Finite Group Databasebeta

← C2×C7×#3242 #13238072

Subgroups — C2×C7×#3242 #13238072

Order 1792.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#544C211yesmaximal, characteristic
2C2×C7×#541C211yesmaximal, characteristic
3C7×#3242C2116yesmaximal, direct product factor
4C2×C7×#501C211yesmaximal, characteristic, complemented
5C2×C7×#499C211yesmaximal, characteristic, complemented
6C2×C7×#491C211yesmaximal, characteristic, complemented
7C2×C7×#487C211yesmaximal, characteristic, complemented
8C2×C7×#484C211yesmaximal, characteristic
9C2×C7×#485C211yesmaximal, characteristic
10C2×C7×#485C211yesmaximal, characteristic
11C2×C7×#483C211yesmaximal, characteristic
12C2×C7×#479C211yesmaximal, characteristic, complemented
13C2×C7×#479C211yesmaximal, characteristic, complemented
14C2×C7×#477C211yesmaximal, characteristic, complemented
15C2×C7×#475C211yesmaximal, characteristic, complemented
16C2×C7×#433C211yesmaximal, characteristic
17C7×#544—24no—
18C7×#544C2218yes—
19C7×#541—24no—
20C7×#541C2218yes—
21C2×C7×C4⋊Q8—21no—
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C7×C4⋊Q8C2211yescharacteristic
24C2×C7×C4⋊Q8C2211yescharacteristic
25C2×C7×#126—21no—
26C2×C7×#126—21no—
27C2×C7×#125—21no—
28C2×C7×#125—21no—
29C2×C7×#125—21no—
30C2×C7×#125C2211yescharacteristic
31C2×C7×#125C2211yescharacteristic
32C2×C7×#125C2211yescharacteristic
33C2×C7×C22⋊Q8—21no—
34C2×C7×C22⋊Q8—21no—
35C2×C7×C22⋊Q8C2211yescharacteristic
36C2×C7×C22⋊Q8C2211yescharacteristic
37C2×C4×C7×Q8C2211yescharacteristic
38C2×C4×C7×Q8C2211yescharacteristic
39C2×C7×#117C2211yescharacteristic
40C2×C7×#117C2211yescharacteristic
41C22×C7×C4⋊C4C2211yescharacteristic
42C7×#501C2218yescomplemented
43C7×#499C2218yescomplemented
44C7×#491C2218yescomplemented
45C7×#487C2218yescomplemented
46C7×#485C2218yes—
47C7×#485C2218yes—
48C7×#484C2218yes—
49C7×#483C2218yes—
50C7×#479C2218yescomplemented
51C7×#479C2218yescomplemented
52C7×#477C2218yescomplemented
53C7×#475C2218yescomplemented
54C7×#433C2218yes—
55C2×C7×#107C2211yescharacteristic
56C2×C7×#107C2211yescharacteristic
57C2×C7×#107C2211yescharacteristic
58C2×C7×#107C2211yescharacteristic
59C2×C7×#106C2211yescharacteristic
60C2×C7×#106C2211yescharacteristic
61C2×C7×#106C2211yescharacteristic
62C2×C7×#106C2211yescharacteristic
63C2×C7×C4⋊C8C2211yescharacteristic
64C2×C7×C4⋊C8C2211yescharacteristic
65C2×C7×#103C2211yescharacteristic
66C2×C7×#103C2211yescharacteristic
67C2×C7×#103C2211yescharacteristic
68C2×C7×#103C2211yescharacteristic
69C2×C7×#103C2211yescharacteristic
70C2×C7×#103C2211yescharacteristic
71C2×C7×#103C2211yescharacteristic
72C2×C7×#103C2211yescharacteristic
73C2×C7×C22⋊C8C2211yescharacteristic
74C2×C7×C22⋊C8C2211yescharacteristic
75C2×C7×#97C2211yescharacteristic
76C2×C4×C7×C8C2211yescharacteristic
77C2×#3242C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—21no—
80C22×C7×Q8C2311yescharacteristic
81C22×C7×Q8C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7C2311yescharacteristic
84C22×C7×C8C2311yescharacteristic
85C22×C7×C8C2311yescharacteristic
86C22×C7×C8C2311yescharacteristic
87C22×C7×C8C2311yescharacteristic
