Finite Group Databasebeta

← C2×C7×#3241 #13238071

Subgroups — C2×C7×#3241 #13238071

Order 1792.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#544C211yesmaximal, characteristic, complemented
2C2×C7×#540C211yesmaximal, characteristic
3C7×#3241C2116yesmaximal, direct product factor
4C2×C7×#501C211yesmaximal, characteristic, complemented
5C2×C7×#499C211yesmaximal, characteristic, complemented
6C2×C7×#490C211yesmaximal, characteristic, complemented
7C2×C7×#486C211yesmaximal, characteristic, complemented
8C2×C7×#481C211yesmaximal, characteristic, complemented
9C2×C7×#482C211yesmaximal, characteristic, complemented
10C2×C7×#482C211yesmaximal, characteristic, complemented
11C2×C7×#480C211yesmaximal, characteristic, complemented
12C2×C7×#478C211yesmaximal, characteristic, complemented
13C2×C7×#478C211yesmaximal, characteristic, complemented
14C2×C7×#476C211yesmaximal, characteristic, complemented
15C2×C7×#474C211yesmaximal, characteristic, complemented
16C2×C7×#433C211yesmaximal, characteristic, complemented
17C7×#544—24no—
18C7×#544C2218yescomplemented
19C7×#540—24no—
20C7×#540C2218yes—
21C2×C7×C4⋊Q8—21no—
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C7×C4⋊Q8C2211yescharacteristic
24C2×C7×#127C2211yescharacteristic
25C2×C7×#125—21no—
26C2×C7×#125C2211yescharacteristic
27C2×C7×#125C2211yescharacteristic
28C2×C7×#125C2211yescharacteristic
29C2×C7×#123—21no—
30C2×C7×#123—21no—
31C2×C7×C22⋊Q8—21no—
32C2×C7×C22⋊Q8—21no—
33C2×C7×#121—21no—
34C2×C7×#121—21no—
35C2×C7×#121C2211yescharacteristic
36C2×C7×#121C2211yescharacteristic
37C2×C4×C7×D4C2211yescharacteristic
38C2×C4×C7×D4C2211yescharacteristic
39C2×C7×#117C2211yescharacteristic
40C2×C7×#117C2211yescharacteristic
41C22×C7×C4⋊C4C2211yescharacteristic
42C7×#501C2218yescomplemented
43C7×#499C2218yescomplemented
44C7×#490C2218yescomplemented
45C7×#486C2218yescomplemented
46C7×#482C2218yescomplemented
47C7×#482C2218yescomplemented
48C7×#481C2218yescomplemented
49C7×#480C2218yescomplemented
50C7×#478C2218yescomplemented
51C7×#478C2218yescomplemented
52C7×#476C2218yescomplemented
53C7×#474C2218yescomplemented
54C7×#433C2218yescomplemented
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×#102C2211yescharacteristic
66C2×C7×#102C2211yescharacteristic
67C2×C7×#102C2211yescharacteristic
68C2×C7×#102C2211yescharacteristic
69C2×C7×#102C2211yescharacteristic
70C2×C7×#102C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×C22⋊C8C2211yescharacteristic
74C2×C7×C22⋊C8C2211yescharacteristic
75C2×C7×#97C2211yescharacteristic
76C2×C4×C7×C8C2211yescharacteristic
77C2×#3241C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—21no—
80C22×C7×D4—21no—
81C22×C7×D4—21no—
82C22×C7×D4—21no—
83C22×C7×D4—21no—
84C22×C7×D4C2311yescharacteristic
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C23×C4×C7—21no—
89C23×C4×C7C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×C4⋊Q8—28no—
95C7×C4⋊Q8—22no—
96C7×C4⋊Q8—22no—
97C7×C4⋊Q8C2314yes—
98C7×C4⋊Q8C2314yes—
99C7×#127—22no—
100C7×#127C2314yes—
101C7×#125—28no—
102C7×#125—22no—
103C7×#125—22no—
104C7×#125—22no—
105C7×#125C2314yes—
106C7×#125C2314yes—
107C7×#125C2314yes—
108C7×#123—28no—
109C7×#123—28no—
