Finite Group Databasebeta

← C7×#14018 #13191234

Subgroups — C7×#14018 #13191234

Order 1792.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C7×D4C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic
3C2×C7×#390C211yesmaximal, characteristic
4C2×C7×#389C211yesmaximal, characteristic, complemented
5C2×C7×#385C212yesmaximal, complemented
6C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
7C7×#1439C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×C4⋊#95C211yesmaximal, characteristic, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C7×C22⋊#95C212yesmaximal, complemented
12C23×C7×D4C2211yescharacteristic
13C24×C4×C7C2212yes—
14C2×C4×C7×D4—24no—
15C2×C4×C7×D4—24no—
16C2×C4×C7×D4—24no—
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2212yes—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2212yes—
24C22×C7×C22⋊C4C2212yes—
25C22×C7×C22⋊C4C2212yes—
26C22×C7×C22⋊C4C2212yes—
27C22×C7×C22⋊C4C2212yes—
28C22×C42×C7C2211yescharacteristic
29C22×C42×C7C2211yescharacteristic
30C22×C42×C7C2211yescharacteristic
31C7×#390—24no—
32C7×#390C418yescomplemented
33C7×#389—24no—
34C7×#385—28no—
35C4×C7×C4⋊C4—24no—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41C2×C7×#95C2212yes—
42C2×C7×#95C2212yes—
43#14018C711yesmaximal, characteristic, direct product factor, Sylow
44C25×C7C2312yes—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4C2×C414yes—
50C22×C7×D4D414yes—
51C22×C7×D4Q814yes—
52C23×C4×C7—24no—
53C23×C4×C7—24no—
54C23×C4×C7—24no—
55C23×C4×C7—24no—
56C23×C4×C7—24no—
57C23×C4×C7—42no—
58C23×C4×C7—42no—
59C23×C4×C7C2312yes—
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2312yes—
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2312yes—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C4×C7×D4—232no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4—22no—
73C2×C7×C4⋊C4—22no—
74C2×C7×C4⋊C4—22no—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—22no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—24no—
80C2×C7×C4⋊C4—24no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—42no—
85C2×C7×C4⋊C4C2×C414yescomplemented
86C2×C7×C4⋊C4D414yes—
87C2×C7×C4⋊C4D414yescomplemented
88C2×C7×C22⋊C4—24no—
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4—24no—
93C2×C7×C22⋊C4—24no—
94C2×C7×C22⋊C4—24no—
95C2×C7×C22⋊C4—24no—
96C2×C7×C22⋊C4—24no—
97C2×C7×C22⋊C4—42no—
98C2×C7×C22⋊C4—42no—
99C2×C7×C22⋊C4—42no—
100C2×C7×C22⋊C4—42no—
101C2×C7×C22⋊C4C2×C418yescomplemented
102C2×C7×C22⋊C4C2×C418yescomplemented
103C2×C42×C7—22no—
104C2×C42×C7—22no—
105C2×C42×C7—22no—
106C2×C42×C7—22no—
107C2×C42×C7—22no—
108C2×C42×C7—22no—
109C2×C42×C7—22no—
110C2×C42×C7C2×C414yescomplemented
111C2×C42×C7D414yes—
112C7×#95—22no—
113C7×#95—22no—
114C7×#95—24no—
115C7×#95—24no—
116C7×#95—24no—
117C7×#95—42no—
118C7×#95—42no—
119C22×C4×D4C2×C711yescharacteristic
120C2×#390C2×C711yescharacteristic
121C2×#390C2×C711yescharacteristic
122C2×#389C2×C711yescharacteristic, complemented
123C2×#385C2×C712yescomplemented
124C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
125#1439C2×C712yescomplemented
126#1439C2×C712yescomplemented
127C4⋊#95C2×C711yescharacteristic, complemented
