Finite Group Databasebeta

← C2×C7×#3377 #13238531

Subgroups — C2×C7×#3377 #13238531

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#557C211yesmaximal, characteristic, complemented
2C2×C7×#556C211yesmaximal, characteristic
3C7×#3377C2116yesmaximal, direct product factor
4C2×C7×#491C211yesmaximal, characteristic, complemented
5C2×C7×#489C211yesmaximal, characteristic
6C2×C7×#488C211yesmaximal, characteristic
7C2×C7×#479C211yesmaximal, characteristic, complemented
8C2×C7×#477C211yesmaximal, characteristic, complemented
9C2×C7×#478C211yesmaximal, characteristic
10C2×C7×#464C211yesmaximal, characteristic
11C2×C7×#464C211yesmaximal, characteristic
12C2×C7×#462C211yesmaximal, characteristic, complemented
13C2×C7×#446C211yesmaximal, characteristic, complemented
14C2×C7×#441C211yesmaximal, characteristic, complemented
15C2×C7×#440C211yesmaximal, characteristic
16C2×C4×C7×Q16C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C7×#557—24no—
21C7×#557C2218yescomplemented
22C7×#556—24no—
23C7×#556C2218yes—
24C2×C7×C4⋊Q8—21no—
25C2×C7×C4⋊Q8C2211yescharacteristic
26C2×C7×C4⋊Q8C2211yescharacteristic
27C2×C7×#126—21no—
28C2×C7×#126—21no—
29C2×C7×#125—21no—
30C2×C7×#125—21no—
31C2×C7×#125C2211yescharacteristic
32C2×C7×#125C2211yescharacteristic
33C2×C7×#124C2211yescharacteristic
34C2×C7×#124C2211yescharacteristic
35C2×C7×C22⋊Q8—21no—
36C2×C4×C7×Q8—21no—
37C2×C4×C7×Q8C2211yescharacteristic
38C2×C4×C7×Q8C2211yescharacteristic
39C2×C4×C7×Q8C2211yescharacteristic
40C2×C4×C7×Q8C2211yescharacteristic
41C2×C4×C7×Q8C2211yescharacteristic
42C2×C4×C7×Q8C2211yescharacteristic
43C2×C4×C7×D4C2211yescharacteristic
44C2×C7×#117—21no—
45C7×#491C2218yescomplemented
46C7×#489C2218yes—
47C7×#488C2218yes—
48C7×#479C2218yescomplemented
49C7×#478C2218yes—
50C7×#477C2218yescomplemented
51C7×#464C2218yes—
52C7×#464C2218yes—
53C7×#462C2218yescomplemented
54C7×#446C2218yescomplemented
55C7×#441C2218yescomplemented
56C7×#440C2218yes—
57C4×C7×Q16C2218yescomplemented
58C2×C7×#107C2211yescharacteristic
59C2×C7×#107C2211yescharacteristic
60C2×C7×#106C2211yescharacteristic
61C2×C7×C4⋊C8C2211yescharacteristic
62C2×C7×C4⋊C8C2211yescharacteristic
63C2×C7×C4⋊C8C2211yescharacteristic
64C2×C7×#103C2211yescharacteristic
65C2×C7×#103C2211yescharacteristic
66C2×C7×#103C2211yescharacteristic
67C2×C7×#103C2211yescharacteristic
68C2×C7×#103C2211yescharacteristic
69C2×C7×#103C2211yescharacteristic
70C2×C7×#103C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×#102C2211yescharacteristic
74C2×C7×#97C2211yescharacteristic
75C2×C7×#97C2211yescharacteristic
76C2×C4×C7×C8C2211yescharacteristic
77C2×#3377C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8D411yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×Q8C2311yescharacteristic
82C22×C7×Q8C2311yescharacteristic
83C22×C7×D4C2311yescharacteristic
84C23×C4×C7—21no—
85C2×C7×Q16—24no—
86C2×C7×Q16—24no—
87C2×C7×Q16C2314yes—
88C2×C7×Q16C2314yes—
89C2×C7×SD16—24no—
90C2×C7×SD16C2314yes—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C7×C4⋊Q8—28no—
