Finite Group Databasebeta

← C7×#24923 #13202139

Subgroups — C7×#24923 #13202139

Order 1792.

980 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#452C211yesmaximal, characteristic
2C2×C7×#440C211yesmaximal, characteristic, complemented
3C7×#2421C211yesmaximal, characteristic, complemented
4C7×#2339C211yesmaximal, characteristic
5C7×#2097C211yesmaximal, characteristic, complemented
6C7×#2076C211yesmaximal, characteristic, complemented
7C7×#2056C211yesmaximal, characteristic, complemented
8C7×#2035C211yesmaximal, characteristic, complemented
9C7×#1935C211yesmaximal, characteristic, complemented
10C7×#1924C211yesmaximal, characteristic, complemented
11C7×#1878C211yesmaximal, characteristic, complemented
12C7×#1877C211yesmaximal, characteristic, complemented
13C7×#1864C211yesmaximal, characteristic, complemented
14C7×#1804C211yesmaximal, characteristic, complemented
15C7×#1788C211yesmaximal, characteristic
16C22×C7×#41C2211yescharacteristic
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×C4×C7×D4C2211yescharacteristic
23C7×#452—24no—
24C7×#440—24no—
25C2×C7×#107C2211yescharacteristic
26C2×C7×#106C2211yescharacteristic
27C2×C7×C4⋊C8C2211yescharacteristic
28C2×C7×#103C2211yescharacteristic
29C2×C7×#103C2211yescharacteristic
30C2×C7×#103C2211yescharacteristic
31C2×C7×#103C2211yescharacteristic
32C2×C7×#103C2211yescharacteristic
33C2×C7×#102C2211yescharacteristic
34C2×C7×#102C2211yescharacteristic
35C2×C7×#102C2211yescharacteristic
36C2×C7×C22⋊C8C2211yescharacteristic
37C2×C7×C22⋊C8C2211yescharacteristic
38C2×C7×#97C2211yescharacteristic
39C7×#400—21no—
40C7×#397—21no—
41C7×#391C2211yescharacteristic
42C7×#391C2211yescharacteristic
43C7×#391C2211yescharacteristic
44C7×#389C2211yescharacteristic
45C7×#388—21no—
46C7×#387—21no—
47C7×#386—21no—
48C7×#386—21no—
49C7×#382C2211yescharacteristic
50C7×#381—21no—
51C7×#380C2211yescharacteristic
52C7×#380C2211yescharacteristic
53C4×C7×C22⋊C4C2211yescharacteristic
54C2×C7×#95—21no—
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#340C2211yescharacteristic
59C7×#336C2211yescharacteristic
60C7×#336C2211yescharacteristic
61#24923C711yesmaximal, characteristic, direct product factor, Sylow
62C2×C7×#41—22no—
63C2×C7×#41—22no—
64C2×C7×#41—22no—
65C2×C7×#41—22no—
66C2×C7×#41—41no—
67C2×C7×#41—41no—
68C22×C7×Q8C2311yescharacteristic
69C22×C7×Q8C2311yescharacteristic
70C22×C7×D4—21no—
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7—21no—
75C23×C4×C7C2311yescharacteristic
76C2×C7×Q16—22no—
77C2×C7×Q16—22no—
78C2×C7×Q16—41no—
79C2×C7×SD16—22no—
80C2×C7×SD16—22no—
81C2×C7×SD16D414yes—
82C22×C7×C8C2311yescharacteristic
83C22×C7×C8C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C7×C22⋊Q8—22no—
87C7×C22⋊Q8—41no—
88C4×C7×Q8—22no—
89C4×C7×Q8—41no—
90C4×C7×D4—22no—
91C4×C7×D4—22no—
92C4×C7×D4—41no—
93C4×C7×D4—41no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C7×C22⋊C4D411yescharacteristic
108C2×C7×C22⋊C4D411yescharacteristic
109C2×C42×C7—21no—
110C2×C42×C7C2311yescharacteristic
111C2×C42×C7C2311yescharacteristic
112C7×#107—22no—
113C7×#106—41no—
114C7×C4⋊C8—41no—
115C7×#103—22no—
116C7×#103—22no—
117C7×#103—22no—
118C7×#103—41no—
119C7×#103—41no—
120C7×#102—22no—
121C7×#102—22no—
122C7×#102—22no—
123C7×C22⋊C8—22no—
124C7×C22⋊C8—41no—
125C7×#97—22no—
126C7×#95—21no—
127C7×#95—21no—
128C7×#95—21no—
129C7×#95—21no—
130C7×#95—21no—
131C7×#95—21no—
132C7×#95—21no—