128C4⋊#95C2×C711yescharacteristic, complemented
129C22⋊#95C2×C712yescomplemented
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7—22no—
138C24×C7—22no—
139C24×C7—22no—
140C24×C7—22no—
141C24×C7—22no—
142C24×C7C22×C414yes—
143C24×C7C2×D414yes—
144C24×C7C2×Q814yes—
145C24×C7C2411yescharacteristic
146C2×C7×D4—28no—
147C2×C7×D4—28no—
148C2×C7×D4—28no—
149C2×C7×D4—28no—
150C2×C7×D4—28no—
151C2×C7×D4—28no—
152C2×C7×D4C4⋊C4116yescomplemented
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—21no—
157C22×C4×C7—21no—
158C22×C4×C7—21no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—216no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—21no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—22no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—22no—
193C22×C4×C7—21no—
194C22×C4×C7—22no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—48no—
206C22×C4×C7—48no—
207C22×C4×C7—48no—
208C22×C4×C7—48no—
209C22×C4×C7—48no—
210C22×C4×C7—48no—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C22×C414yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7C2×D414yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×D412yes—
223C22×C4×C7C2×D412yes—
224C22×C4×C7C2×Q812yes—
225C22×C4×C7#4112yes—
226C22×C4×C7#4112yes—
227C22×C4×C7#4112yes—
228C22×C4×C7#4112yes—
229C22×C4×C7#4112yes—
230C7×C4⋊C4—28no—
231C7×C4⋊C4—28no—
232C7×C4⋊C4—28no—
233C7×C4⋊C4—28no—
234C7×C4⋊C4—48no—
235C7×C4⋊C4—44no—
236C7×C22⋊C4—216no—
237C7×C22⋊C4—216no—
238C7×C22⋊C4—48no—
239C7×C22⋊C4—48no—
240C7×C22⋊C4—48no—
241C42×C7—28no—
242C42×C7—28no—
243C42×C7—44no—
244C23×D4C22×C711yescharacteristic
245C24×C4C22×C712yes—
246C2×C4×D4—24no—
247C2×C4×D4—24no—
248C2×C4×D4—24no—
249C22×C4⋊C4C22×C711yescharacteristic
250C22×C4⋊C4C22×C711yescharacteristic
251C22×C4⋊C4C22×C712yes—
252C22×C4⋊C4C22×C711yescharacteristic
253C22×C4⋊C4C22×C711yescharacteristic
254C22×C4⋊C4C22×C711yescharacteristic
255C22×C22⋊C4C22×C712yes—
256C22×C22⋊C4C22×C712yes—
257C22×C22⋊C4C22×C712yes—
258C22×C22⋊C4C22×C712yes—
259C22×C22⋊C4C22×C712yes—
260C22×C42C22×C711yescharacteristic
261C22×C42C22×C711yescharacteristic
262C22×C42C22×C711yescharacteristic
263#390—24no—
264#390C4×C718yescomplemented
265#389—24no—
266#385—28no—
267C4×C4⋊C4—24no—
268C2×#95C22×C711yescharacteristic
269C2×#95C22×C712yes—
270C2×#95C22×C712yes—
271C2×#95C22×C712yes—
272C2×#95C22×C711yescharacteristic
273C2×#95C22×C712yes—
274C2×#95C22×C712yes—
275C23×C7—24no—
276C23×C7—24no—
277C23×C7—24no—
278C23×C7—24no—
279C23×C7—24no—
280C23×C7—24no—
281C23×C7—24no—
282C23×C7—24no—
283C23×C7—24no—
284C23×C7—24no—
285C23×C7—24no—
286C23×C7—24no—
287C23×C7—24no—
288C23×C7—24no—
289C23×C7—24no—
290C23×C7—24no—
291C23×C7—24no—
292C23×C7—24no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7—42no—
296C23×C7—42no—
297C23×C7—42no—
298C23×C7—42no—
299C23×C7—42no—
300C23×C7—42no—
301C23×C7—42no—
302C23×C7—42no—
303C23×C7—42no—
304C23×C7—42no—
305C23×C7—42no—
306C23×C7—42no—
307C23×C7—42no—
308C23×C7—42no—
309C23×C7C2×C4⋊C418yes—
310C23×C7C23×C411yescharacteristic
311C23×C7C22×D411yescharacteristic
312C23×C7C22×D411yescharacteristic
313C23×C7C22×D411yescharacteristic
314C23×C7C22×D411yescharacteristic
315C23×C7C22×Q811yescharacteristic
