×#3124C711yesmaximal, characteristic, direct product factor, Sylow
78C2×C7×#41—24no—
79C2×C7×#41—24no—
80C2×C7×#41—22no—
81C2×C7×#41C2314yes—
82C22×C7×Q8—21no—
83C22×C7×Q8C2311yescharacteristic
84C22×C7×Q8C2311yescharacteristic
85C22×C7×D4—21no—
86C22×C7×D4—21no—
87C22×C7×D4C2311yescharacteristic
88C22×C7×D4C2311yescharacteristic
89C23×C4×C7—21no—
90C23×C4×C7—21no—
91C23×C4×C7—21no—
92C23×C4×C7—21no—
93C23×C4×C7—21no—
94C23×C4×C7C2311yescharacteristic
95C2×C7×Q16—24no—
96C2×C7×Q16C2314yes—
97C2×C7×SD16—24no—
98C2×C7×SD16—24no—
99C2×C7×SD16C2314yes—
100C2×C7×SD16C2314yes—
101C2×C7×D8—24no—
102C2×C7×D8C2314yes—
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C22×C7×C8C2311yescharacteristic
106C22×C7×C8C2311yescharacteristic
107C7×C4⋊Q8—22no—
108C7×C4⋊Q8C2314yes—
109C7×#126—28no—
110C7×#124—28no—
111C7×#124—22no—
112C7×#124C2314yes—
113C7×#123—28no—
114C7×C22⋊Q8—22no—
115C7×C22⋊Q8—28no—
116C7×C22⋊Q8C2314yes—
117C7×#121—22no—
118C7×#121C2314yes—
119C4×C7×Q8—22no—
120C4×C7×Q8—22no—
121C4×C7×Q8—22no—
122C4×C7×Q8C2314yes—
123C4×C7×Q8C2314yes—
124C4×C7×Q8C2314yes—
125C4×C7×D4—28no—
126C4×C7×D4—28no—
127C4×C7×D4—22no—
128C4×C7×D4—22no—
129C4×C7×D4—22no—
130C4×C7×D4C2314yes—
131C4×C7×D4C2314yes—
132C4×C7×D4C2314yes—
133C7×#117—28no—
134C7×#117D414yes—
135C7×#117C2314yes—
136C2×C7×C4⋊C4—21no—
137C2×C7×C4⋊C4—21no—
138C2×C7×C4⋊C4—21no—
139C2×C7×C4⋊C4—22no—
140C2×C7×C4⋊C4—21no—
141C2×C7×C4⋊C4—21no—
142C2×C7×C4⋊C4—21no—
143C2×C7×C4⋊C4—28no—
144C2×C7×C4⋊C4D411yescharacteristic
145C2×C7×C4⋊C4D411yescharacteristic
146C2×C7×C4⋊C4C2314yes—
147C2×C7×C4⋊C4C2311yescharacteristic
148C2×C7×C4⋊C4C2311yescharacteristic
149C2×C7×C4⋊C4C2311yescharacteristic
150C2×C7×C4⋊C4C2311yescharacteristic
151C2×C7×C22⋊C4—21no—
152C2×C7×C22⋊C4—21no—
153C2×C7×C22⋊C4—21no—
154C2×C7×C22⋊C4—21no—
155C2×C7×C22⋊C4—21no—
156C2×C7×C22⋊C4—21no—
157C2×C7×C22⋊C4—21no—
158C2×C7×C22⋊C4D411yescharacteristic
159C2×C7×C22⋊C4D411yescharacteristic
160C2×C42×C7—21no—
161C2×C42×C7—21no—
162C2×C42×C7—21no—
163C2×C42×C7C2311yescharacteristic
164C2×C42×C7C2311yescharacteristic
165C7×#107C2314yes—
166C7×#107C2314yes—
167C7×#107C2314yes—
168C7×#107C2314yes—
169C7×C4⋊C8C2314yes—
170C7×C4⋊C8C2314yes—
171C7×#103C2314yes—
172C7×#103C2314yes—
173C7×#103C2314yes—
174C7×#103C2314yes—
175C7×#102C2314yes—
176C7×#102C2314yes—
177C7×#102C2314yes—
178C7×#102C2314yes—
179C7×C22⋊C8C2314yes—
180C7×C22⋊C8C2314yes—
181C7×#97C2314yes—
182C4×C7×C8C2314yes—
183C2×#542C2×C711yescharacteristic, complemented
184C2×#520C2×C711yescharacteristic, complemented
185#3124C2×C7116yesdirect product factor
186C2×#484C2×C711yescharacteristic, complemented
187C2×#480C2×C711yescharacteristic, complemented
188C2×#477C2×C711yescharacteristic, complemented
189C2×#474C2×C711yescharacteristic, complemented
190C2×#464C2×C711yescharacteristic, complemented
191C2×#463C2×C711yescharacteristic, complemented
192C2×#452C2×C711yescharacteristic, complemented
193C2×#449C2×C711yescharacteristic
194C2×#440C2×C711yescharacteristic, complemented
195C2×#440C2×C711yescharacteristic, complemented