88C7×C4⋊Q8—28no—
89C7×C4⋊Q8—22no—
90C7×C4⋊Q8—22no—
91C7×C4⋊Q8—22no—
92C7×C4⋊Q8C2314yes—
93C7×C4⋊Q8C2314yes—
94C7×C4⋊Q8C2314yes—
95C7×#126—28no—
96C7×#126—28no—
97C7×#125—28no—
98C7×#125—28no—
99C7×#125—28no—
100C7×#125—22no—
101C7×#125—22no—
102C7×#125—22no—
103C7×#125C2314yes—
104C7×#125C2314yes—
105C7×#125C2314yes—
106C7×C22⋊Q8—22no—
107C7×C22⋊Q8—22no—
108C7×C22⋊Q8—28no—
109C7×C22⋊Q8—28no—
110C7×C22⋊Q8C2314yes—
111C7×C22⋊Q8C2314yes—
112C4×C7×Q8—22no—
113C4×C7×Q8—22no—
114C4×C7×Q8C2314yes—
115C4×C7×Q8C2314yes—
116C7×#117—22no—
117C7×#117D414yes—
118C7×#117C2314yes—
119C7×#117C2314yes—
120C2×C7×C4⋊C4—21no—
121C2×C7×C4⋊C4—22no—
122C2×C7×C4⋊C4—21no—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—21no—
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—21no—
128C2×C7×C4⋊C4—21no—
129C2×C7×C4⋊C4—21no—
130C2×C7×C4⋊C4—21no—
131C2×C7×C4⋊C4—21no—
132C2×C7×C4⋊C4—21no—
133C2×C7×C4⋊C4—21no—
134C2×C7×C4⋊C4—21no—
135C2×C7×C4⋊C4—21no—
136C2×C7×C4⋊C4D411yescharacteristic
137C2×C7×C4⋊C4D411yescharacteristic
138C2×C7×C4⋊C4C2314yes—
139C2×C7×C4⋊C4C2311yescharacteristic
140C2×C7×C4⋊C4C2311yescharacteristic
141C2×C7×C4⋊C4C2311yescharacteristic
142C2×C7×C4⋊C4C2311yescharacteristic
143C2×C7×C4⋊C4C2311yescharacteristic
144C2×C7×C4⋊C4C2311yescharacteristic
145C2×C7×C22⋊C4—21no—
146C2×C7×C22⋊C4—21no—
147C2×C7×C22⋊C4—21no—
148C2×C7×C22⋊C4D411yescharacteristic
149C2×C7×C22⋊C4D411yescharacteristic
150C2×C42×C7—21no—
151C2×C42×C7—21no—
152C2×C42×C7—21no—
153C2×C42×C7C2311yescharacteristic
154C2×C42×C7C2311yescharacteristic
155C7×#107C2314yes—
156C7×#107C2314yes—
157C7×#107C2314yes—
158C7×#107C2314yes—
159C7×#106C2314yes—
160C7×#106C2314yes—
161C7×#106C2314yes—
162C7×#106C2314yes—
163C7×C4⋊C8C2314yes—
164C7×C4⋊C8C2314yes—
165C7×#103C2314yes—
166C7×#103C2314yes—
167C7×#103C2314yes—
168C7×#103C2314yes—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172C7×#103C2314yes—
173C7×C22⋊C8C2314yes—
174C7×C22⋊C8C2314yes—
175C7×#97C2314yes—
176C4×C7×C8C2314yes—
177C2×#544C2×C711yescharacteristic
178C2×#541C2×C711yescharacteristic
179#3242C2×C7116yesdirect product factor
180C2×#501C2×C711yescharacteristic, complemented
181C2×#499C2×C711yescharacteristic, complemented
182C2×#491C2×C711yescharacteristic, complemented
183C2×#487C2×C711yescharacteristic, complemented
184C2×#484C2×C711yescharacteristic
185C2×#485C2×C711yescharacteristic
186C2×#485C2×C711yescharacteristic
187C2×#483C2×C711yescharacteristic
188C2×#479C2×C711yescharacteristic, complemented
189C2×#479C2×C711yescharacteristic, complemented
190C2×#477C2×C711yescharacteristic, complemented
191C2×#475C2×C711yescharacteristic, complemented
192C2×#433C2×C711yescharacteristic
193C24×C7C2×D411yescharacteristic
194C2×C7×Q8—21no—
195C2×C7×Q8—21no—
196C2×C7×Q8—24no—
197C2×C7×Q8—24no—
198C2×C7×Q8—22no—
199C2×C7×Q8—22no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8—82no—
203C2×C7×Q8—82no—
204C2×C7×Q8C2412yes—
205C2×C7×Q8C2412yes—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—24no—
217C22×C4×C7—82no—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2412yes—
225C22×C4×C7C2411yescharacteristic
226C2×C7×C8—22no—