316C23×C7C2×#4111yescharacteristic
317C23×C7C2×#4111yescharacteristic
318C23×C7C2×#4111yescharacteristic
319C23×C7C2×#4111yescharacteristic
320C23×C7C2×#4111yescharacteristic
321C23×C7H(5,𝔽2)11yescharacteristic
322C23×C7H(5,𝔽2)11yescharacteristic
323C23×C7H(5,𝔽2)11yescharacteristic
324C23×C72−1+411yescharacteristic
325C7×D4—232no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—24no—
340C2×C4×C7—24no—
341C2×C4×C7—22no—
342C2×C4×C7—24no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—24no—
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—24no—
353C2×C4×C7—22no—
354C2×C4×C7—24no—
355C2×C4×C7—22no—
356C2×C4×C7—432no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—42no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—42no—
363C2×C4×C7—41no—
364C2×C4×C7—41no—
365C2×C4×C7—41no—
366C2×C4×C7—41no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—41no—
370C2×C4×C7—41no—
371C2×C4×C7—41no—
372C2×C4×C7—42no—
373C2×C4×C7—41no—
374C2×C4×C7—41no—
375C2×C4×C7—41no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—41no—
379C2×C4×C7—41no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7C2×C4⋊C414yes—
389C2×C4×C7C4×D414yes—
390C2×C4×C7C4×D414yes—
391C2×C4×C7C4×D414yescomplemented
392C2×C4×C7#12014yes—
393C2×C4×C7#12114yes—
394C2×C4×C7C22⋊Q814yes—
395C2×C4×C7C22⋊Q814yes—
396C2×C4×C7#12314yes—
397C25C23×C712yes—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—22no—
402C22×D4C2×C4×C714yes—
403C22×D4C7×D414yes—
404C22×D4C7×Q814yes—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4C23×C712yes—
413C23×C4C23×C712yes—
414C23×C4C23×C711yescharacteristic
415C23×C4C23×C711yescharacteristic
416C23×C4C23×C711yescharacteristic
417C23×C4C23×C712yes—
418C23×C4C23×C711yescharacteristic
419C23×C4C23×C711yescharacteristic
420C23×C4C23×C711yescharacteristic
421C23×C4C23×C711yescharacteristic
422C4×D4—232no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4C2×C4×C714yescomplemented
439C2×C4⋊C4C7×D414yes—
440C2×C4⋊C4C7×D414yescomplemented
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4C2×C4×C718yescomplemented
455C2×C22⋊C4C2×C4×C718yescomplemented
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42C2×C4×C714yescomplemented
464C2×C42C7×D414yes—
465#95—22no—
466#95—22no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—42no—
471#95—42no—
472C22×C7—28no—
473C22×C7—28no—
474C22×C7—28no—
475C22×C7—44no—
476C22×C7—44no—
477C22×C7—44no—
478C22×C7—44no—
479C22×C7—44no—
480C22×C7—44no—
481C22×C7—44no—
482C22×C7—44no—
483C22×C7—44no—
484C22×C7—44no—
485C22×C7—44no—
486C22×C7—44no—
487C22×C7C22×C4⋊C411yescharacteristic
488C22×C7C2×C4×D411yescharacteristic
489C22×C7C2×C4×D411yescharacteristic
490C22×C7C2×C4×D411yescharacteristic
491C22×C7C4×#4111yescharacteristic
492C22×C7#51811yescharacteristic
493C22×C7#52011yescharacteristic
494C22×C7C2×#12011yescharacteristic
495C22×C7C2×#12111yescharacteristic
496C22×C7C2×C22⋊Q811yescharacteristic
497C22×C7C2×C22⋊Q811yescharacteristic
498C22×C7C2×#12311yescharacteristic
499C22×C7#52511yescharacteristic
500C22×C7#52911yescharacteristic
501C22×C7#53211yescharacteristic
502C22×C7#53511yescharacteristic
503C22×C7#53711yescharacteristic
