Finite Group Databasebeta

← C7×#14022 #13191238

Subgroups — C7×#14022 #13191238

Order 1792.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#390C211yesmaximal, characteristic
2C2×C7×#390C211yesmaximal, characteristic
3C2×C7×#390C211yesmaximal, characteristic
4C2×C7×#388C212yesmaximal, complemented
5C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
7C7×#1440C212yesmaximal, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1437C212yesmaximal, complemented
10C7×C4⋊#95C211yesmaximal, characteristic, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2212yes—
26C22×C42×C7C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C7×#390—24no—
29C7×#390—24no—
30C7×#390C418yescomplemented
31C7×#388—28no—
32C4×C7×C4⋊C4—24no—
33C4×C7×C4⋊C4—24no—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2212yes—
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2212yes—
41#14022C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2312yes—
43C22×C7×D4—22no—
44C22×C7×D4—22no—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—22no—
48C22×C7×D4—22no—
49C22×C7×D4C2×C414yes—
50C23×C4×C7C2312yes—
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2312yes—
53C23×C4×C7C2311yescharacteristic
54C23×C4×C7C2312yes—
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—22no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—22no—
65C2×C7×C4⋊C4—22no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—22no—
68C2×C7×C4⋊C4—22no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—22no—
71C2×C7×C4⋊C4—22no—
72C2×C7×C4⋊C4C2×C414yes—
73C2×C7×C4⋊C4D414yes—
74C2×C7×C4⋊C4D414yescomplemented
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—42no—
86C2×C7×C22⋊C4—42no—
87C2×C7×C22⋊C4—42no—
88C2×C7×C22⋊C4—42no—
89C2×C7×C22⋊C4—42no—
90C2×C7×C22⋊C4—42no—
91C2×C7×C22⋊C4C2×C418yes—
92C2×C7×C22⋊C4C2×C418yes—
93C2×C42×C7—22no—
94C2×C42×C7—22no—
95C2×C42×C7—22no—
96C2×C42×C7—22no—
97C2×C42×C7—24no—
98C2×C42×C7—22no—
99C2×C42×C7—24no—
100C2×C42×C7—22no—
101C2×C42×C7—22no—
102C2×C42×C7—42no—
103C2×C42×C7C2×C414yes—
104C2×C42×C7D414yes—
105C7×#95—24no—
106C7×#95—22no—
107C7×#95—22no—
108C7×#95—24no—
109C7×#95—24no—
110C7×#95—42no—
111C7×#95—42no—
112C2×#390C2×C711yescharacteristic
113C2×#390C2×C711yescharacteristic
114C2×#390C2×C711yescharacteristic
115C2×#388C2×C712yescomplemented
116C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
117C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
118#1440C2×C712yescomplemented
119#1439C2×C712yescomplemented
120#1437C2×C712yescomplemented
121C4⋊#95C2×C711yescharacteristic, complemented
122C4⋊#95C2×C711yescharacteristic, complemented
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7—22no—
132C24×C7—22no—
133C24×C7—22no—
134C24×C7—22no—
135C24×C7—22no—
136C24×C7—22no—
137C24×C7C22×C414yes—
138C24×C7C2411yescharacteristic
139C2×C7×D4—28no—
140C2×C7×D4—28no—
141C2×C7×D4—28no—
142C2×C7×D4—44no—
143C2×C7×D4—44no—
144C2×C7×D4—44no—
145C2×C7×D4—44no—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—21no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—21no—
153C22×C4×C7—21no—
154C22×C4×C7—21no—
155C22×C4×C7—21no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—21no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7C22×C412yes—
198C22×C4×C7C22×C414yes—
199C22×C4×C7C22×C412yes—
200C22×C4×C7C22×C412yes—
201C22×C4×C7C2×D412yes—
202C22×C4×C7C2×D414yes—
203C22×C4×C7C2×D412yes—
204C22×C4×C7C2×D412yes—
205C22×C4×C7C2×D412yes—
206C22×C4×C7C2×D412yes—
207C22×C4×C7C2×D412yes—
208C22×C4×C7C2×D412yes—
209C22×C4×C7#4112yes—