227C2×C7×C8—22no—
228C2×C7×C8—22no—
229C2×C7×C8—22no—
230C2×C7×C8C2412yes—
231C2×C7×C8C2412yes—
232C2×C7×C8C2412yes—
233C2×C7×C8C2412yes—
234C7×C4⋊C4—24no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4—24no—
238C7×C4⋊C4—24no—
239C7×C4⋊C4—24no—
240C7×C4⋊C4—24no—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—24no—
244C7×C4⋊C4—24no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—21no—
255C7×C4⋊C4C2×D414yes—
256C7×C4⋊C4C2×D414yes—
257C7×C4⋊C4C2412yes—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C4⋊C4C2412yes—
263C7×C22⋊C4—24no—
264C7×C22⋊C4—24no—
265C7×C22⋊C4—24no—
266C7×C22⋊C4C2×D414yes—
267C7×C22⋊C4C2×D414yes—
268C42×C7—24no—
269C42×C7—24no—
270C42×C7—24no—
271C42×C7C2×D412yes—
272C42×C7C2×D412yes—
273C42×C7C2412yes—
274C42×C7C2412yes—
275#544—24no—
276#544C22×C718yes—
277#541—24no—
278#541C22×C718yes—
279C2×C4⋊Q8—21no—
280C2×C4⋊Q8C22×C711yescharacteristic
281C2×C4⋊Q8C22×C711yescharacteristic
282C2×C4⋊Q8C22×C711yescharacteristic
283C2×#126—21no—
284C2×#126—21no—
285C2×#125—21no—
286C2×#125—21no—
287C2×#125—21no—
288C2×#125C22×C711yescharacteristic
289C2×#125C22×C711yescharacteristic
290C2×#125C22×C711yescharacteristic
291C2×C22⋊Q8—21no—
292C2×C22⋊Q8—21no—
293C2×C22⋊Q8C22×C711yescharacteristic
294C2×C22⋊Q8C22×C711yescharacteristic
295C2×C4×Q8C22×C711yescharacteristic
296C2×C4×Q8C22×C711yescharacteristic
297C2×#117C22×C711yescharacteristic
298C2×#117C22×C711yescharacteristic
299C22×C4⋊C4C22×C711yescharacteristic
300#501C22×C718yescomplemented
301#499C22×C718yescomplemented
302#491C22×C718yescomplemented
303#487C22×C718yescomplemented
304#485C22×C718yes—
305#485C22×C718yes—
306#484C22×C718yes—
307#483C22×C718yes—
308#479C22×C718yescomplemented
309#479C22×C718yescomplemented
310#477C22×C718yescomplemented
311#475C22×C718yescomplemented
312#433C22×C718yes—
313C2×#107C22×C711yescharacteristic
314C2×#107C22×C711yescharacteristic
315C2×#107C22×C711yescharacteristic
316C2×#107C22×C711yescharacteristic
317C2×#106C22×C711yescharacteristic
318C2×#106C22×C711yescharacteristic
319C2×#106C22×C711yescharacteristic
320C2×#106C22×C711yescharacteristic
321C2×C4⋊C8C22×C711yescharacteristic
322C2×C4⋊C8C22×C711yescharacteristic
323C2×#103C22×C711yescharacteristic
324C2×#103C22×C711yescharacteristic
325C2×#103C22×C711yescharacteristic
326C2×#103C22×C711yescharacteristic
327C2×#103C22×C711yescharacteristic
328C2×#103C22×C711yescharacteristic
329C2×#103C22×C711yescharacteristic
330C2×#103C22×C711yescharacteristic
331C2×C22⋊C8C22×C711yescharacteristic
332C2×C22⋊C8C22×C711yescharacteristic
333C2×#97C22×C711yescharacteristic
334C2×C4×C8C22×C711yescharacteristic
335C23×C7—22no—
336C23×C7—22no—
337C23×C7—22no—
338C23×C7C22×D412yes—
339C23×C7C22×D411yescharacteristic
340C7×Q8—22no—
341C7×Q8—22no—
342C7×Q8—22no—
343C7×Q8—22no—
344C7×Q8—42no—
345C7×Q8—42no—
346C7×Q8—84no—
347C7×Q8—84no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—22no—
352C2×C4×C7—22no—
353C2×C4×C7—24no—
354C2×C4×C7—22no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
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—84no—