110C7×C22⋊Q8—28no—
111C7×C22⋊Q8—28no—
112C7×#121—22no—
113C7×#121—22no—
114C7×#121—28no—
115C7×#121—28no—
116C7×#121C2314yes—
117C7×#121C2314yes—
118C4×C7×D4—22no—
119C4×C7×D4—22no—
120C4×C7×D4C2314yes—
121C4×C7×D4C2314yes—
122C7×#117—22no—
123C7×#117D414yes—
124C7×#117C2314yes—
125C7×#117C2314yes—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—22no—
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⋊C4—21no—
149C2×C7×C22⋊C4—21no—
150C2×C7×C22⋊C4D411yescharacteristic
151C2×C7×C22⋊C4D411yescharacteristic
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×#102C2314yes—
166C7×#102C2314yes—
167C7×#102C2314yes—
168C7×#102C2314yes—
169C7×#102C2314yes—
170C7×#102C2314yes—
171C7×#102C2314yes—
172C7×#102C2314yes—
173C7×C22⋊C8C2314yes—
174C7×C22⋊C8C2314yes—
175C7×#97C2314yes—
176C4×C7×C8C2314yes—
177C2×#544C2×C711yescharacteristic, complemented
178C2×#540C2×C711yescharacteristic
179#3241C2×C7116yesdirect product factor
180C2×#501C2×C711yescharacteristic, complemented
181C2×#499C2×C711yescharacteristic, complemented
182C2×#490C2×C711yescharacteristic, complemented
183C2×#486C2×C711yescharacteristic, complemented
184C2×#481C2×C711yescharacteristic, complemented
185C2×#482C2×C711yescharacteristic, complemented
186C2×#482C2×C711yescharacteristic, complemented
187C2×#480C2×C711yescharacteristic, complemented
188C2×#478C2×C711yescharacteristic, complemented
189C2×#478C2×C711yescharacteristic, complemented
190C2×#476C2×C711yescharacteristic, complemented
191C2×#474C2×C711yescharacteristic, complemented
192C2×#433C2×C711yescharacteristic, complemented
193C24×C7—21no—
194C24×C7—21no—
195C24×C7C2×D411yescharacteristic
196C2×C7×Q8—24no—
197C2×C7×Q8—24no—
198C2×C7×Q8—82no—
199C2×C7×Q8—82no—
200C2×C7×D4—24no—
201C2×C7×D4—24no—
202C2×C7×D4—21no—
203C2×C7×D4—21no—
204C2×C7×D4—24no—
205C2×C7×D4—24no—
206C2×C7×D4—22no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4—82no—
211C2×C7×D4—82no—
212C2×C7×D4—82no—
213C2×C7×D4—82no—
214C2×C7×D4C2412yes—
215C2×C7×D4C2412yes—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—24no—
225C22×C4×C7—24no—
226C22×C4×C7—24no—
227C22×C4×C7—82no—
228C22×C4×C7—82no—
229C22×C4×C7—82no—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2412yes—
237C22×C4×C7C2411yescharacteristic
238C2×C7×C8—22no—
239C2×C7×C8—22no—
240C2×C7×C8—22no—
241C2×C7×C8—22no—
242C2×C7×C8C2412yes—
243C2×C7×C8C2412yes—
244C2×C7×C8C2412yes—
245C2×C7×C8C2412yes—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—24no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—24no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4C2×D414yes—
262C7×C4⋊C4C2×D414yes—
263C7×C4⋊C4C2412yes—
264C7×C4⋊C4C2412yes—
265C7×C4⋊C4C2412yes—
266C7×C4⋊C4C2412yes—
267C7×C4⋊C4C2412yes—
268C7×C4⋊C4C2412yes—
269C7×C22⋊C4—24no—
270C7×C22⋊C4—24no—
271C7×C22⋊C4—24no—
272C7×C22⋊C4—24no—
273C7×C22⋊C4—24no—
274C7×C22⋊C4C2×D414yes—
275C7×C22⋊C4C2×D414yes—
276C42×C7—24no—
277C42×C7C2×D412yes—
278C42×C7C2×D412yes—
279C42×C7C2412yes—
280C42×C7C2412yes—
281#544—24no—
282#544C22×C718yescomplemented
283#540—24no—
284#540C22×C718yes—
285C2×C4⋊Q8—21no—
286C2×C4⋊Q8C22×C711yescharacteristic
287C2×C4⋊Q8C22×C711yescharacteristic
288C2×#127C22×C711yescharacteristic
