Finite Group Databasebeta

← C7×#23106 #13200322

Subgroups — C7×#23106 #13200322

Order 1792.

946 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#460C211yesmaximal, characteristic
2C7×#2366C211yesmaximal, characteristic
3C7×#2356C211yesmaximal, characteristic, complemented
4C7×#1973C211yesmaximal, characteristic, complemented
5C7×#1968C211yesmaximal, characteristic, complemented
6C7×#1961C211yesmaximal, characteristic
7C7×#1949C211yesmaximal, characteristic, complemented
8C7×#1926C211yesmaximal, characteristic, complemented
9C7×#1925C211yesmaximal, characteristic, complemented
10C7×#1877C211yesmaximal, characteristic, complemented
11C7×#1877C211yesmaximal, characteristic, complemented
12C7×#1771C211yesmaximal, characteristic, complemented
13C7×#1763C211yesmaximal, characteristic, complemented
14C7×#1762C211yesmaximal, characteristic, complemented
15C4×C7×#102C211yesmaximal, characteristic, complemented
16C22×C7×SD16C2211yescharacteristic
17C22×C7×SD16C2211yescharacteristic
18C2×C7×#127C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4—21no—
21C2×C4×C7×D4C2211yescharacteristic
22C2×C4×C7×D4C2211yescharacteristic
23C7×#460C418yescomplemented
24C2×C7×#107C2211yescharacteristic
25C2×C7×#106C2211yescharacteristic
26C2×C7×C4⋊C8C2211yescharacteristic
27C2×C7×#103C2211yescharacteristic
28C2×C7×#103C2211yescharacteristic
29C2×C7×#102C2211yescharacteristic
30C2×C7×#102C2211yescharacteristic
31C2×C7×#102C2211yescharacteristic
32C2×C7×#102C2211yescharacteristic
33C2×C7×#102C2211yescharacteristic
34C2×C7×#102C2211yescharacteristic
35C2×C7×#97C2211yescharacteristic
36C2×C7×#97C2211yescharacteristic
37C2×C4×C7×C8C2211yescharacteristic
38C7×#391C2211yescharacteristic
39C7×#391C2211yescharacteristic
40C7×#390—21no—
41C7×#390C2211yescharacteristic
42C7×#390C2211yescharacteristic
43C7×#387—21no—
44C7×#387—21no—
45C7×#386—21no—
46C7×#386—21no—
47C7×#383—21no—
48C7×#382C2211yescharacteristic
49C4×C7×C4⋊C4C2211yescharacteristic
50C4×C7×C4⋊C4C2211yescharacteristic
51C4×C7×C4⋊C4C2211yescharacteristic
52C4×C7×C4⋊C4C2211yescharacteristic
53C7×#376—21no—
54C7×#340C2211yescharacteristic
55C7×#340C2211yescharacteristic
56C7×#340C2211yescharacteristic
57C7×#340C2211yescharacteristic
58C7×#336C2211yescharacteristic
59C7×#336C2211yescharacteristic
60#23106C711yesmaximal, characteristic, direct product factor, Sylow
61C22×C7×Q8C2311yescharacteristic
62C22×C7×D4—21no—
63C22×C7×D4—21no—
64C22×C7×D4C2311yescharacteristic
65C22×C7×D4C2311yescharacteristic
66C23×C4×C7—21no—
67C23×C4×C7—21no—
68C2×C7×SD16—41no—
69C2×C7×SD16—41no—
70C2×C7×SD16—41no—
71C2×C7×SD16—41no—
72C2×C7×SD16C2×C414yescomplemented
73C2×C7×SD16C2×C414yescomplemented
74C22×C7×C8C2311yescharacteristic
75C22×C7×C8C2311yescharacteristic
76C22×C7×C8C2311yescharacteristic
77C22×C7×C8C2311yescharacteristic
78C7×#127—22no—
79C7×#127C2×C414yes—
80C4×C7×Q8—22no—
81C4×C7×Q8C2×C414yescomplemented
82C4×C7×D4—22no—
83C4×C7×D4—22no—
84C4×C7×D4—41no—
85C4×C7×D4—41no—
86C4×C7×D4—44no—
87C2×C7×C4⋊C4—21no—
88C2×C7×C4⋊C4D411yescharacteristic
89C2×C7×C4⋊C4D411yescharacteristic