373C2×C4×C7C22×D412yes—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D411yescharacteristic
379C2×C4×C72−1+412yes—
380C2×C4×C72−1+412yes—
381C2×C4×C7C2511yescharacteristic
382C7×C8—22no—
383C7×C8—22no—
384C7×C8—22no—
385C7×C8—22no—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8C23×C711yescharacteristic
389C22×Q8C23×C711yescharacteristic
390C23×C4—21no—
391C23×C4C23×C711yescharacteristic
392C22×C8C23×C711yescharacteristic
393C22×C8C23×C711yescharacteristic
394C22×C8C23×C711yescharacteristic
395C22×C8C23×C711yescharacteristic
396C4⋊Q8—28no—
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399C4⋊Q8—22no—
400C4⋊Q8C23×C714yes—
401C4⋊Q8C23×C714yes—
402C4⋊Q8C23×C714yes—
403#126—28no—
404#126—28no—
405#125—28no—
406#125—28no—
407#125—28no—
408#125—22no—
409#125—22no—
410#125—22no—
411#125C23×C714yes—
412#125C23×C714yes—
413#125C23×C714yes—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—28no—
417C22⋊Q8—28no—
418C22⋊Q8C23×C714yes—
419C22⋊Q8C23×C714yes—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8C23×C714yes—
423C4×Q8C23×C714yes—
424#117—22no—
425#117C7×D414yes—
426#117C23×C714yes—
427#117C23×C714yes—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4C7×D411yescharacteristic
445C2×C4⋊C4C7×D411yescharacteristic
446C2×C4⋊C4C23×C711yescharacteristic
447C2×C4⋊C4C23×C711yescharacteristic
448C2×C4⋊C4C23×C714yes—
449C2×C4⋊C4C23×C711yescharacteristic
450C2×C4⋊C4C23×C711yescharacteristic
451C2×C4⋊C4C23×C711yescharacteristic
452C2×C4⋊C4C23×C711yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4C7×D411yescharacteristic
457C2×C22⋊C4C7×D411yescharacteristic
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C23×C711yescharacteristic
462C2×C42C23×C711yescharacteristic
463#107C23×C714yes—
464#107C23×C714yes—
465#107C23×C714yes—
466#107C23×C714yes—
467#106C23×C714yes—
468#106C23×C714yes—
469#106C23×C714yes—
470#106C23×C714yes—
471C4⋊C8C23×C714yes—
472C4⋊C8C23×C714yes—
473#103C23×C714yes—
474#103C23×C714yes—
475#103C23×C714yes—
476#103C23×C714yes—
477#103C23×C714yes—
478#103C23×C714yes—
479#103C23×C714yes—
480#103C23×C714yes—
481C22⋊C8C23×C714yes—
482C22⋊C8C23×C714yes—
483#97C23×C714yes—
484C4×C8C23×C714yes—
485C22×C7—22no—
486C22×C7—22no—
487C22×C7—22no—
488C22×C7—44no—
489C22×C7#53612yes—
490C22×C7#57712yes—
491C22×C7#57812yes—
492C22×C7C23×D411yescharacteristic
493C4×C7—22no—
494C4×C7—22no—
495C4×C7—22no—
496C4×C7—22no—
497C4×C7—22no—
498C4×C7—42no—
499C4×C7—42no—
500C4×C7—42no—
501C4×C7—42no—
502C4×C7—42no—
503C4×C7—42no—
504C4×C7—42no—
505C4×C7—42no—
506C4×C7#53612yes—
507C4×C7C2×2−1+411yescharacteristic
508C4×C7C2×2−1+411yescharacteristic
509C24C2×C7×D411yescharacteristic
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—24no—
513C2×Q8—24no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—82no—
519C2×Q8—82no—
520C2×Q8C24×C712yes—
521C2×Q8C24×C712yes—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—82no—
534C22×C4C2×C7×D411yescharacteristic
535C22×C4C2×C7×D411yescharacteristic
536C22×C4C2×C7×D411yescharacteristic
537C22×C4C2×C7×D411yescharacteristic
538C22×C4C2×C7×D411yescharacteristic
539C22×C4C2×C7×D412yes—
540C22×C4C24×C712yes—