133C7×#95—21no—
134C7×#95—21no—
135C7×#95—21no—
136C7×#95—21no—
137C7×#95D411yescharacteristic
138C7×#95D411yescharacteristic
139C2×#452C2×C711yescharacteristic
140C2×#440C2×C711yescharacteristic, complemented
141#2421C2×C711yescharacteristic, complemented
142#2339C2×C711yescharacteristic
143#2097C2×C711yescharacteristic, complemented
144#2076C2×C711yescharacteristic, complemented
145#2056C2×C711yescharacteristic, complemented
146#2035C2×C711yescharacteristic, complemented
147#1935C2×C711yescharacteristic, complemented
148#1924C2×C711yescharacteristic, complemented
149#1878C2×C711yescharacteristic, complemented
150#1877C2×C711yescharacteristic, complemented
151#1864C2×C711yescharacteristic, complemented
152#1804C2×C711yescharacteristic, complemented
153#1788C2×C711yescharacteristic
154C24×C7—21no—
155C24×C7C2×D411yescharacteristic
156C7×#41—44no—
157C7×#41—44no—
158C7×#41—44no—
159C7×#41—44no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8—21no—
170C2×C7×Q8C2×D412yes—
171C2×C7×Q8#4112yes—
172C2×C7×D4—24no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—42no—
177C2×C7×D4—42no—
178C2×C7×D4C2×D412yes—
179C2×C7×D4#4112yes—
180C2×C7×D4#4112yes—
181C22×C4×C7—24no—
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—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—42no—
196C22×C4×C7—42no—
197C22×C4×C7—42no—
198C22×C4×C7—42no—
199C22×C4×C7—42no—
200C22×C4×C7—42no—
201C22×C4×C7—81no—
202C22×C4×C7—81no—
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2411yescharacteristic
209C7×Q16—44no—
210C7×SD16—28no—
211C2×C7×C8—21no—
212C2×C7×C8—21no—
213C2×C7×C8—21no—
214C2×C7×C8—21no—
215C2×C7×C8—21no—
216C2×C7×C8—21no—
217C2×C7×C8—21no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8C2×D412yes—
223C7×C4⋊C4—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—42no—
234C7×C4⋊C4—42no—
235C7×C4⋊C4—42no—
236C7×C22⋊C4—41no—
237C7×C22⋊C4—41no—
238C7×C22⋊C4—42no—
239C7×C22⋊C4—42no—
240C7×C22⋊C4—42no—
241C7×C22⋊C4—42no—
242C7×C22⋊C4—81no—
243C42×C7—21no—
244C42×C7—21no—
245C42×C7—21no—
246C42×C7—21no—
247C42×C7—42no—
248C22×#41C22×C711yescharacteristic
249C22×Q16C22×C711yescharacteristic
250C22×SD16C22×C711yescharacteristic
251C2×C22⋊Q8C22×C711yescharacteristic
252C2×C4×Q8C22×C711yescharacteristic
253C2×C4×D4C22×C711yescharacteristic
254C2×C4×D4C22×C711yescharacteristic
255#452—24no—
256#440—24no—
257C2×#107C22×C711yescharacteristic
258C2×#106C22×C711yescharacteristic
259C2×C4⋊C8C22×C711yescharacteristic
260C2×#103C22×C711yescharacteristic
261C2×#103C22×C711yescharacteristic
262C2×#103C22×C711yescharacteristic
263C2×#103C22×C711yescharacteristic
264C2×#103C22×C711yescharacteristic
265C2×#102C22×C711yescharacteristic
266C2×#102C22×C711yescharacteristic
267C2×#102C22×C711yescharacteristic
268C2×C22⋊C8C22×C711yescharacteristic
269C2×C22⋊C8C22×C711yescharacteristic
270C2×#97C22×C711yescharacteristic
271#400—21no—
272#397—21no—
273#391C22×C711yescharacteristic
274#391C22×C711yescharacteristic
275#391C22×C711yescharacteristic
276#389C22×C711yescharacteristic
277#388—21no—
278#387—21no—
279#386—21no—
280#386—21no—
281#382C22×C711yescharacteristic
282#381—21no—
283#380C22×C711yescharacteristic
284#380C22×C711yescharacteristic
285C4×C22⋊C4C22×C711yescharacteristic
286C2×#95—21no—
287#340C22×C711yescharacteristic
288#340C22×C711yescharacteristic
289#340C22×C711yescharacteristic
290#340C22×C711yescharacteristic
