Finite Group Databasebeta

← C7×#21874 #13199090

Subgroups — C7×#21874 #13199090

Order 1792.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#525C211yesmaximal, characteristic
2C7×#2280C211yesmaximal, characteristic, complemented
3C2×C7×#380C211yesmaximal, characteristic, complemented
4C7×#1996C212yesmaximal, complemented
5C7×#1964C212yesmaximal, complemented
6C7×#1898C214yesmaximal, complemented
7C7×#1799C214yesmaximal, complemented
8C22×C7×#41C411yescharacteristic, complemented
9C24×C4×C7C2211yescharacteristic
10C7×#525—21no—
11C7×#525—21no—
12C7×#525—21no—
13C7×#525—21no—
14C7×#525—21no—
15C7×#525—21no—
16C7×#525—21no—
17C7×#525—21no—
18C2×C7×#123C412yescomplemented
19C2×C7×C22⋊Q8C411yescharacteristic, complemented
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×C7×#121C411yescharacteristic, complemented
22C2×C7×#121C2211yescharacteristic
23C2×C7×#120C2212yes—
24C2×C4×C7×D4C412yescomplemented
25C2×C4×C7×D4C2212yes—
26C2×C7×#117—21no—
27C2×C7×#117C411yescharacteristic, complemented
28C22×C7×C4⋊C4—21no—
29C22×C7×C22⋊C4C2212yes—
30C2×C7×#99C2218yes—
31C7×#381—21no—
32C7×#380—21no—
33C7×#380—21no—
34C7×#380—21no—
35C7×#380C2212yes—
36C7×#380C2212yes—
37C7×#380C2212yes—
38C7×#379C2212yes—
39C4×C7×C22⋊C4—21no—
40C4×C7×C22⋊C4C2212yes—
41C2×C7×#95—21no—
42C7×#342C2218yes—
43#21874C711yesmaximal, characteristic, direct product factor, Sylow
44C25×C7C2311yescharacteristic
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—44no—
50C22×C7×Q8C2×C411yescharacteristic, complemented
51C22×C7×D4C2×C412yes—
52C22×C7×D4C2×C412yes—
53C22×C7×D4C2×C411yescharacteristic, complemented
54C22×C7×D4C2312yes—
55C23×C4×C7—22no—
56C23×C4×C7—44no—
57C23×C4×C7C2×C411yescharacteristic
58C23×C4×C7C2×C411yescharacteristic
59C23×C4×C7C2×C411yescharacteristic
60C23×C4×C7C2×C411yescharacteristic
61C23×C4×C7C2×C412yescomplemented
62C23×C4×C7D411yescharacteristic
63C23×C4×C7D411yescharacteristic
64C23×C4×C7D411yescharacteristic
65C23×C4×C7D411yescharacteristic
66C23×C4×C7D411yescharacteristic
67C23×C4×C7D411yescharacteristic
68C23×C4×C7D411yescharacteristic
69C23×C4×C7D411yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C7×#123—22no—
73C7×#123—22no—
74C7×#123—22no—
75C7×#123—22no—
76C7×C22⋊Q8—21no—
77C7×C22⋊Q8—21no—
78C7×C22⋊Q8—21no—
79C7×C22⋊Q8—21no—
80C7×C22⋊Q8—21no—
81C7×C22⋊Q8—21no—
82C7×C22⋊Q8—21no—
83C7×C22⋊Q8—21no—
84C7×#121—21no—
85C7×#121—21no—
86C7×#121—21no—
87C7×#121—21no—
88C7×#121—21no—
89C7×#121—21no—
90C7×#121—21no—
91C7×#121—21no—
92C7×#120—22no—
93C7×#120—22no—
94C7×#120—22no—
95C7×#120—22no—
96C4×C7×D4—22no—
97C4×C7×D4—22no—
98C4×C7×D4—22no—
99C4×C7×D4—22no—
100C4×C7×D4—22no—
101C4×C7×D4—22no—
102C4×C7×D4—22no—
103C4×C7×D4—22no—
104C7×#117—21no—
105C7×#117—21no—
106C7×#117—21no—
107C7×#117—21no—
108C7×#117—44no—
109C2×C7×C4⋊C4—22no—
110C2×C7×C4⋊C4—22no—