196C2×C4×Q16C2×C711yescharacteristic, complemented
197C2×C4×D8C2×C711yescharacteristic, complemented
198C2×#433C2×C711yescharacteristic, complemented
199C24×C7—21no—
200C24×C7—21no—
201C24×C7C2×D411yescharacteristic
202C7×#41—216no—
203C7×#41—28no—
204C7×#41—28no—
205C2×C7×Q8—21no—
206C2×C7×Q8—21no—
207C2×C7×Q8—24no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8—82no—
212C2×C7×Q8#4114yes—
213C2×C7×Q8C2412yes—
214C2×C7×Q8C2412yes—
215C2×C7×D4—28no—
216C2×C7×D4—24no—
217C2×C7×D4—24no—
218C2×C7×D4—21no—
219C2×C7×D4—21no—
220C2×C7×D4—22no—
221C2×C7×D4—22no—
222C2×C7×D4—22no—
223C2×C7×D4—82no—
224C2×C7×D4#4114yes—
225C2×C7×D4C2412yes—
226C2×C7×D4C2412yes—
227C22×C4×C7—28no—
228C22×C4×C7—21no—
229C22×C4×C7—24no—
230C22×C4×C7—22no—
231C22×C4×C7—22no—
232C22×C4×C7—21no—
233C22×C4×C7—21no—
234C22×C4×C7—21no—
235C22×C4×C7—21no—
236C22×C4×C7—21no—
237C22×C4×C7—24no—
238C22×C4×C7—24no—
239C22×C4×C7—24no—
240C22×C4×C7—24no—
241C22×C4×C7—82no—
242C22×C4×C7—82no—
243C22×C4×C7—82no—
244C22×C4×C7—82no—
245C22×C4×C7C2×D412yes—
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7C2×D411yescharacteristic
251C22×C4×C7C2412yes—
252C22×C4×C7C2411yescharacteristic
253C7×Q16—28no—
254C7×SD16—28no—
255C7×SD16—28no—
256C7×D8—28no—
257C2×C7×C8—22no—
258C2×C7×C8—22no—
259C2×C7×C8—22no—
260C2×C7×C8—22no—
261C2×C7×C8C2412yes—
262C2×C7×C8C2412yes—
263C2×C7×C8C2412yes—
264C2×C7×C8C2412yes—
265C7×C4⋊C4—24no—
266C7×C4⋊C4—24no—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—21no—
269C7×C4⋊C4—21no—
270C7×C4⋊C4—24no—
271C7×C4⋊C4—24no—
272C7×C4⋊C4—24no—
273C7×C4⋊C4—21no—
274C7×C4⋊C4—21no—
275C7×C4⋊C4C2×D414yes—
276C7×C4⋊C4C2×D414yes—
277C7×C4⋊C4C2412yes—
278C7×C4⋊C4C2412yes—
279C7×C4⋊C4C2412yes—
280C7×C4⋊C4C2412yes—
281C7×C22⋊C4—24no—
282C7×C22⋊C4—24no—
283C7×C22⋊C4—24no—
284C7×C22⋊C4—24no—
285C7×C22⋊C4—24no—
286C7×C22⋊C4—24no—
287C7×C22⋊C4—24no—
288C7×C22⋊C4C2×D414yes—
289C7×C22⋊C4C2×D414yes—
290C42×C7—24no—
291C42×C7—24no—
292C42×C7—24no—
293C42×C7C2×D412yes—
294C42×C7C2×D412yes—
295C42×C7C2412yes—
296C42×C7C2412yes—
297C22×#41C22×C711yescharacteristic
298C22×Q16C22×C711yescharacteristic
299C22×SD16C22×C711yescharacteristic
300C22×SD16C22×C711yescharacteristic
301C22×D8C22×C711yescharacteristic
302#542—24no—
303#542C22×C718yescomplemented
304C2×C4⋊Q8C22×C711yescharacteristic
305C2×#126—21no—
306C2×#124—21no—
307C2×#124C22×C711yescharacteristic
308C2×#123—21no—
309C2×C22⋊Q8—21no—
310C2×C22⋊Q8C22×C711yescharacteristic
311C2×#121C22×C711yescharacteristic
312#520—24no—
313#520C22×C718yescomplemented
314C2×C4×Q8C22×C711yescharacteristic
315C2×C4×Q8C22×C711yescharacteristic
316C2×C4×Q8C22×C711yescharacteristic
317C2×C4×D4—21no—
318C2×C4×D4—21no—
319C2×C4×D4C22×C711yescharacteristic
320C2×C4×D4C22×C711yescharacteristic
321C2×C4×D4C22×C711yescharacteristic
322C2×#117—21no—
323C2×#117C22×C711yescharacteristic
324C22×C4⋊C4—21no—
325C22×C4⋊C4C22×C711yescharacteristic
326#484C22×C718yescomplemented
327#480C22×C718yescomplemented
328#477C22×C718yescomplemented
329#474C22×C718yescomplemented
330#464C22×C718yescomplemented