291#336C22×C711yescharacteristic
292#336C22×C711yescharacteristic
293C23×C7—22no—
294C23×C7—22no—
295C23×C7—22no—
296C23×C7—21no—
297C23×C7—21no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—41no—
304C23×C7—41no—
305C23×C7—41no—
306C23×C7—41no—
307C23×C7C22×D411yescharacteristic
308C7×Q8—22no—
309C7×Q8—22no—
310C7×Q8—22no—
311C7×Q8—22no—
312C7×Q8—41no—
313C7×Q8—41no—
314C7×Q8—41no—
315C7×Q8—41no—
316C7×D4—22no—
317C7×D4—22no—
318C7×D4—22no—
319C7×D4—48no—
320C7×D4#12314yes—
321C2×C4×C7—21no—
322C2×C4×C7—22no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—22no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—21no—
331C2×C4×C7—21no—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—21no—
338C2×C4×C7—48no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—41no—
353C2×C4×C7—41no—
354C2×C4×C7—41no—
355C2×C4×C7—41no—
356C2×C4×C7—41no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—84no—
363C2×C4×C7—84no—
364C2×C4×C7C22×D411yescharacteristic
365C2×C4×C7C2×#4111yescharacteristic
366C2×C4×C7C2×#4111yescharacteristic
367C2×C4×C7C2×#4111yescharacteristic
368C2×C4×C7H(5,𝔽2)11yescharacteristic
369C2×C4×C7H(5,𝔽2)11yescharacteristic
370C7×C8—22no—
371C7×C8—41no—
372C7×C8—41no—
373C7×C8—41no—
374C2×#41—22no—
375C2×#41—22no—
376C2×#41—22no—
377C2×#41—22no—
378C2×#41—41no—
379C2×#41—41no—
380C22×Q8C23×C711yescharacteristic
381C22×Q8C23×C711yescharacteristic
382C22×D4—21no—
383C22×D4C23×C711yescharacteristic
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—21no—
387C23×C4C23×C711yescharacteristic
388C2×Q16—22no—
389C2×Q16—22no—
390C2×Q16—41no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16C7×D414yes—
394C22×C8C23×C711yescharacteristic
395C22×C8C23×C711yescharacteristic
396C22×C8C23×C711yescharacteristic
397C22×C8C23×C711yescharacteristic
398C22⋊Q8—22no—
399C22⋊Q8—41no—
400C4×Q8—22no—
401C4×Q8—41no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—41no—
405C4×D4—41no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4C23×C711yescharacteristic
410C2×C4⋊C4C23×C711yescharacteristic
411C2×C4⋊C4C23×C711yescharacteristic
412C2×C4⋊C4C23×C711yescharacteristic
413C2×C4⋊C4C23×C711yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4C7×D411yescharacteristic
420C2×C22⋊C4C7×D411yescharacteristic
421C2×C42—21no—
422C2×C42C23×C711yescharacteristic
423C2×C42C23×C711yescharacteristic
424#107—22no—
425#106—41no—
426C4⋊C8—41no—
427#103—22no—
428#103—22no—
429#103—22no—
430#103—41no—
431#103—41no—
432#102—22no—
433#102—22no—
434#102—22no—
435C22⋊C8—22no—
436C22⋊C8—41no—
437#97—22no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95C7×D411yescharacteristic
450#95C7×D411yescharacteristic
451C22×C7—24no—
452C22×C7—42no—
453C22×C7—42no—
454C22×C7—42no—
455C22×C7—42no—
456C22×C7—42no—
457C22×C7—42no—
458C22×C7—41no—
459C22×C7—41no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7#52511yescharacteristic
466C22×C7D4211yescharacteristic
467C22×C7#54611yescharacteristic
468C22×C7#57511yescharacteristic
469C22×C7#57511yescharacteristic
470C22×C7#57711yescharacteristic
471C22×C7#57811yescharacteristic
472C4×C7—41no—
473C4×C7—42no—
474C4×C7—42no—
475C4×C7—41no—
476C4×C7—41no—
477C4×C7—41no—
478C4×C7—41no—
479C4×C7—81no—
480C4×C7—81no—
481C4×C7—81no—
482C4×C7—81no—
483C4×C7—81no—
484C4×C7C2×#12311yescharacteristic
485C4×C7#53811yescharacteristic
486C4×C7#54611yescharacteristic
487C4×C7#55111yescharacteristic
488C24—21no—