111C2×C7×C4⋊C4—22no—
112C2×C7×C4⋊C4—44no—
113C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
114C2×C7×C4⋊C4C2×C411yescharacteristic, complemented
115C2×C7×C4⋊C4C2×C412yescomplemented
116C2×C7×C4⋊C4C2×C412yescomplemented
117C2×C7×C22⋊C4—22no—
118C2×C7×C22⋊C4—22no—
119C2×C7×C22⋊C4—22no—
120C2×C7×C22⋊C4—44no—
121C2×C7×C22⋊C4C2×C412yes—
122C2×C7×C22⋊C4C2×C412yes—
123C2×C7×C22⋊C4C2×C412yescomplemented
124C2×C7×C22⋊C4C2×C412yescomplemented
125C2×C7×C22⋊C4C2314yes—
126C2×C7×C22⋊C4C2314yes—
127C2×C7×C22⋊C4C2312yes—
128C2×C42×C7—22no—
129C2×C42×C7C2×C412yescomplemented
130C7×#99—48no—
131C7×#95—22no—
132C7×#95—22no—
133C7×#95—22no—
134C7×#95—22no—
135C2×#525C2×C711yescharacteristic
136#2280C2×C711yescharacteristic, complemented
137C2×#380C2×C711yescharacteristic, complemented
138#1996C2×C712yescomplemented
139#1964C2×C712yescomplemented
140#1898C2×C714yescomplemented
141#1799C2×C714yescomplemented
142C24×C7—22no—
143C24×C7—22no—
144C24×C7—42no—
145C24×C7—42no—
146C24×C7C22×C411yescharacteristic
147C24×C7C22×C411yescharacteristic
148C24×C7C22×C412yes—
149C24×C7C2×D411yescharacteristic
150C24×C7C2×D411yescharacteristic
151C24×C7C2×D411yescharacteristic
152C24×C7C2×D411yescharacteristic
153C24×C7C2411yescharacteristic
154C7×#41—44no—
155C7×#41—44no—
156C7×#41—44no—
157C7×#41—44no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—42no—
161C2×C7×D4—22no—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—22no—
166C2×C7×D4—22no—
167C2×C7×D4—24no—
168C2×C7×D4—24no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—42no—
172C2×C7×D4—44no—
173C2×C7×D4—44no—
174C22×C4×C7—24no—
175C22×C4×C7—24no—
176C22×C4×C7—24no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—24no—
180C22×C4×C7—24no—
181C22×C4×C7—42no—
182C22×C4×C7—42no—
183C22×C4×C7—42no—
184C22×C4×C7—42no—
185C22×C4×C7—42no—
186C22×C4×C7—42no—
187C22×C4×C7—42no—
188C22×C4×C7—42no—
189C22×C4×C7—42no—
190C22×C4×C7—42no—
191C22×C4×C7—42no—
192C22×C4×C7—44no—
193C22×C4×C7—44no—
194C22×C4×C7—44no—
195C22×C4×C7—44no—
196C22×C4×C7C22⋊C411yescharacteristic
197C22×C4×C7C22⋊C411yescharacteristic
198C22×C4×C7C22⋊C411yescharacteristic
199C22×C4×C7C22⋊C411yescharacteristic
200C22×C4×C7C22⋊C411yescharacteristic
201C22×C4×C7C22⋊C411yescharacteristic
202C22×C4×C7C22⋊C411yescharacteristic
203C22×C4×C7C22⋊C411yescharacteristic
204C22×C4×C7C22⋊C411yescharacteristic
205C22×C4×C7C22⋊C411yescharacteristic
206C22×C4×C7C22⋊C411yescharacteristic
207C22×C4×C7C22⋊C411yescharacteristic
208C22×C4×C7C22⋊C411yescharacteristic
209C22×C4×C7C22⋊C411yescharacteristic
210C22×C4×C7C22⋊C411yescharacteristic
211C22×C4×C7C22⋊C411yescharacteristic
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C411yescharacteristic
214C22×C4×C7C22×C411yescharacteristic
215C22×C4×C7C22×C412yes—
216C22×C4×C7C22×C412yes—
217C22×C4×C7C22×C411yescharacteristic