210C22×C4×C7#4112yes—
211C22×C4×C7#4112yes—
212C22×C4×C7#4112yes—
213C22×C4×C7#4112yes—
214C22×C4×C7#4112yes—
215C22×C4×C7#4112yes—
216C7×C4⋊C4—28no—
217C7×C4⋊C4—28no—
218C7×C4⋊C4—28no—
219C7×C4⋊C4—28no—
220C7×C4⋊C4—44no—
221C7×C22⋊C4—216no—
222C7×C22⋊C4—48no—
223C7×C22⋊C4—48no—
224C7×C22⋊C4—48no—
225C7×C22⋊C4—48no—
226C7×C22⋊C4—48no—
227C42×C7—28no—
228C42×C7—28no—
229C42×C7—48no—
230C42×C7—44no—
231C23×D4C22×C711yescharacteristic
232C22×C4⋊C4C22×C711yescharacteristic
233C22×C4⋊C4C22×C711yescharacteristic
234C22×C4⋊C4C22×C711yescharacteristic
235C22×C4⋊C4C22×C711yescharacteristic
236C22×C4⋊C4C22×C711yescharacteristic
237C22×C22⋊C4C22×C712yes—
238C22×C22⋊C4C22×C712yes—
239C22×C22⋊C4C22×C712yes—
240C22×C22⋊C4C22×C712yes—
241C22×C22⋊C4C22×C712yes—
242C22×C22⋊C4C22×C712yes—
243C22×C42C22×C711yescharacteristic
244C22×C42C22×C712yes—
245C22×C42C22×C711yescharacteristic
246C22×C42C22×C711yescharacteristic
247#390—24no—
248#390—24no—
249#390C4×C718yescomplemented
250#388—28no—
251C4×C4⋊C4—24no—
252C4×C4⋊C4—24no—
253C2×#95C22×C712yes—
254C2×#95C22×C712yes—
255C2×#95C22×C711yescharacteristic
256C2×#95C22×C712yes—
257C2×#95C22×C711yescharacteristic
258C2×#95C22×C712yes—
259C2×#95C22×C712yes—
260C23×C7—24no—
261C23×C7—24no—
262C23×C7—24no—
263C23×C7—24no—
264C23×C7—24no—
265C23×C7—24no—
266C23×C7—24no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7—42no—
278C23×C7—42no—
279C23×C7—42no—
280C23×C7—42no—
281C23×C7—42no—
282C23×C7—42no—
283C23×C7—42no—
284C23×C7—42no—
285C23×C7—42no—
286C23×C7—42no—
287C23×C7—42no—
288C23×C7—42no—
289C23×C7—42no—
290C23×C7—42no—
291C23×C7—42no—
292C23×C7—42no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7C23×C411yescharacteristic
296C23×C7C22×D411yescharacteristic
297C23×C7C22×D411yescharacteristic
298C23×C7C22×D411yescharacteristic
299C23×C7C2×#4111yescharacteristic
300C23×C7C2×#4111yescharacteristic
301C23×C7C2×#4111yescharacteristic
302C23×C7C2×#4111yescharacteristic
303C23×C7C2×#4111yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C23×C7C2×#4111yescharacteristic
306C23×C7H(5,𝔽2)11yescharacteristic
307C23×C7H(5,𝔽2)11yescharacteristic
308C23×C7H(5,𝔽2)11yescharacteristic
309C23×C72−1+411yescharacteristic
310C7×D4—416no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—22no—
319C2×C4×C7—22no—
320C2×C4×C7—22no—
321C2×C4×C7—22no—
322C2×C4×C7—22no—
323C2×C4×C7—22no—
324C2×C4×C7—24no—
325C2×C4×C7—24no—
326C2×C4×C7—22no—
327C2×C4×C7—24no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
330C2×C4×C7—22no—
331C2×C4×C7—24no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—24no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—24no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—42no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—42no—
350C2×C4×C7—41no—
351C2×C4×C7—42no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—42no—
355C2×C4×C7—42no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—42no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7#11714yes—
373C2×C4×C7C4×D414yes—
374C2×C4×C7C4×D414yes—
375C2×C4×C7C4×D414yes—
376C2×C4×C7#12114yes—
377C2×C4×C7#12114yes—
378C2×C4×C7#12314yes—
379C2×C4×C7#12414yes—
380C2×C4×C7#12614yes—
381C25C23×C712yes—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4C2×C4×C714yes—
389C23×C4C23×C712yes—
390C23×C4C23×C712yes—
391C23×C4C23×C711yescharacteristic
392C23×C4C23×C711yescharacteristic
393C23×C4C23×C712yes—
394C23×C4C23×C711yescharacteristic
395C23×C4C23×C711yescharacteristic
396C23×C4C23×C711yescharacteristic
397C23×C4C23×C711yescharacteristic