504C22×C7#54011yescharacteristic
505C22×C7#54211yescharacteristic
506C22×C7D4211yescharacteristic
507C22×C7D4211yescharacteristic
508C22×C7#54611yescharacteristic
509C22×C7#54611yescharacteristic
510C22×C7#54611yescharacteristic
511C22×C7#54711yescharacteristic
512C22×C7#54811yescharacteristic
513C22×C7D4×Q811yescharacteristic
514C22×C7#55011yescharacteristic
515C22×C7#55011yescharacteristic
516C22×C7#55411yescharacteristic
517C22×C7#55411yescharacteristic
518C22×C7#55411yescharacteristic
519C22×C7#55611yescharacteristic
520C22×C7#55911yescharacteristic
521C22×C7#55911yescharacteristic
522C4×C7—24no—
523C4×C7—24no—
524C4×C7—42no—
525C4×C7—44no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7—44no—
530C4×C7—82no—
531C4×C7#38518yescomplemented
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C22×C4×C714yes—
545C24C2×C7×D414yes—
546C24C2×C7×Q814yes—
547C24C24×C711yescharacteristic
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4C7×C4⋊C4116yescomplemented
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—216no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4C22×C4×C712yes—
614C22×C4C22×C4×C714yes—
615C22×C4C22×C4×C712yes—
616C22×C4C22×C4×C712yes—
617C22×C4C2×C7×D412yes—
618C22×C4C2×C7×D414yes—
619C22×C4C2×C7×D412yes—
620C22×C4C2×C7×D412yes—
621C22×C4C2×C7×D412yes—
622C22×C4C2×C7×D412yes—
623C22×C4C2×C7×D412yes—
624C22×C4C2×C7×D412yes—
625C22×C4C2×C7×D412yes—
626C22×C4C2×C7×Q812yes—
627C22×C4C7×#4112yes—
628C22×C4C7×#4112yes—
629C22×C4C7×#4112yes—
630C22×C4C7×#4112yes—
631C22×C4C7×#4112yes—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C42—28no—
644C42—28no—
645C42—44no—
646C2×C7—48no—
647C2×C7C2×#38511yescharacteristic
648C2×C7C4×#12111yescharacteristic
649C2×C7#232411yescharacteristic
650C2×C7D4×C4⋊C411yescharacteristic
651C2×C7#234911yescharacteristic
652C2×C7#236611yescharacteristic
653C2×C7#236711yescharacteristic
654C2×C7#240711yescharacteristic
655C2×C7#240811yescharacteristic
656C2×C7#244511yescharacteristic
657C2×C7#244711yescharacteristic
658C2×C7#245211yescharacteristic
659C2×C7#245411yescharacteristic
660C2×C7#253811yescharacteristic
661C2×C7#258011yescharacteristic
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23C2×C7×C4⋊C418yes—
697C23C23×C4×C711yescharacteristic
698C23C22×C7×D411yescharacteristic
699C23C22×C7×D411yescharacteristic
700C23C22×C7×D411yescharacteristic
701C23C22×C7×D411yescharacteristic
702C23C22×C7×Q811yescharacteristic
703C23C2×C7×#4111yescharacteristic
704C23C2×C7×#4111yescharacteristic
705C23C2×C7×#4111yescharacteristic
706C23C2×C7×#4111yescharacteristic
707C23C2×C7×#4111yescharacteristic
708C23C7×H(5,𝔽2)11yescharacteristic
709C23C7×H(5,𝔽2)11yescharacteristic
710C23C7×H(5,𝔽2)11yescharacteristic
711C23C7×2−1+411yescharacteristic
712D4—232no—
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—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—432no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4C2×C7×C4⋊C414yes—
776C2×C4C4×C7×D414yes—
777C2×C4C4×C7×D414yes—
778C2×C4C4×C7×D414yescomplemented
779C2×C4C7×#12014yes—
780C2×C4C7×#12114yes—
781C2×C4C7×C22⋊Q814yes—
782C2×C4C7×C22⋊Q814yes—
783C2×C4C7×#12314yes—