218C22×C4×C7C22×C411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D411yescharacteristic
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—22no—
232C7×C4⋊C4—22no—
233C7×C4⋊C4—22no—
234C7×C4⋊C4—22no—
235C7×C4⋊C4—44no—
236C7×C4⋊C4—44no—
237C7×C4⋊C4—44no—
238C7×C22⋊C4—22no—
239C7×C22⋊C4—22no—
240C7×C22⋊C4—22no—
241C7×C22⋊C4—22no—
242C7×C22⋊C4—22no—
243C7×C22⋊C4—22no—
244C7×C22⋊C4—22no—
245C7×C22⋊C4—22no—
246C7×C22⋊C4—22no—
247C7×C22⋊C4—22no—
248C7×C22⋊C4—24no—
249C7×C22⋊C4—28no—
250C7×C22⋊C4—24no—
251C7×C22⋊C4—44no—
252C7×C22⋊C4—44no—
253C7×C22⋊C4—44no—
254C42×C7—22no—
255C42×C7—22no—
256C42×C7—44no—
257C22×#41C4×C711yescharacteristic, complemented
258C24×C4C22×C711yescharacteristic
259#525—21no—
260#525—21no—
261#525—21no—
262#525—21no—
263#525—21no—
264#525—21no—
265#525—21no—
266#525—21no—
267C2×#123C4×C712yescomplemented
268C2×C22⋊Q8C4×C711yescharacteristic, complemented
269C2×C22⋊Q8C22×C711yescharacteristic
270C2×#121C4×C711yescharacteristic, complemented
271C2×#121C22×C711yescharacteristic
272C2×#120C22×C712yes—
273C2×C4×D4C4×C712yescomplemented
274C2×C4×D4C22×C712yes—
275C2×#117—21no—
276C2×#117C4×C711yescharacteristic, complemented
277C22×C4⋊C4—21no—
278C22×C22⋊C4C22×C712yes—
279C2×#99C22×C718yes—
280#381—21no—
281#380—21no—
282#380—21no—
283#380—21no—
284#380C22×C712yes—
285#380C22×C712yes—
286#380C22×C712yes—
287#379C22×C712yes—
288C4×C22⋊C4—21no—
289C4×C22⋊C4C22×C712yes—
290C2×#95—21no—
291#342C22×C718yes—
292C23×C7—21no—
293C23×C7—21no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—22no—
297C23×C7—22no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—22no—
301C23×C7—22no—
302C23×C7—22no—
303C23×C7—22no—
304C23×C7—22no—
305C23×C7—22no—
306C23×C7—22no—
307C23×C7—24no—
308C23×C7—41no—
309C23×C7—41no—
310C23×C7—41no—
311C23×C7—41no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—48no—
317C23×C7—48no—
318C23×C7—42no—
319C23×C7—42no—
320C23×C7C2×C22⋊C411yescharacteristic
321C23×C7C2×C22⋊C411yescharacteristic
322C23×C7C2×C22⋊C411yescharacteristic
323C23×C7C2×C22⋊C411yescharacteristic
324C23×C7C23×C411yescharacteristic
325C23×C7C22×D411yescharacteristic
326C23×C7C22×D411yescharacteristic
327C23×C7H(5,𝔽2)12yes—
328C23×C72−1+412yes—
329C7×Q8—42no—
330C7×Q8—42no—
331C7×D4—42no—
332C7×D4—44no—
333C7×D4—44no—
334C7×D4—42no—
335C7×D4—42no—
336C7×D4—44no—
337C7×D4—44no—
338C7×D4—44no—
339C7×D4—42no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—22no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—24no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—41no—
368C2×C4×C7—41no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—44no—
372C2×C4×C7—44no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—44no—
376C2×C4×C7—44no—
377C2×C4×C7—44no—
378C2×C4×C7—44no—
379C2×C4×C7—44no—
380C2×C4×C7—44no—
381C2×C4×C7—88no—