541C22×C4C24×C711yescharacteristic
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8C24×C712yes—
547C2×C8C24×C712yes—
548C2×C8C24×C712yes—
549C2×C8C24×C712yes—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4C2×C7×D414yes—
572C4⋊C4C2×C7×D414yes—
573C4⋊C4C24×C712yes—
574C4⋊C4C24×C712yes—
575C4⋊C4C24×C712yes—
576C4⋊C4C24×C712yes—
577C4⋊C4C24×C712yes—
578C4⋊C4C24×C712yes—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4C2×C7×D414yes—
583C22⋊C4C2×C7×D414yes—
584C42—24no—
585C42—24no—
586C42—24no—
587C42C2×C7×D412yes—
588C42C2×C7×D412yes—
589C42C24×C712yes—
590C42C24×C712yes—
591C2×C7—42no—
592C2×C7#324214yesdirect product factor
593C2×C7C2×#53611yescharacteristic
594C2×C7C2×#57711yescharacteristic
595C2×C7C2×#57811yescharacteristic
596C23—22no—
597C23—22no—
598C23—22no—
599C23C22×C7×D412yes—
600C23C22×C7×D411yescharacteristic
601Q8—22no—
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—42no—
606Q8—42no—
607Q8—84no—
608Q8—84no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—84no—
634C2×C4C22×C7×D412yes—
635C2×C4C22×C7×D412yes—
636C2×C4C22×C7×D412yes—
637C2×C4C22×C7×D412yes—
638C2×C4C22×C7×D412yes—
639C2×C4C22×C7×D411yescharacteristic
640C2×C4C7×2−1+412yes—
641C2×C4C7×2−1+412yes—
642C2×C4C25×C711yescharacteristic
643C8—22no—
644C8—22no—
645C8—22no—
646C8—22no—
647C7C2×#324211yescharacteristic, direct product factor, Sylow
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22C7×#53612yes—
653C22C7×#57712yes—
654C22C7×#57812yes—
655C22C23×C7×D411yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4C7×#53612yes—
670C4C2×C7×2−1+411yescharacteristic
671C4C2×C7×2−1+411yescharacteristic
672C2—42no—
673C2C7×#324214yesdirect product factor
674C2C2×C7×#53611yescharacteristic
675C2C2×C7×#57711yescharacteristic
676C2C2×C7×#57811yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC24×C7C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C7×#3242C2direct (N × H)
4. C2×C7×#501C2semidirect
5. C2×C7×#499C2semidirect
6. C2×C7×#491C2semidirect
7. C2×C7×#487C2semidirect
12. C2×C7×#479C2semidirect
13. C2×C7×#479C2semidirect
14. C2×C7×#477C2semidirect
15. C2×C7×#475C2semidirect
42. C7×#501C22semidirect
43. C7×#499C22semidirect
44. C7×#491C22semidirect
45. C7×#487C22semidirect
50. C7×#479C22semidirect
51. C7×#479C22semidirect
52. C7×#477C22semidirect
53. C7×#475C22semidirect
77. C2×#3242C7direct (N × H)
179. #3242C2×C7direct (N × H)
180. C2×#501C2×C7semidirect
181. C2×#499C2×C7semidirect
182. C2×#491C2×C7semidirect
183. C2×#487C2×C7semidirect
188. C2×#479C2×C7semidirect
189. C2×#479C2×C7semidirect
190. C2×#477C2×C7semidirect
191. C2×#475C2×C7semidirect
300. #501C22×C7semidirect
301. #499C22×C7semidirect
302. #491C22×C7semidirect
303. #487C22×C7semidirect
308. #479C22×C7semidirect
309. #479C22×C7semidirect
310. #477C22×C7semidirect
311. #475C22×C7semidirect
592. C2×C7#3242direct (N × H)
647. C7C2×#3242direct (N × H)
673. C2C7×#3242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5442
C2×C7×#5412
C7×#32422
C2×C7×#5012
C2×C7×#4992
C2×C7×#4912
C2×C7×#4872
C2×C7×#4842
C2×C7×#4852
C2×C7×#4832
C2×C7×#4792
C2×C7×#4772
C2×C7×#4752
C2×C7×#4332
C2×#32427