289C2×#125—21no—
290C2×#125C22×C711yescharacteristic
291C2×#125C22×C711yescharacteristic
292C2×#125C22×C711yescharacteristic
293C2×#123—21no—
294C2×#123—21no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8—21no—
297C2×#121—21no—
298C2×#121—21no—
299C2×#121C22×C711yescharacteristic
300C2×#121C22×C711yescharacteristic
301C2×C4×D4C22×C711yescharacteristic
302C2×C4×D4C22×C711yescharacteristic
303C2×#117C22×C711yescharacteristic
304C2×#117C22×C711yescharacteristic
305C22×C4⋊C4C22×C711yescharacteristic
306#501C22×C718yescomplemented
307#499C22×C718yescomplemented
308#490C22×C718yescomplemented
309#486C22×C718yescomplemented
310#482C22×C718yescomplemented
311#482C22×C718yescomplemented
312#481C22×C718yescomplemented
313#480C22×C718yescomplemented
314#478C22×C718yescomplemented
315#478C22×C718yescomplemented
316#476C22×C718yescomplemented
317#474C22×C718yescomplemented
318#433C22×C718yescomplemented
319C2×#107C22×C711yescharacteristic
320C2×#107C22×C711yescharacteristic
321C2×#107C22×C711yescharacteristic
322C2×#107C22×C711yescharacteristic
323C2×#106C22×C711yescharacteristic
324C2×#106C22×C711yescharacteristic
325C2×#106C22×C711yescharacteristic
326C2×#106C22×C711yescharacteristic
327C2×C4⋊C8C22×C711yescharacteristic
328C2×C4⋊C8C22×C711yescharacteristic
329C2×#102C22×C711yescharacteristic
330C2×#102C22×C711yescharacteristic
331C2×#102C22×C711yescharacteristic
332C2×#102C22×C711yescharacteristic
333C2×#102C22×C711yescharacteristic
334C2×#102C22×C711yescharacteristic
335C2×#102C22×C711yescharacteristic
336C2×#102C22×C711yescharacteristic
337C2×C22⋊C8C22×C711yescharacteristic
338C2×C22⋊C8C22×C711yescharacteristic
339C2×#97C22×C711yescharacteristic
340C2×C4×C8C22×C711yescharacteristic
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—42no—
347C23×C7—42no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7C22×D412yes—
353C23×C7C22×D411yescharacteristic
354C7×Q8—84no—
355C7×Q8—84no—
356C7×D4—22no—
357C7×D4—22no—
358C7×D4—22no—
359C7×D4—22no—
360C7×D4—42no—
361C7×D4—42no—
362C7×D4—84no—
363C7×D4—84no—
364C7×D4—84no—
365C7×D4—84no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—24no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
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—84no—
387C2×C4×C7—84no—
388C2×C4×C7—84no—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D411yescharacteristic
395C2×C4×C72−1+412yes—
396C2×C4×C72−1+412yes—
397C2×C4×C7C2511yescharacteristic
398C7×C8—22no—
399C7×C8—22no—
400C7×C8—22no—
401C7×C8—22no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×D4—21no—
405C22×D4—21no—
406C22×D4—21no—
407C22×D4—21no—
408C22×D4C23×C711yescharacteristic
409C22×D4C23×C711yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—21no—
413C23×C4C23×C711yescharacteristic
414C22×C8C23×C711yescharacteristic
415C22×C8C23×C711yescharacteristic
416C22×C8C23×C711yescharacteristic
417C22×C8C23×C711yescharacteristic
418C4⋊Q8—28no—
419C4⋊Q8—22no—
420C4⋊Q8—22no—
421C4⋊Q8C23×C714yes—
422C4⋊Q8C23×C714yes—
423#127—22no—
424#127C23×C714yes—
425#125—28no—
426#125—22no—
427#125—22no—
428#125—22no—
429#125C23×C714yes—
430#125C23×C714yes—
431#125C23×C714yes—
432#123—28no—
433#123—28no—