398C23×C4C23×C711yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4C2×C4×C714yes—
412C2×C4⋊C4C7×D414yes—
413C2×C4⋊C4C7×D414yescomplemented
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—42no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4C2×C4×C718yes—
431C2×C22⋊C4C2×C4×C718yes—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—24no—
437C2×C42—22no—
438C2×C42—24no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—42no—
442C2×C42C2×C4×C714yes—
443C2×C42C7×D414yes—
444#95—24no—
445#95—22no—
446#95—22no—
447#95—24no—
448#95—24no—
449#95—42no—
450#95—42no—
451C22×C7—44no—
452C22×C7—44no—
453C22×C7—44no—
454C22×C7—44no—
455C22×C7—44no—
456C22×C7—44no—
457C22×C7—44no—
458C22×C7—82no—
459C22×C7—82no—
460C22×C7—82no—
461C22×C7—82no—
462C22×C7—82no—
463C22×C7—82no—
464C22×C7—82no—
465C22×C7—82no—
466C22×C7C2×#11711yescharacteristic
467C22×C7C2×C4×D411yescharacteristic
468C22×C7C2×C4×D411yescharacteristic
469C22×C7C2×C4×D411yescharacteristic
470C22×C7C4×#4111yescharacteristic
471C22×C7#51811yescharacteristic
472C22×C7#52011yescharacteristic
473C22×C7C2×#12111yescharacteristic
474C22×C7C2×#12111yescharacteristic
475C22×C7C2×#12311yescharacteristic
476C22×C7#52511yescharacteristic
477C22×C7C2×#12411yescharacteristic
478C22×C7C2×#12611yescharacteristic
479C22×C7#52911yescharacteristic
480C22×C7#53211yescharacteristic
481C22×C7#53511yescharacteristic
482C22×C7#53711yescharacteristic
483C22×C7#54011yescharacteristic
484C22×C7#54211yescharacteristic
485C22×C7D4211yescharacteristic
486C22×C7#54611yescharacteristic
487C22×C7#54711yescharacteristic
488C22×C7#54811yescharacteristic
489C22×C7#55011yescharacteristic
490C22×C7#55011yescharacteristic
491C22×C7#55011yescharacteristic
492C22×C7#55311yescharacteristic
493C22×C7#55311yescharacteristic
494C22×C7#55511yescharacteristic
495C22×C7#55611yescharacteristic
496C22×C7#55611yescharacteristic
497C22×C7#55911yescharacteristic
498C22×C7#55911yescharacteristic
499C22×C7#55911yescharacteristic
500C22×C7#55911yescharacteristic
501C4×C7—24no—
502C4×C7—24no—
503C4×C7—42no—
504C4×C7—44no—
505C4×C7—42no—
506C4×C7—42no—
507C4×C7—42no—
508C4×C7—44no—
509C4×C7—82no—
510C4×C7#38818yescomplemented
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24C22×C4×C714yes—
526C24C24×C711yescharacteristic
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4C22×C4×C712yes—
586C22×C4C22×C4×C714yes—
587C22×C4C22×C4×C712yes—
588C22×C4C22×C4×C712yes—
589C22×C4C2×C7×D412yes—
590C22×C4C2×C7×D414yes—
591C22×C4C2×C7×D412yes—
592C22×C4C2×C7×D412yes—
593C22×C4C2×C7×D412yes—
594C22×C4C2×C7×D412yes—
595C22×C4C2×C7×D412yes—
596C22×C4C2×C7×D412yes—
597C22×C4C7×#4112yes—
598C22×C4C7×#4112yes—
599C22×C4C7×#4112yes—
600C22×C4C7×#4112yes—
601C22×C4C7×#4112yes—
602C22×C4C7×#4112yes—
603C22×C4C7×#4112yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—44no—
609C22⋊C4—216no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C42—28no—
616C42—28no—
617C42—48no—
618C42—44no—
619C2×C7—84no—
620C2×C7C2×#38811yescharacteristic
621C2×C7C4×#12111yescharacteristic
622C2×C7#232411yescharacteristic
623C2×C7#235411yescharacteristic
624C2×C7#235711yescharacteristic
625C2×C7#236611yescharacteristic
626C2×C7#236711yescharacteristic
627C2×C7#241411yescharacteristic
628C2×C7#241611yescharacteristic
629C2×C7#244511yescharacteristic
630C2×C7#244811yescharacteristic
631C2×C7#251211yescharacteristic
632C2×C7#251311yescharacteristic
633C2×C7#254811yescharacteristic
634C2×C7#259211yescharacteristic
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23C23×C4×C711yescharacteristic