96C7×C4⋊Q8—22no—
97C7×C4⋊Q8—22no—
98C7×C4⋊Q8C2314yes—
99C7×C4⋊Q8C2314yes—
100C7×#126—28no—
101C7×#126—28no—
102C7×#125—28no—
103C7×#125—28no—
104C7×#125—22no—
105C7×#125—22no—
106C7×#125C2314yes—
107C7×#125C2314yes—
108C7×#124—22no—
109C7×#124—22no—
110C7×#124C2314yes—
111C7×#124C2314yes—
112C7×C22⋊Q8—28no—
113C4×C7×Q8—28no—
114C4×C7×Q8—22no—
115C4×C7×Q8—22no—
116C4×C7×Q8—22no—
117C4×C7×Q8—22no—
118C4×C7×Q8—22no—
119C4×C7×Q8D414yes—
120C4×C7×Q8C2314yes—
121C4×C7×Q8C2314yes—
122C4×C7×Q8C2314yes—
123C4×C7×Q8C2314yes—
124C4×C7×Q8C2314yes—
125C4×C7×Q8C2314yes—
126C4×C7×D4—22no—
127C4×C7×D4C2314yes—
128C7×#117—28no—
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⋊C4—21no—
137C2×C7×C4⋊C4—21no—
138C2×C7×C4⋊C4—21no—
139C2×C7×C4⋊C4—21no—
140C2×C7×C4⋊C4—21no—
141C2×C7×C4⋊C4D411yescharacteristic
142C2×C7×C4⋊C4D411yescharacteristic
143C2×C7×C4⋊C4D411yescharacteristic
144C2×C7×C4⋊C4C2311yescharacteristic
145C2×C7×C4⋊C4C2311yescharacteristic
146C2×C7×C4⋊C4C2311yescharacteristic
147C2×C7×C4⋊C4C2311yescharacteristic
148C2×C7×C22⋊C4—21no—
149C2×C7×C22⋊C4—21no—
150C2×C7×C22⋊C4—21no—
151C2×C7×C22⋊C4—21no—
152C2×C7×C22⋊C4—21no—
153C2×C42×C7—21no—
154C2×C42×C7—21no—
155C2×C42×C7—21no—
156C2×C42×C7—21no—
157C2×C42×C7—21no—
158C2×C42×C7C2311yescharacteristic
159C2×C42×C7C2311yescharacteristic
160C2×C42×C7C2311yescharacteristic
161C7×#107C2314yes—
162C7×#107C2314yes—
163C7×#106C2314yes—
164C7×C4⋊C8C2314yes—
165C7×C4⋊C8C2314yes—
166C7×C4⋊C8C2314yes—
167C7×#103C2314yes—
168C7×#103C2314yes—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172C7×#103C2314yes—
173C7×#103C2314yes—
174C7×#102C2314yes—
175C7×#102C2314yes—
176C7×#102C2314yes—
177C7×#97C2314yes—
178C7×#97C2314yes—
179C4×C7×C8C2314yes—
180C2×#557C2×C711yescharacteristic, complemented
181C2×#556C2×C711yescharacteristic
182#3377C2×C7116yesdirect product factor
183C2×#491C2×C711yescharacteristic, complemented
184C2×#489C2×C711yescharacteristic
185C2×#488C2×C711yescharacteristic
186C2×#479C2×C711yescharacteristic, complemented
187C2×#477C2×C711yescharacteristic, complemented
188C2×#478C2×C711yescharacteristic
189C2×#464C2×C711yescharacteristic
190C2×#464C2×C711yescharacteristic
191C2×#462C2×C711yescharacteristic, complemented
192C2×#446C2×C711yescharacteristic, complemented
193C2×#441C2×C711yescharacteristic, complemented
194C2×#440C2×C711yescharacteristic
195C2×C4×Q16C2×C711yescharacteristic, complemented
196C24×C7—21no—
197C2×C7×Q8—21no—
198C2×C7×Q8—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—24no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8—42no—
207C2×C7×Q8—44no—
208C2×C7×Q8C2×D414yes—
209C2×C7×Q8#4114yes—
210C2×C7×Q8C2412yes—
211C2×C7×Q8C2412yes—
212C2×C7×Q8C2412yes—
213C2×C7×D4—21no—
214C2×C7×D4—22no—
215C2×C7×D4—22no—
216C2×C7×D4C2412yes—
217C22×C4×C7—21no—
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—44no—
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D411yescharacteristic