331#463C22×C718yescomplemented
332#452C22×C718yescomplemented
333#449C22×C718yes—
334#440C22×C718yescomplemented
335#440C22×C718yescomplemented
336C4×Q16C22×C718yescomplemented
337C4×D8C22×C718yescomplemented
338#433C22×C718yescomplemented
339C2×#107C22×C711yescharacteristic
340C2×#107C22×C711yescharacteristic
341C2×#107C22×C711yescharacteristic
342C2×#107C22×C711yescharacteristic
343C2×C4⋊C8C22×C711yescharacteristic
344C2×C4⋊C8C22×C711yescharacteristic
345C2×#103C22×C711yescharacteristic
346C2×#103C22×C711yescharacteristic
347C2×#103C22×C711yescharacteristic
348C2×#103C22×C711yescharacteristic
349C2×#102C22×C711yescharacteristic
350C2×#102C22×C711yescharacteristic
351C2×#102C22×C711yescharacteristic
352C2×#102C22×C711yescharacteristic
353C2×C22⋊C8C22×C711yescharacteristic
354C2×C22⋊C8C22×C711yescharacteristic
355C2×#97C22×C711yescharacteristic
356C2×C4×C8C22×C711yescharacteristic
357C23×C7—22no—
358C23×C7—24no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7C22×D412yes—
369C23×C7C22×D411yescharacteristic
370C7×Q8—24no—
371C7×Q8—22no—
372C7×Q8—22no—
373C7×Q8—22no—
374C7×Q8—42no—
375C7×Q8—84no—
376C7×Q8C2×#4114yes—
377C7×D4—216no—
378C7×D4—24no—
379C7×D4—22no—
380C7×D4—22no—
381C7×D4—22no—
382C7×D4—42no—
383C7×D4—84no—
384C7×D4C2×#4114yes—
385C2×C4×C7—216no—
386C2×C4×C7—22no—
387C2×C4×C7—24no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—24no—
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—42no—
402C2×C4×C7—42no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7—42no—
406C2×C4×C7—84no—
407C2×C4×C7—84no—
408C2×C4×C7—84no—
409C2×C4×C7—84no—
410C2×C4×C7C22×D412yes—
411C2×C4×C7C22×D412yes—
412C2×C4×C7C22×D412yes—
413C2×C4×C7C22×D412yes—
414C2×C4×C7C22×D412yes—
415C2×C4×C7C22×D411yescharacteristic
416C2×C4×C7C2×#4112yes—
417C2×C4×C7C2×#4112yes—
418C2×C4×C7C2511yescharacteristic
419C7×C8—22no—
420C7×C8—22no—
421C7×C8—22no—
422C7×C8—22no—
423C2×#41—24no—
424C2×#41—24no—
425C2×#41—22no—
426C2×#41C23×C714yes—
427C22×Q8—21no—
428C22×Q8C23×C711yescharacteristic
429C22×Q8C23×C711yescharacteristic
430C22×D4—21no—
431C22×D4—21no—
432C22×D4C23×C711yescharacteristic
433C22×D4C23×C711yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4C23×C711yescharacteristic
440C2×Q16—24no—
441C2×Q16C23×C714yes—
442C2×SD16—24no—
443C2×SD16—24no—
444C2×SD16C23×C714yes—
445C2×SD16C23×C714yes—
446C2×D8—24no—
447C2×D8C23×C714yes—
448C22×C8C23×C711yescharacteristic
449C22×C8C23×C711yescharacteristic
450C22×C8C23×C711yescharacteristic
451C22×C8C23×C711yescharacteristic
452C4⋊Q8—22no—
453C4⋊Q8C23×C714yes—
454#126—28no—
455#124—28no—
456#124—22no—
457#124C23×C714yes—
458#123—28no—
459C22⋊Q8—22no—
460C22⋊Q8—28no—
461C22⋊Q8C23×C714yes—
462#121—22no—
463#121C23×C714yes—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8C23×C714yes—
468C4×Q8C23×C714yes—
469C4×Q8C23×C714yes—
470C4×D4—28no—
471C4×D4—28no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—22no—
475C4×D4C23×C714yes—
476C4×D4C23×C714yes—
477C4×D4C23×C714yes—
478#117—28no—
479#117C7×D414yes—
480#117C23×C714yes—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—28no—