671C23C22×C7×D411yescharacteristic
672C23C22×C7×D411yescharacteristic
673C23C22×C7×D411yescharacteristic
674C23C2×C7×#4111yescharacteristic
675C23C2×C7×#4111yescharacteristic
676C23C2×C7×#4111yescharacteristic
677C23C2×C7×#4111yescharacteristic
678C23C2×C7×#4111yescharacteristic
679C23C2×C7×#4111yescharacteristic
680C23C2×C7×#4111yescharacteristic
681C23C7×H(5,𝔽2)11yescharacteristic
682C23C7×H(5,𝔽2)11yescharacteristic
683C23C7×H(5,𝔽2)11yescharacteristic
684C23C7×2−1+411yescharacteristic
685D4—416no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4C7×#11714yes—
748C2×C4C4×C7×D414yes—
749C2×C4C4×C7×D414yes—
750C2×C4C4×C7×D414yes—
751C2×C4C7×#12114yes—
752C2×C4C7×#12114yes—
753C2×C4C7×#12314yes—
754C2×C4C7×#12414yes—
755C2×C4C7×#12614yes—
756C7#1402211yescharacteristic, direct product factor, Sylow
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C2×C7×#11711yescharacteristic
773C22C2×C4×C7×D411yescharacteristic
774C22C2×C4×C7×D411yescharacteristic
775C22C2×C4×C7×D411yescharacteristic
776C22C4×C7×#4111yescharacteristic
777C22C7×#51811yescharacteristic
778C22C7×#52011yescharacteristic
779C22C2×C7×#12111yescharacteristic
780C22C2×C7×#12111yescharacteristic
781C22C2×C7×#12311yescharacteristic
782C22C7×#52511yescharacteristic
783C22C2×C7×#12411yescharacteristic
784C22C2×C7×#12611yescharacteristic
785C22C7×#52911yescharacteristic
786C22C7×#53211yescharacteristic
787C22C7×#53511yescharacteristic
788C22C7×#53711yescharacteristic
789C22C7×#54011yescharacteristic
790C22C7×#54211yescharacteristic
791C22C7×D4211yescharacteristic
792C22C7×#54611yescharacteristic
793C22C7×#54711yescharacteristic
794C22C7×#54811yescharacteristic
795C22C7×#55011yescharacteristic
796C22C7×#55011yescharacteristic
797C22C7×#55011yescharacteristic
798C22C7×#55311yescharacteristic
799C22C7×#55311yescharacteristic
800C22C7×#55511yescharacteristic
801C22C7×#55611yescharacteristic
802C22C7×#55611yescharacteristic
803C22C7×#55911yescharacteristic
804C22C7×#55911yescharacteristic
805C22C7×#55911yescharacteristic
806C22C7×#55911yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—44no—
813C4—42no—
814C4—44no—
815C4—82no—
816C4C7×#38818yescomplemented
817C2—84no—
818C2C2×C7×#38811yescharacteristic
819C2C4×C7×#12111yescharacteristic
820C2C7×#232411yescharacteristic
821C2C7×#235411yescharacteristic
822C2C7×#235711yescharacteristic
823C2C7×#236611yescharacteristic
824C2C7×#236711yescharacteristic
825C2C7×#241411yescharacteristic
826C2C7×#241611yescharacteristic
827C2C7×#244511yescharacteristic
828C2C7×#244811yescharacteristic
829C2C7×#251211yescharacteristic
830C2C7×#251311yescharacteristic
831C2C7×#254811yescharacteristic
832C2C7×#259211yescharacteristic
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×#388C2semidirect
5. C2×C4×C7×C4⋊C4C2semidirect
6. C2×C4×C7×C4⋊C4C2semidirect
7. C7×#1440C2semidirect
8. C7×#1439C2semidirect
9. C7×#1437C2semidirect
10. C7×C4⋊#95C2semidirect
11. C7×C4⋊#95C2semidirect
30. C7×#390C4semidirect
41. #14022C7direct (N × H)
74. C2×C7×C4⋊C4D4semidirect
115. C2×#388C2×C7semidirect
116. C2×C4×C4⋊C4C2×C7semidirect
117. C2×C4×C4⋊C4C2×C7semidirect
118. #1440C2×C7semidirect
119. #1439C2×C7semidirect
120. #1437C2×C7semidirect
121. C4⋊#95C2×C7semidirect
122. C4⋊#95C2×C7semidirect
249. #390C4×C7semidirect
413. C2×C4⋊C4C7×D4semidirect
510. C4×C7#388semidirect
756. C7#14022direct (N × H)
816. C4C7×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3902
C2×C7×#3882
C2×C4×C7×C4⋊C42
C7×#14402
C7×#14392
C7×#14372
C7×C4⋊#952
#140227