382C2×C4×C7#9914yescomplemented
383C2×C4×C7C2×C22⋊C411yescharacteristic
384C2×C4×C7C2×C22⋊C411yescharacteristic
385C2×C4×C7C2×C22⋊C411yescharacteristic
386C2×C4×C7C2×C22⋊C411yescharacteristic
387C2×C4×C7C2×C22⋊C411yescharacteristic
388C2×C4×C7C2×C22⋊C411yescharacteristic
389C2×C4×C7C2×C22⋊C411yescharacteristic
390C2×C4×C7C2×C22⋊C411yescharacteristic
391C25C23×C711yescharacteristic
392C2×#41—21no—
393C2×#41—21no—
394C2×#41—21no—
395C2×#41—21no—
396C2×#41—44no—
397C22×Q8C2×C4×C711yescharacteristic, complemented
398C22×D4C2×C4×C712yes—
399C22×D4C2×C4×C712yes—
400C22×D4C2×C4×C711yescharacteristic, complemented
401C22×D4C23×C712yes—
402C23×C4—22no—
403C23×C4—44no—
404C23×C4C2×C4×C711yescharacteristic
405C23×C4C2×C4×C711yescharacteristic
406C23×C4C2×C4×C711yescharacteristic
407C23×C4C2×C4×C711yescharacteristic
408C23×C4C2×C4×C712yescomplemented
409C23×C4C7×D411yescharacteristic
410C23×C4C7×D411yescharacteristic
411C23×C4C7×D411yescharacteristic
412C23×C4C7×D411yescharacteristic
413C23×C4C7×D411yescharacteristic
414C23×C4C7×D411yescharacteristic
415C23×C4C7×D411yescharacteristic
416C23×C4C7×D411yescharacteristic
417C23×C4C23×C711yescharacteristic
418C23×C4C23×C711yescharacteristic
419#123—22no—
420#123—22no—
421#123—22no—
422#123—22no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—21no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121—21no—
437#121—21no—
438#121—21no—
439#120—22no—
440#120—22no—
441#120—22no—
442#120—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451#117—21no—
452#117—21no—
453#117—21no—
454#117—21no—
455#117—44no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—44no—
460C2×C4⋊C4C2×C4×C711yescharacteristic, complemented
461C2×C4⋊C4C2×C4×C711yescharacteristic, complemented
462C2×C4⋊C4C2×C4×C712yescomplemented
463C2×C4⋊C4C2×C4×C712yescomplemented
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—44no—
468C2×C22⋊C4C2×C4×C712yes—
469C2×C22⋊C4C2×C4×C712yes—
470C2×C22⋊C4C2×C4×C712yescomplemented
471C2×C22⋊C4C2×C4×C712yescomplemented
472C2×C22⋊C4C23×C714yes—
473C2×C22⋊C4C23×C714yes—
474C2×C22⋊C4C23×C712yes—
475C2×C42—22no—
476C2×C42C2×C4×C712yescomplemented
477#99—48no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482C22×C7—24no—
483C22×C7—24no—
484C22×C7—21no—
485C22×C7—21no—
486C22×C7—21no—
487C22×C7—21no—
488C22×C7—21no—
489C22×C7—21no—
490C22×C7—21no—
491C22×C7—21no—
492C22×C7—21no—
493C22×C7—21no—
494C22×C7—21no—
495C22×C7—21no—
496C22×C7—21no—
497C22×C7—21no—
498C22×C7—21no—
499C22×C7—21no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—44no—
503C22×C7—44no—
504C22×C7—44no—
505C22×C7—44no—
506C22×C7—42no—
507C22×C7—42no—
508C22×C7—42no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—84no—
512C22×C7C2×#9912yes—
513C22×C7#41012yes—
514C22×C7C22×C22⋊C411yescharacteristic
515C22×C7#52012yes—