90C2×C7×C4⋊C4C2311yescharacteristic
91C2×C7×C4⋊C4C2311yescharacteristic
92C2×C7×C4⋊C4C2311yescharacteristic
93C2×C7×C4⋊C4C2311yescharacteristic
94C2×C7×C4⋊C4C2311yescharacteristic
95C2×C7×C22⋊C4—21no—
96C2×C7×C22⋊C4—21no—
97C2×C7×C22⋊C4—21no—
98C2×C7×C22⋊C4—21no—
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C42×C7—21no—
102C2×C42×C7—21no—
103C2×C42×C7—21no—
104C2×C42×C7—21no—
105C2×C42×C7C2311yescharacteristic
106C2×C42×C7C2311yescharacteristic
107C2×C42×C7C2311yescharacteristic
108C7×#107—41no—
109C7×#106—41no—
110C7×C4⋊C8C2×C414yescomplemented
111C7×#103—22no—
112C7×#103—22no—
113C7×#102—22no—
114C7×#102—22no—
115C7×#102—41no—
116C7×#102—41no—
117C7×#102C2×C414yescomplemented
118C7×#102C2×C414yescomplemented
119C7×#97—22no—
120C7×#97—41no—
121C4×C7×C8—41no—
122C7×#95—21no—
123C7×#95—21no—
124C7×#95—21no—
125C7×#95—21no—
126C7×#95—21no—
127C7×#95—21no—
128C7×#95—21no—
129C7×#95—21no—
130C7×#95—21no—
131C7×#95D411yescharacteristic
132C7×#95D411yescharacteristic
133C2×#460C2×C711yescharacteristic
134#2366C2×C711yescharacteristic
135#2356C2×C711yescharacteristic, complemented
136#1973C2×C711yescharacteristic, complemented
137#1968C2×C711yescharacteristic, complemented
138#1961C2×C711yescharacteristic
139#1949C2×C711yescharacteristic, complemented
140#1926C2×C711yescharacteristic, complemented
141#1925C2×C711yescharacteristic, complemented
142#1877C2×C711yescharacteristic, complemented
143#1877C2×C711yescharacteristic, complemented
144#1771C2×C711yescharacteristic, complemented
145#1763C2×C711yescharacteristic, complemented
146#1762C2×C711yescharacteristic, complemented
147C4×#102C2×C711yescharacteristic, complemented
148C24×C7—21no—
149C24×C7—21no—
150C2×C7×Q8—21no—
151C2×C7×Q8—21no—
152C2×C7×Q8—21no—
153C2×C7×Q8—21no—
154C2×C7×Q8—21no—
155C2×C7×Q8C22×C412yes—
156C2×C7×D4—24no—
157C2×C7×D4—24no—
158C2×C7×D4—21no—
159C2×C7×D4—21no—
160C2×C7×D4—21no—
161C2×C7×D4—21no—
162C2×C7×D4—21no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—42no—
169C2×C7×D4—42no—
170C2×C7×D4—81no—
171C2×C7×D4—81no—
172C2×C7×D4C22×C412yes—
173C2×C7×D4C22×C412yes—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—42no—
181C22×C4×C7—42no—
182C22×C4×C7—42no—
183C22×C4×C7—42no—
184C22×C4×C7—81no—
185C22×C4×C7—81no—
186C22×C4×C7C2×D411yescharacteristic
187C22×C4×C7C2×D411yescharacteristic
188C22×C4×C7C2×D411yescharacteristic
189C22×C4×C7C2×D411yescharacteristic
190C22×C4×C7C2×D411yescharacteristic
191C22×C4×C7C2×D411yescharacteristic
192C22×C4×C7C2411yescharacteristic
193C7×SD16—44no—
194C7×SD16—44no—
195C2×C7×C8—21no—
196C2×C7×C8—21no—
197C2×C7×C8—21no—
198C2×C7×C8—21no—
199C2×C7×C8—21no—
200C2×C7×C8—21no—
201C2×C7×C8—21no—
202C2×C7×C8—21no—
203C2×C7×C8—21no—
204C2×C7×C8C22×C412yes—
205C2×C7×C8C22×C412yes—
206C2×C7×C8#4112yes—
207C7×C4⋊C4—24no—
208C7×C4⋊C4—22no—
209C7×C4⋊C4—21no—
210C7×C4⋊C4—21no—
211C7×C4⋊C4—21no—
212C7×C4⋊C4—21no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C4⋊C4—41no—
218C7×C4⋊C4C22×C412yes—
219C7×C4⋊C4#4112yes—
220C7×C22⋊C4—42no—
221C7×C22⋊C4—42no—
222C7×C22⋊C4—42no—
223C7×C22⋊C4—42no—