784C7#1401811yescharacteristic, direct product factor, Sylow
785C22—28no—
786C22—28no—
787C22—28no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22C22×C7×C4⋊C411yescharacteristic
801C22C2×C4×C7×D411yescharacteristic
802C22C2×C4×C7×D411yescharacteristic
803C22C2×C4×C7×D411yescharacteristic
804C22C4×C7×#4111yescharacteristic
805C22C7×#51811yescharacteristic
806C22C7×#52011yescharacteristic
807C22C2×C7×#12011yescharacteristic
808C22C2×C7×#12111yescharacteristic
809C22C2×C7×C22⋊Q811yescharacteristic
810C22C2×C7×C22⋊Q811yescharacteristic
811C22C2×C7×#12311yescharacteristic
812C22C7×#52511yescharacteristic
813C22C7×#52911yescharacteristic
814C22C7×#53211yescharacteristic
815C22C7×#53511yescharacteristic
816C22C7×#53711yescharacteristic
817C22C7×#54011yescharacteristic
818C22C7×#54211yescharacteristic
819C22C7×D4211yescharacteristic
820C22C7×D4211yescharacteristic
821C22C7×#54611yescharacteristic
822C22C7×#54611yescharacteristic
823C22C7×#54611yescharacteristic
824C22C7×#54711yescharacteristic
825C22C7×#54811yescharacteristic
826C22C7×D4×Q811yescharacteristic
827C22C7×#55011yescharacteristic
828C22C7×#55011yescharacteristic
829C22C7×#55411yescharacteristic
830C22C7×#55411yescharacteristic
831C22C7×#55411yescharacteristic
832C22C7×#55611yescharacteristic
833C22C7×#55911yescharacteristic
834C22C7×#55911yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—44no—
840C4—42no—
841C4—42no—
842C4—44no—
843C4—82no—
844C4C7×#38518yescomplemented
845C2—48no—
846C2C2×C7×#38511yescharacteristic
847C2C4×C7×#12111yescharacteristic
848C2C7×#232411yescharacteristic
849C2C7×D4×C4⋊C411yescharacteristic
850C2C7×#234911yescharacteristic
851C2C7×#236611yescharacteristic
852C2C7×#236711yescharacteristic
853C2C7×#240711yescharacteristic
854C2C7×#240811yescharacteristic
855C2C7×#244511yescharacteristic
856C2C7×#244711yescharacteristic
857C2C7×#245211yescharacteristic
858C2C7×#245411yescharacteristic
859C2C7×#253811yescharacteristic
860C2C7×#258011yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C7×#389C2semidirect
5. C2×C7×#385C2semidirect
6. C2×C4×C7×C4⋊C4C2semidirect
7. C7×#1439C2semidirect
8. C7×#1439C2semidirect
9. C7×C4⋊#95C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×C22⋊#95C2semidirect
32. C7×#390C4semidirect
43. #14018C7direct (N × H)
85. C2×C7×C4⋊C4C2×C4semidirect
87. C2×C7×C4⋊C4D4semidirect
101. C2×C7×C22⋊C4C2×C4semidirect
102. C2×C7×C22⋊C4C2×C4semidirect
110. C2×C42×C7C2×C4semidirect
122. C2×#389C2×C7semidirect
123. C2×#385C2×C7semidirect
124. C2×C4×C4⋊C4C2×C7semidirect
125. #1439C2×C7semidirect
126. #1439C2×C7semidirect
127. C4⋊#95C2×C7semidirect
128. C4⋊#95C2×C7semidirect
129. C22⋊#95C2×C7semidirect
152. C2×C7×D4C4⋊C4semidirect
264. #390C4×C7semidirect
391. C2×C4×C7C4×D4semidirect
438. C2×C4⋊C4C2×C4×C7semidirect
440. C2×C4⋊C4C7×D4semidirect
454. C2×C22⋊C4C2×C4×C7semidirect
455. C2×C22⋊C4C2×C4×C7semidirect
463. C2×C42C2×C4×C7semidirect
531. C4×C7#385semidirect
554. C2×D4C7×C4⋊C4semidirect
778. C2×C4C4×C7×D4semidirect
784. C7#14018direct (N × H)
844. C4C7×#385semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C7×D42
C2×C7×#3902
C2×C7×#3892
C2×C7×#3852
C2×C4×C7×C4⋊C42
C7×#14392
C7×C4⋊#952
C7×C22⋊#952
#140187