489C24C2×C7×D411yescharacteristic
490#41—44no—
491#41—44no—
492#41—44no—
493#41—44no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C2×C7×D412yes—
505C2×Q8C7×#4112yes—
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4C2×C7×D412yes—
513C2×D4C7×#4112yes—
514C2×D4C7×#4112yes—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4C2×C7×D411yescharacteristic
538C22×C4C2×C7×D411yescharacteristic
539C22×C4C2×C7×D411yescharacteristic
540C22×C4C2×C7×D411yescharacteristic
541C22×C4C2×C7×D411yescharacteristic
542C22×C4C24×C711yescharacteristic
543Q16—44no—
544SD16—28no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8C2×C7×D412yes—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—42no—
582C2×C7—44no—
583C2×C7—81no—
584C2×C7#241811yescharacteristic
585C2×C7#311111yescharacteristic
586C2×C7#312011yescharacteristic
587C2×C7#326911yescharacteristic
588C2×C7#327511yescharacteristic
589C2×C7#331111yescharacteristic
590C2×C7#331511yescharacteristic
591C23—22no—
592C23—22no—
593C23—22no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×C7×D411yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614D4—22no—
615D4—22no—
616D4—22no—
617D4—48no—
618D4C7×#12314yes—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—48no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4C22×C7×D411yescharacteristic
663C2×C4C2×C7×#4111yescharacteristic
664C2×C4C2×C7×#4111yescharacteristic
665C2×C4C2×C7×#4111yescharacteristic
666C2×C4C7×H(5,𝔽2)11yescharacteristic
667C2×C4C7×H(5,𝔽2)11yescharacteristic
668C8—22no—
669C8—41no—
670C8—41no—
671C8—41no—
672C7#2492311yescharacteristic, direct product factor, Sylow
673C22—24no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22C7×#52511yescharacteristic
688C22C7×D4211yescharacteristic
689C22C7×#54611yescharacteristic
690C22C7×#57511yescharacteristic
691C22C7×#57511yescharacteristic
692C22C7×#57711yescharacteristic
693C22C7×#57811yescharacteristic
694C4—41no—
695C4—42no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4C2×C7×#12311yescharacteristic
707C4C7×#53811yescharacteristic
708C4C7×#54611yescharacteristic
709C4C7×#55111yescharacteristic
710C2—44no—
711C2—81no—
712C2C7×#241811yescharacteristic
713C2C7×#311111yescharacteristic
714C2C7×#312011yescharacteristic
715C2C7×#326911yescharacteristic
716C2C7×#327511yescharacteristic
717C2C7×#331111yescharacteristic
718C2C7×#331511yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC22×C7×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C4×C7×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#440C2semidirect
3. C7×#2421C2semidirect
5. C7×#2097C2semidirect
6. C7×#2076C2semidirect
7. C7×#2056C2semidirect
8. C7×#2035C2semidirect
9. C7×#1935C2semidirect
10. C7×#1924C2semidirect
11. C7×#1878C2semidirect
12. C7×#1877C2semidirect
13. C7×#1864C2semidirect
14. C7×#1804C2semidirect
61. #24923C7direct (N × H)
140. C2×#440C2×C7semidirect
141. #2421C2×C7semidirect
143. #2097C2×C7semidirect
144. #2076C2×C7semidirect
145. #2056C2×C7semidirect
146. #2035C2×C7semidirect
147. #1935C2×C7semidirect
148. #1924C2×C7semidirect
149. #1878C2×C7semidirect
150. #1877C2×C7semidirect
151. #1864C2×C7semidirect
152. #1804C2×C7semidirect
672. C7#24923direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4522
C2×C7×#4402
C7×#24212
C7×#23392
C7×#20972
C7×#20762
C7×#20562
C7×#20352
C7×#19352
C7×#19242
C7×#18782
C7×#18772
C7×#18642
C7×#18042
C7×#17882
#249237