489C2×C4⋊C4C7×D411yescharacteristic
490C2×C4⋊C4C7×D411yescharacteristic
491C2×C4⋊C4C23×C711yescharacteristic
492C2×C4⋊C4C23×C711yescharacteristic
493C2×C4⋊C4C23×C714yes—
494C2×C4⋊C4C23×C711yescharacteristic
495C2×C4⋊C4C23×C711yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4C7×D411yescharacteristic
504C2×C22⋊C4C7×D411yescharacteristic
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42C23×C711yescharacteristic
509C2×C42C23×C711yescharacteristic
510#107C23×C714yes—
511#107C23×C714yes—
512#107C23×C714yes—
513#107C23×C714yes—
514C4⋊C8C23×C714yes—
515C4⋊C8C23×C714yes—
516#103C23×C714yes—
517#103C23×C714yes—
518#103C23×C714yes—
519#103C23×C714yes—
520#102C23×C714yes—
521#102C23×C714yes—
522#102C23×C714yes—
523#102C23×C714yes—
524C22⋊C8C23×C714yes—
525C22⋊C8C23×C714yes—
526#97C23×C714yes—
527C4×C8C23×C714yes—
528C22×C7—22no—
529C22×C7—24no—
530C22×C7—22no—
531C22×C7—22no—
532C22×C7—44no—
533C22×C7—48no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—84no—
540C22×C7#52512yes—
541C22×C7#57612yes—
542C22×C7#57812yes—
543C22×C7C23×D411yescharacteristic
544C4×C7—22no—
545C4×C7—24no—
546C4×C7—22no—
547C4×C7—22no—
548C4×C7—22no—
549C4×C7—22no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7#52512yes—
556C4×C7C22×#4111yescharacteristic
557C4×C7C22×#4111yescharacteristic
558C24—21no—
559C24—21no—
560C24C2×C7×D411yescharacteristic
561#41—216no—
562#41—28no—
563#41—28no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—24no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—82no—
571C2×Q8C7×#4114yes—
572C2×Q8C24×C712yes—
573C2×Q8C24×C712yes—
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—82no—
583C2×D4C7×#4114yes—
584C2×D4C24×C712yes—
585C2×D4C24×C712yes—
586C22×C4—28no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4C2×C7×D411yescharacteristic
605C22×C4C2×C7×D411yescharacteristic
606C22×C4C2×C7×D411yescharacteristic
607C22×C4C2×C7×D411yescharacteristic
608C22×C4C2×C7×D411yescharacteristic
609C22×C4C2×C7×D412yes—
610C22×C4C24×C712yes—
611C22×C4C24×C711yescharacteristic
612Q16—28no—
613SD16—28no—
614SD16—28no—
615D8—28no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C24×C712yes—
621C2×C8C24×C712yes—
622C2×C8C24×C712yes—
623C2×C8C24×C712yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4C2×C7×D414yes—
635C4⋊C4C2×C7×D414yes—
636C4⋊C4C24×C712yes—
637C4⋊C4C24×C712yes—
638C4⋊C4C24×C712yes—
639C4⋊C4C24×C712yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4C2×C7×D414yes—
648C22⋊C4C2×C7×D414yes—
649C42—24no—
650C42—24no—
651C42—24no—
652C42C2×C7×D412yes—
653C42C2×C7×D412yes—
654C42C24×C712yes—
655C42C24×C712yes—
656C2×C7—42no—
657C2×C7—44no—
658C2×C7—82no—
659C2×C7#312414yesdirect product factor
660C2×C7C2×#52511yescharacteristic
661C2×C7C2×#57611yescharacteristic
662C2×C7C2×#57811yescharacteristic
663C23—22no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23C22×C7×D412yes—
675C23C22×C7×D411yescharacteristic
676Q8—22no—
677Q8—24no—
678Q8—22no—
679Q8—22no—
680Q8—42no—
681Q8—84no—
682Q8C2×C7×#4114yes—