224C7×C22⋊C4—81no—
225C7×C22⋊C4—81no—
226C42×C7—24no—
227C42×C7—21no—
228C42×C7—21no—
229C42×C7—21no—
230C42×C7—21no—
231C42×C7—42no—
232C42×C7—42no—
233C42×C7—42no—
234C42×C7C22×C412yes—
235C42×C7#4112yes—
236C22×SD16C22×C711yescharacteristic
237C22×SD16C22×C711yescharacteristic
238C2×#127C22×C711yescharacteristic
239C2×C4×Q8C22×C711yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C22×C711yescharacteristic
242C2×C4×D4C22×C711yescharacteristic
243#460C4×C718yescomplemented
244C2×#107C22×C711yescharacteristic
245C2×#106C22×C711yescharacteristic
246C2×C4⋊C8C22×C711yescharacteristic
247C2×#103C22×C711yescharacteristic
248C2×#103C22×C711yescharacteristic
249C2×#102C22×C711yescharacteristic
250C2×#102C22×C711yescharacteristic
251C2×#102C22×C711yescharacteristic
252C2×#102C22×C711yescharacteristic
253C2×#102C22×C711yescharacteristic
254C2×#102C22×C711yescharacteristic
255C2×#97C22×C711yescharacteristic
256C2×#97C22×C711yescharacteristic
257C2×C4×C8C22×C711yescharacteristic
258#391C22×C711yescharacteristic
259#391C22×C711yescharacteristic
260#390—21no—
261#390C22×C711yescharacteristic
262#390C22×C711yescharacteristic
263#387—21no—
264#387—21no—
265#386—21no—
266#386—21no—
267#383—21no—
268#382C22×C711yescharacteristic
269C4×C4⋊C4C22×C711yescharacteristic
270C4×C4⋊C4C22×C711yescharacteristic
271C4×C4⋊C4C22×C711yescharacteristic
272C4×C4⋊C4C22×C711yescharacteristic
273#376—21no—
274#340C22×C711yescharacteristic
275#340C22×C711yescharacteristic
276#340C22×C711yescharacteristic
277#340C22×C711yescharacteristic
278#336C22×C711yescharacteristic
279#336C22×C711yescharacteristic
280C23×C7—22no—
281C23×C7—22no—
282C23×C7—41no—
283C23×C7—41no—
284C23×C7—41no—
285C23×C7—41no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7—41no—
289C23×C7—41no—
290C23×C7—41no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—41no—
294C23×C7C22×D411yescharacteristic
295C7×Q8—22no—
296C7×Q8—22no—
297C7×Q8—41no—
298C7×Q8—41no—
299C7×D4—22no—
300C7×D4—22no—
301C7×D4—22no—
302C7×D4—22no—
303C7×D4—48no—
304C7×D4—41no—
305C7×D4—41no—
306C7×D4—41no—
307C7×D4—41no—
308C7×D4—84no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—21no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—22no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—21no—
326C2×C4×C7—21no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—84no—
343C2×C4×C7—84no—
344C2×C4×C7C4×D412yes—
345C2×C4×C7C4×D412yes—
346C2×C4×C7AGL(1,ℤ/8)12yes—
347C2×C4×C7C23×C411yescharacteristic
348C2×C4×C7C2×#4111yescharacteristic
349C2×C4×C7C2×#4111yescharacteristic
350C2×C4×C7C2×#4111yescharacteristic
351C2×C4×C7H(5,𝔽2)11yescharacteristic
352C2×C4×C7H(5,𝔽2)11yescharacteristic
353C7×C8—22no—
354C7×C8—22no—
355C7×C8—22no—
356C7×C8—41no—
357C22×Q8C23×C711yescharacteristic
358C22×D4—21no—
359C22×D4—21no—
360C22×D4C23×C711yescharacteristic
361C22×D4C23×C711yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C2×SD16—41no—
365C2×SD16—41no—
366C2×SD16—41no—
367C2×SD16—41no—
368C2×SD16C2×C4×C714yescomplemented
369C2×SD16C2×C4×C714yescomplemented
370C22×C8C23×C711yescharacteristic