516C22×C7#53511yescharacteristic
517C22×C7#53611yescharacteristic
518C22×C7#53712yes—
519C4×C7—21no—
520C4×C7—21no—
521C4×C7—21no—
522C4×C7—21no—
523C4×C7—21no—
524C4×C7—21no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—84no—
529C4×C7—84no—
530C4×C7C2×#9912yes—
531C4×C7C2×#9912yes—
532C24—22no—
533C24—22no—
534C24—42no—
535C24—42no—
536C24C22×C4×C711yescharacteristic
537C24C22×C4×C711yescharacteristic
538C24C22×C4×C712yes—
539C24C2×C7×D411yescharacteristic
540C24C2×C7×D411yescharacteristic
541C24C2×C7×D411yescharacteristic
542C24C2×C7×D411yescharacteristic
543C24C24×C711yescharacteristic
544#41—44no—
545#41—44no—
546#41—44no—
547#41—44no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—44no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4C7×C22⋊C411yescharacteristic
587C22×C4C7×C22⋊C411yescharacteristic
588C22×C4C7×C22⋊C411yescharacteristic
589C22×C4C7×C22⋊C411yescharacteristic
590C22×C4C7×C22⋊C411yescharacteristic
591C22×C4C7×C22⋊C411yescharacteristic
592C22×C4C7×C22⋊C411yescharacteristic
593C22×C4C7×C22⋊C411yescharacteristic
594C22×C4C7×C22⋊C411yescharacteristic
595C22×C4C7×C22⋊C411yescharacteristic
596C22×C4C7×C22⋊C411yescharacteristic
597C22×C4C7×C22⋊C411yescharacteristic
598C22×C4C7×C22⋊C411yescharacteristic
599C22×C4C7×C22⋊C411yescharacteristic
600C22×C4C7×C22⋊C411yescharacteristic
601C22×C4C7×C22⋊C411yescharacteristic
602C22×C4C22×C4×C712yes—
603C22×C4C22×C4×C711yescharacteristic
604C22×C4C22×C4×C711yescharacteristic
605C22×C4C22×C4×C712yes—
606C22×C4C22×C4×C712yes—
607C22×C4C22×C4×C711yescharacteristic
608C22×C4C22×C4×C711yescharacteristic
609C22×C4C2×C7×D411yescharacteristic
610C22×C4C2×C7×D411yescharacteristic
611C22×C4C2×C7×D411yescharacteristic
612C22×C4C2×C7×D411yescharacteristic
613C22×C4C2×C7×D411yescharacteristic
614C22×C4C2×C7×D411yescharacteristic
615C22×C4C2×C7×D411yescharacteristic
616C22×C4C2×C7×D411yescharacteristic
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—24no—
639C22⋊C4—28no—
640C22⋊C4—24no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C42—22no—
645C42—22no—
646C42—44no—
647C2×C7—21no—
648C2×C7—22no—
649C2×C7—21no—
650C2×C7—22no—
651C2×C7—22no—
652C2×C7—22no—
653C2×C7—41no—
654C2×C7—41no—
655C2×C7—82no—
656C2×C7#231111yescharacteristic
657C2×C7C22×#9911yescharacteristic
658C2×C7C2×#41011yescharacteristic
659C23—21no—
660C23—21no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—21no—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—48no—
684C23—48no—
685C23—42no—
686C23—42no—
687C23C2×C7×C22⋊C411yescharacteristic
688C23C2×C7×C22⋊C411yescharacteristic
689C23C2×C7×C22⋊C411yescharacteristic
690C23C2×C7×C22⋊C411yescharacteristic
691C23C23×C4×C711yescharacteristic
692C23C22×C7×D411yescharacteristic
693C23C22×C7×D411yescharacteristic
694C23C7×H(5,𝔽2)12yes—
695C23C7×2−1+412yes—
696Q8—42no—
697Q8—42no—