434C22⋊Q8—28no—
435C22⋊Q8—28no—
436#121—22no—
437#121—22no—
438#121—28no—
439#121—28no—
440#121C23×C714yes—
441#121C23×C714yes—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4C23×C714yes—
445C4×D4C23×C714yes—
446#117—22no—
447#117C7×D414yes—
448#117C23×C714yes—
449#117C23×C714yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4C7×D411yescharacteristic
461C2×C4⋊C4C7×D411yescharacteristic
462C2×C4⋊C4C23×C711yescharacteristic
463C2×C4⋊C4C23×C711yescharacteristic
464C2×C4⋊C4C23×C714yes—
465C2×C4⋊C4C23×C711yescharacteristic
466C2×C4⋊C4C23×C711yescharacteristic
467C2×C4⋊C4C23×C711yescharacteristic
468C2×C4⋊C4C23×C711yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4C7×D411yescharacteristic
475C2×C22⋊C4C7×D411yescharacteristic
476C2×C42—21no—
477C2×C42C23×C711yescharacteristic
478C2×C42C23×C711yescharacteristic
479#107C23×C714yes—
480#107C23×C714yes—
481#107C23×C714yes—
482#107C23×C714yes—
483#106C23×C714yes—
484#106C23×C714yes—
485#106C23×C714yes—
486#106C23×C714yes—
487C4⋊C8C23×C714yes—
488C4⋊C8C23×C714yes—
489#102C23×C714yes—
490#102C23×C714yes—
491#102C23×C714yes—
492#102C23×C714yes—
493#102C23×C714yes—
494#102C23×C714yes—
495#102C23×C714yes—
496#102C23×C714yes—
497C22⋊C8C23×C714yes—
498C22⋊C8C23×C714yes—
499#97C23×C714yes—
500C4×C8C23×C714yes—
501C22×C7—22no—
502C22×C7—22no—
503C22×C7—22no—
504C22×C7—44no—
505C22×C7—42no—
506C22×C7—42no—
507C22×C7—42no—
508C22×C7—42no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—84no—
512C22×C7—84no—
513C22×C7#53612yes—
514C22×C7#57612yes—
515C22×C7#57712yes—
516C22×C7C23×D411yescharacteristic
517C4×C7—22no—
518C4×C7—22no—
519C4×C7—22no—
520C4×C7—22no—
521C4×C7—22no—
522C4×C7—42no—
523C4×C7—42no—
524C4×C7—42no—
525C4×C7—42no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7#53612yes—
529C4×C7C2×2−1+411yescharacteristic
530C4×C7C2×2−1+411yescharacteristic
531C24—21no—
532C24—21no—
533C24C2×C7×D411yescharacteristic
534C2×Q8—24no—
535C2×Q8—24no—
536C2×Q8—82no—
537C2×Q8—82no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—82no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4C24×C712yes—
553C2×D4C24×C712yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—82no—
566C22×C4—82no—
567C22×C4—82no—
568C22×C4C2×C7×D411yescharacteristic
569C22×C4C2×C7×D411yescharacteristic
570C22×C4C2×C7×D411yescharacteristic
571C22×C4C2×C7×D411yescharacteristic
572C22×C4C2×C7×D411yescharacteristic
573C22×C4C2×C7×D412yes—
574C22×C4C24×C712yes—
575C22×C4C24×C711yescharacteristic
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8C24×C712yes—
581C2×C8C24×C712yes—
582C2×C8C24×C712yes—
583C2×C8C24×C712yes—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4C2×C7×D414yes—
600C4⋊C4C2×C7×D414yes—
601C4⋊C4C24×C712yes—
602C4⋊C4C24×C712yes—
603C4⋊C4C24×C712yes—
604C4⋊C4C24×C712yes—
605C4⋊C4C24×C712yes—
606C4⋊C4C24×C712yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4C2×C7×D414yes—
613C22⋊C4C2×C7×D414yes—
614C42—24no—
615C42C2×C7×D412yes—
616C42C2×C7×D412yes—
617C42C24×C712yes—
618C42C24×C712yes—
619C2×C7—42no—
620C2×C7—82no—
621C2×C7—82no—
622C2×C7#324114yesdirect product factor
623C2×C7C2×#53611yescharacteristic
624C2×C7C2×#57611yescharacteristic