371C22×C8C23×C711yescharacteristic
372C22×C8C23×C711yescharacteristic
373C22×C8C23×C711yescharacteristic
374#127—22no—
375#127C2×C4×C714yes—
376C4×Q8—22no—
377C4×Q8C2×C4×C714yescomplemented
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—41no—
381C4×D4—41no—
382C4×D4—44no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C7×D411yescharacteristic
385C2×C4⋊C4C7×D411yescharacteristic
386C2×C4⋊C4C23×C711yescharacteristic
387C2×C4⋊C4C23×C711yescharacteristic
388C2×C4⋊C4C23×C711yescharacteristic
389C2×C4⋊C4C23×C711yescharacteristic
390C2×C4⋊C4C23×C711yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C23×C711yescharacteristic
402C2×C42C23×C711yescharacteristic
403C2×C42C23×C711yescharacteristic
404#107—41no—
405#106—41no—
406C4⋊C8C2×C4×C714yescomplemented
407#103—22no—
408#103—22no—
409#102—22no—
410#102—22no—
411#102—41no—
412#102—41no—
413#102C2×C4×C714yescomplemented
414#102C2×C4×C714yescomplemented
415#97—22no—
416#97—41no—
417C4×C8—41no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95C7×D411yescharacteristic
428#95C7×D411yescharacteristic
429C22×C7—42no—
430C22×C7—42no—
431C22×C7—42no—
432C22×C7—42no—
433C22×C7—42no—
434C22×C7—42no—
435C22×C7—81no—
436C22×C7—81no—
437C22×C7—81no—
438C22×C7—81no—
439C22×C7—81no—
440C22×C7—81no—
441C22×C7—81no—
442C22×C7—81no—
443C22×C7C2×C4×D411yescharacteristic
444C22×C7#54611yescharacteristic
445C22×C7#55011yescharacteristic
446C22×C7C2×AGL(1,ℤ/8)11yescharacteristic
447C22×C7#57511yescharacteristic
448C22×C7#57711yescharacteristic
449C22×C7#57711yescharacteristic
450C4×C7—22no—
451C4×C7—22no—
452C4×C7—22no—
453C4×C7—42no—
454C4×C7—42no—
455C4×C7—41no—
456C4×C7—42no—
457C4×C7—41no—
458C4×C7—41no—
459C4×C7—81no—
460C4×C7—81no—
461C4×C7—81no—
462C4×C7C4×#4111yescharacteristic
463C4×C7#51811yescharacteristic
464C4×C7#55311yescharacteristic
465C4×C7#55511yescharacteristic
466C24—21no—
467C24—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8C22×C4×C712yes—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—81no—
489C2×D4—81no—
490C2×D4C22×C4×C712yes—
491C2×D4C22×C4×C712yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4C2×C7×D411yescharacteristic
505C22×C4C2×C7×D411yescharacteristic
506C22×C4C2×C7×D411yescharacteristic
507C22×C4C2×C7×D411yescharacteristic
508C22×C4C2×C7×D411yescharacteristic
509C22×C4C2×C7×D411yescharacteristic
510C22×C4C24×C711yescharacteristic
511SD16—44no—
512SD16—44no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8C22×C4×C712yes—
523C2×C8C22×C4×C712yes—
524C2×C8C7×#4112yes—
525C4⋊C4—24no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—41no—
536C4⋊C4C22×C4×C712yes—
537C4⋊C4C7×#4112yes—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C42—24no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—42no—
550C42—42no—
551C42—42no—
552C42C22×C4×C712yes—
553C42C7×#4112yes—
554C2×C7—82no—
555C2×C7—82no—
556C2×C7#236311yescharacteristic
557C2×C7C4×AGL(1,ℤ/8)11yescharacteristic
558C2×C7#294911yescharacteristic
559C2×C7#331011yescharacteristic
560C2×C7#331711yescharacteristic
561C2×C7#339711yescharacteristic