698D4—42no—
699D4—44no—
700D4—44no—
701D4—42no—
702D4—42no—
703D4—44no—
704D4—44no—
705D4—44no—
706D4—42no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—88no—
749C2×C4C7×#9914yescomplemented
750C2×C4C2×C7×C22⋊C411yescharacteristic
751C2×C4C2×C7×C22⋊C411yescharacteristic
752C2×C4C2×C7×C22⋊C411yescharacteristic
753C2×C4C2×C7×C22⋊C411yescharacteristic
754C2×C4C2×C7×C22⋊C411yescharacteristic
755C2×C4C2×C7×C22⋊C411yescharacteristic
756C2×C4C2×C7×C22⋊C411yescharacteristic
757C2×C4C2×C7×C22⋊C411yescharacteristic
758C7#2187411yescharacteristic, direct product factor, Sylow
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×C7×#9912yes—
790C22C7×#41012yes—
791C22C22×C7×C22⋊C411yescharacteristic
792C22C7×#52012yes—
793C22C7×#53511yescharacteristic
794C22C7×#53611yescharacteristic
795C22C7×#53712yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—84no—
806C4—84no—
807C4C2×C7×#9912yes—
808C4C2×C7×#9912yes—
809C2—21no—
810C2—22no—
811C2—21no—
812C2—22no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2C7×#231111yescharacteristic
819C2C22×C7×#9911yescharacteristic
820C2C2×C7×#41011yescharacteristic
subgroupG/H
center, socleC22×C7C22×C22⋊C4
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC2×C7×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C24×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2280C2semidirect
3. C2×C7×#380C2semidirect
4. C7×#1996C2semidirect
5. C7×#1964C2semidirect
6. C7×#1898C2semidirect
7. C7×#1799C2semidirect
8. C22×C7×#41C4semidirect
18. C2×C7×#123C4semidirect
19. C2×C7×C22⋊Q8C4semidirect
21. C2×C7×#121C4semidirect
24. C2×C4×C7×D4C4semidirect
27. C2×C7×#117C4semidirect
43. #21874C7direct (N × H)
50. C22×C7×Q8C2×C4semidirect
53. C22×C7×D4C2×C4semidirect
61. C23×C4×C7C2×C4semidirect
113. C2×C7×C4⋊C4C2×C4semidirect
114. C2×C7×C4⋊C4C2×C4semidirect
115. C2×C7×C4⋊C4C2×C4semidirect
116. C2×C7×C4⋊C4C2×C4semidirect
123. C2×C7×C22⋊C4C2×C4semidirect
124. C2×C7×C22⋊C4C2×C4semidirect
129. C2×C42×C7C2×C4semidirect
136. #2280C2×C7semidirect
137. C2×#380C2×C7semidirect
138. #1996C2×C7semidirect
139. #1964C2×C7semidirect
140. #1898C2×C7semidirect
141. #1799C2×C7semidirect
257. C22×#41C4×C7semidirect
267. C2×#123C4×C7semidirect
268. C2×C22⋊Q8C4×C7semidirect
270. C2×#121C4×C7semidirect
273. C2×C4×D4C4×C7semidirect
276. C2×#117C4×C7semidirect
382. C2×C4×C7#99semidirect
397. C22×Q8C2×C4×C7semidirect
400. C22×D4C2×C4×C7semidirect
408. C23×C4C2×C4×C7semidirect
460. C2×C4⋊C4C2×C4×C7semidirect
461. C2×C4⋊C4C2×C4×C7semidirect
462. C2×C4⋊C4C2×C4×C7semidirect
463. C2×C4⋊C4C2×C4×C7semidirect
470. C2×C22⋊C4C2×C4×C7semidirect
471. C2×C22⋊C4C2×C4×C7semidirect
476. C2×C42C2×C4×C7semidirect
749. C2×C4C7×#99semidirect
758. C7#21874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5252
C7×#22802
C2×C7×#3802
C7×#19962
C7×#19642
C7×#18982
C7×#17992
#218747