625C2×C7C2×#57711yescharacteristic
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23C22×C7×D412yes—
638C23C22×C7×D411yescharacteristic
639Q8—84no—
640Q8—84no—
641D4—22no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—42no—
646D4—42no—
647D4—84no—
648D4—84no—
649D4—84no—
650D4—84no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—84no—
672C2×C4—84no—
673C2×C4—84no—
674C2×C4C22×C7×D412yes—
675C2×C4C22×C7×D412yes—
676C2×C4C22×C7×D412yes—
677C2×C4C22×C7×D412yes—
678C2×C4C22×C7×D412yes—
679C2×C4C22×C7×D411yescharacteristic
680C2×C4C7×2−1+412yes—
681C2×C4C7×2−1+412yes—
682C2×C4C25×C711yescharacteristic
683C8—22no—
684C8—22no—
685C8—22no—
686C8—22no—
687C7C2×#324111yescharacteristic, direct product factor, Sylow
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—84no—
699C22—84no—
700C22C7×#53612yes—
701C22C7×#57612yes—
702C22C7×#57712yes—
703C22C23×C7×D411yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4C7×#53612yes—
716C4C2×C7×2−1+411yescharacteristic
717C4C2×C7×2−1+411yescharacteristic
718C2—42no—
719C2—82no—
720C2—82no—
721C2C7×#324114yesdirect product factor
722C2C2×C7×#53611yescharacteristic
723C2C2×C7×#57611yescharacteristic
724C2C2×C7×#57711yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC2×C7×#540C2
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
1. C2×C7×#544C2semidirect
3. C7×#3241C2direct (N × H)
4. C2×C7×#501C2semidirect
5. C2×C7×#499C2semidirect
6. C2×C7×#490C2semidirect
7. C2×C7×#486C2semidirect
8. C2×C7×#481C2semidirect
9. C2×C7×#482C2semidirect
10. C2×C7×#482C2semidirect
11. C2×C7×#480C2semidirect
12. C2×C7×#478C2semidirect
13. C2×C7×#478C2semidirect
14. C2×C7×#476C2semidirect
15. C2×C7×#474C2semidirect
16. C2×C7×#433C2semidirect
18. C7×#544C22semidirect
42. C7×#501C22semidirect
43. C7×#499C22semidirect
44. C7×#490C22semidirect
45. C7×#486C22semidirect
46. C7×#482C22semidirect
47. C7×#482C22semidirect
48. C7×#481C22semidirect
49. C7×#480C22semidirect
50. C7×#478C22semidirect
51. C7×#478C22semidirect
52. C7×#476C22semidirect
53. C7×#474C22semidirect
54. C7×#433C22semidirect
77. C2×#3241C7direct (N × H)
177. C2×#544C2×C7semidirect
179. #3241C2×C7direct (N × H)
180. C2×#501C2×C7semidirect
181. C2×#499C2×C7semidirect
182. C2×#490C2×C7semidirect
183. C2×#486C2×C7semidirect
184. C2×#481C2×C7semidirect
185. C2×#482C2×C7semidirect
186. C2×#482C2×C7semidirect
187. C2×#480C2×C7semidirect
188. C2×#478C2×C7semidirect
189. C2×#478C2×C7semidirect
190. C2×#476C2×C7semidirect
191. C2×#474C2×C7semidirect
192. C2×#433C2×C7semidirect
282. #544C22×C7semidirect
306. #501C22×C7semidirect
307. #499C22×C7semidirect
308. #490C22×C7semidirect
309. #486C22×C7semidirect
310. #482C22×C7semidirect
311. #482C22×C7semidirect
312. #481C22×C7semidirect
313. #480C22×C7semidirect
314. #478C22×C7semidirect
315. #478C22×C7semidirect
316. #476C22×C7semidirect
317. #474C22×C7semidirect
318. #433C22×C7semidirect
622. C2×C7#3241direct (N × H)
687. C7C2×#3241direct (N × H)
721. C2C7×#3241direct (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×#5402
C7×#32412
C2×C7×#5012
C2×C7×#4992
C2×C7×#4902
C2×C7×#4862
C2×C7×#4812
C2×C7×#4822
C2×C7×#4802
C2×C7×#4782
C2×C7×#4762
C2×C7×#4742
C2×C7×#4332
C2×#32417