683D4—216no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—24no—
688D4—42no—
689D4—84no—
690D4C2×C7×#4114yes—
691C2×C4—216no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—84no—
713C2×C4—84no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4C22×C7×D412yes—
717C2×C4C22×C7×D412yes—
718C2×C4C22×C7×D412yes—
719C2×C4C22×C7×D412yes—
720C2×C4C22×C7×D412yes—
721C2×C4C22×C7×D411yescharacteristic
722C2×C4C2×C7×#4112yes—
723C2×C4C2×C7×#4112yes—
724C2×C4C25×C711yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8—22no—
729C7C2×#312411yescharacteristic, direct product factor, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—48no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—84no—
742C22C7×#52512yes—
743C22C7×#57612yes—
744C22C7×#57812yes—
745C22C23×C7×D411yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4C7×#52512yes—
758C4C22×C7×#4111yescharacteristic
759C4C22×C7×#4111yescharacteristic
760C2—42no—
761C2—44no—
762C2—82no—
763C2C7×#312414yesdirect product factor
764C2C2×C7×#52511yescharacteristic
765C2C2×C7×#57611yescharacteristic
766C2C2×C7×#57811yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC2×C7×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#542C2semidirect
2. C2×C7×#520C2semidirect
3. C7×#3124C2direct (N × H)
4. C2×C7×#484C2semidirect
5. C2×C7×#480C2semidirect
6. C2×C7×#477C2semidirect
7. C2×C7×#474C2semidirect
8. C2×C7×#464C2semidirect
9. C2×C7×#463C2semidirect
10. C2×C7×#452C2semidirect
12. C2×C7×#440C2semidirect
13. C2×C7×#440C2semidirect
14. C2×C4×C7×Q16C2semidirect
15. C2×C4×C7×D8C2semidirect
16. C2×C7×#433C2semidirect
23. C7×#542C22semidirect
33. C7×#520C22semidirect
46. C7×#484C22semidirect
47. C7×#480C22semidirect
48. C7×#477C22semidirect
49. C7×#474C22semidirect
50. C7×#464C22semidirect
51. C7×#463C22semidirect
52. C7×#452C22semidirect
54. C7×#440C22semidirect
55. C7×#440C22semidirect
56. C4×C7×Q16C22semidirect
57. C4×C7×D8C22semidirect
58. C7×#433C22semidirect
77. C2×#3124C7direct (N × H)
183. C2×#542C2×C7semidirect
184. C2×#520C2×C7semidirect
185. #3124C2×C7direct (N × H)
186. C2×#484C2×C7semidirect
187. C2×#480C2×C7semidirect
188. C2×#477C2×C7semidirect
189. C2×#474C2×C7semidirect
190. C2×#464C2×C7semidirect
191. C2×#463C2×C7semidirect
192. C2×#452C2×C7semidirect
194. C2×#440C2×C7semidirect
195. C2×#440C2×C7semidirect
196. C2×C4×Q16C2×C7semidirect
197. C2×C4×D8C2×C7semidirect
198. C2×#433C2×C7semidirect
303. #542C22×C7semidirect
313. #520C22×C7semidirect
326. #484C22×C7semidirect
327. #480C22×C7semidirect
328. #477C22×C7semidirect
329. #474C22×C7semidirect
330. #464C22×C7semidirect
331. #463C22×C7semidirect
332. #452C22×C7semidirect
334. #440C22×C7semidirect
335. #440C22×C7semidirect
336. C4×Q16C22×C7semidirect
337. C4×D8C22×C7semidirect
338. #433C22×C7semidirect
659. C2×C7#3124direct (N × H)
729. C7C2×#3124direct (N × H)
763. C2C7×#3124direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
C2×C7×#5202
C7×#31242
C2×C7×#4842
C2×C7×#4802
C2×C7×#4772
C2×C7×#4742
C2×C7×#4642
C2×C7×#4632
C2×C7×#4522
C2×C7×#4492
C2×C7×#4402
C2×C4×C7×Q162
C2×C4×C7×D82
C2×C7×#4332
C2×#31247