562C2×C7#340111yescharacteristic
563C23—22no—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C22×C7×D411yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—41no—
581Q8—41no—
582D4—22no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—48no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—84no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—84no—
626C2×C4—84no—
627C2×C4C4×C7×D412yes—
628C2×C4C4×C7×D412yes—
629C2×C4C7×AGL(1,ℤ/8)12yes—
630C2×C4C23×C4×C711yescharacteristic
631C2×C4C2×C7×#4111yescharacteristic
632C2×C4C2×C7×#4111yescharacteristic
633C2×C4C2×C7×#4111yescharacteristic
634C2×C4C7×H(5,𝔽2)11yescharacteristic
635C2×C4C7×H(5,𝔽2)11yescharacteristic
636C8—22no—
637C8—22no—
638C8—22no—
639C8—41no—
640C7#2310611yescharacteristic, direct product factor, Sylow
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×C4×C7×D411yescharacteristic
656C22C7×#54611yescharacteristic
657C22C7×#55011yescharacteristic
658C22C2×C7×AGL(1,ℤ/8)11yescharacteristic
659C22C7×#57511yescharacteristic
660C22C7×#57711yescharacteristic
661C22C7×#57711yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—42no—
666C4—41no—
667C4—42no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4C4×C7×#4111yescharacteristic
675C4C7×#51811yescharacteristic
676C4C7×#55311yescharacteristic
677C4C7×#55511yescharacteristic
678C2—82no—
679C2—82no—
680C2C7×#236311yescharacteristic
681C2C4×C7×AGL(1,ℤ/8)11yescharacteristic
682C2C7×#294911yescharacteristic
683C2C7×#331011yescharacteristic
684C2C7×#331711yescharacteristic
685C2C7×#339711yescharacteristic
686C2C7×#340111yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutatorC2×C4C23×C4×C7
Frattini, cosocleC22×C4C24×C7
prime radicalC2×C7×#127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C4×C7×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#2356C2semidirect
4. C7×#1973C2semidirect
5. C7×#1968C2semidirect
7. C7×#1949C2semidirect
8. C7×#1926C2semidirect
9. C7×#1925C2semidirect
10. C7×#1877C2semidirect
11. C7×#1877C2semidirect
12. C7×#1771C2semidirect
13. C7×#1763C2semidirect
14. C7×#1762C2semidirect
15. C4×C7×#102C2semidirect
23. C7×#460C4semidirect
60. #23106C7direct (N × H)
72. C2×C7×SD16C2×C4semidirect
73. C2×C7×SD16C2×C4semidirect
81. C4×C7×Q8C2×C4semidirect
110. C7×C4⋊C8C2×C4semidirect
117. C7×#102C2×C4semidirect
118. C7×#102C2×C4semidirect
135. #2356C2×C7semidirect
136. #1973C2×C7semidirect
137. #1968C2×C7semidirect
139. #1949C2×C7semidirect
140. #1926C2×C7semidirect
141. #1925C2×C7semidirect
142. #1877C2×C7semidirect
143. #1877C2×C7semidirect
144. #1771C2×C7semidirect
145. #1763C2×C7semidirect
146. #1762C2×C7semidirect
147. C4×#102C2×C7semidirect
243. #460C4×C7semidirect
368. C2×SD16C2×C4×C7semidirect
369. C2×SD16C2×C4×C7semidirect
377. C4×Q8C2×C4×C7semidirect
406. C4⋊C8C2×C4×C7semidirect
413. #102C2×C4×C7semidirect
414. #102C2×C4×C7semidirect
640. C7#23106direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4602
C7×#23662
C7×#23562
C7×#19732
C7×#19682
C7×#19612
C7×#19492
C7×#19262
C7×#19252
C7×#18772
C7×#17712
C7×#17632
C7×#17622
C4×C7×#1022
#231067