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2411yescharacteristic
233C7×Q16—28no—
234C7×Q16—28no—
235C7×SD16—28no—
236C2×C7×C8—22no—
237C2×C7×C8—22no—
238C2×C7×C8—22no—
239C2×C7×C8—22no—
240C2×C7×C8C2412yes—
241C2×C7×C8C2412yes—
242C2×C7×C8C2412yes—
243C2×C7×C8C2412yes—
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—24no—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4C2×D414yes—
261C7×C4⋊C4C2×D414yes—
262C7×C4⋊C4C2×D414yes—
263C7×C4⋊C4C2412yes—
264C7×C4⋊C4C2412yes—
265C7×C4⋊C4C2412yes—
266C7×C4⋊C4C2412yes—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C7×C22⋊C4—24no—
270C7×C22⋊C4—24no—
271C7×C22⋊C4—24no—
272C42×C7—24no—
273C42×C7—24no—
274C42×C7—24no—
275C42×C7—24no—
276C42×C7—24no—
277C42×C7C2×D412yes—
278C42×C7C2×D412yes—
279C42×C7C2×D412yes—
280C42×C7C2412yes—
281C42×C7C2412yes—
282C42×C7C2412yes—
283C22×Q16C22×C711yescharacteristic
284C22×Q16C22×C711yescharacteristic
285C22×SD16C22×C711yescharacteristic
286#557—24no—
287#557C22×C718yescomplemented
288#556—24no—
289#556C22×C718yes—
290C2×C4⋊Q8—21no—
291C2×C4⋊Q8C22×C711yescharacteristic
292C2×C4⋊Q8C22×C711yescharacteristic
293C2×#126—21no—
294C2×#126—21no—
295C2×#125—21no—
296C2×#125—21no—
297C2×#125C22×C711yescharacteristic
298C2×#125C22×C711yescharacteristic
299C2×#124C22×C711yescharacteristic
300C2×#124C22×C711yescharacteristic
301C2×C22⋊Q8—21no—
302C2×C4×Q8—21no—
303C2×C4×Q8C22×C711yescharacteristic
304C2×C4×Q8C22×C711yescharacteristic
305C2×C4×Q8C22×C711yescharacteristic
306C2×C4×Q8C22×C711yescharacteristic
307C2×C4×Q8C22×C711yescharacteristic
308C2×C4×Q8C22×C711yescharacteristic
309C2×C4×D4C22×C711yescharacteristic
310C2×#117—21no—
311#491C22×C718yescomplemented
312#489C22×C718yes—
313#488C22×C718yes—
314#479C22×C718yescomplemented
315#478C22×C718yes—
316#477C22×C718yescomplemented
317#464C22×C718yes—
318#464C22×C718yes—
319#462C22×C718yescomplemented
320#446C22×C718yescomplemented
321#441C22×C718yescomplemented
322#440C22×C718yes—
323C4×Q16C22×C718yescomplemented
324C2×#107C22×C711yescharacteristic
325C2×#107C22×C711yescharacteristic
326C2×#106C22×C711yescharacteristic
327C2×C4⋊C8C22×C711yescharacteristic
328C2×C4⋊C8C22×C711yescharacteristic
329C2×C4⋊C8C22×C711yescharacteristic
330C2×#103C22×C711yescharacteristic
331C2×#103C22×C711yescharacteristic
332C2×#103C22×C711yescharacteristic
333C2×#103C22×C711yescharacteristic
334C2×#103C22×C711yescharacteristic
335C2×#103C22×C711yescharacteristic
336C2×#103C22×C711yescharacteristic
337C2×#102C22×C711yescharacteristic
338C2×#102C22×C711yescharacteristic
339C2×#102C22×C711yescharacteristic
340C2×#97C22×C711yescharacteristic
341C2×#97C22×C711yescharacteristic
342C2×C4×C8C22×C711yescharacteristic
343C23×C7—22no—
344C23×C7—42no—
345C23×C7—42no—
346C23×C7—42no—
347C23×C7C22×D411yescharacteristic
348C7×Q8—24no—
349C7×Q8—22no—
350C7×Q8—22no—
351C7×Q8—22no—
352C7×Q8—22no—
353C7×Q8—22no—
354C7×Q8—44no—
355C7×Q8—48no—
356C7×Q8—42no—
357C7×Q8—42no—
358C7×Q8C2×#4114yes—
359C7×D4—22no—
360C7×D4—22no—
361C7×D4—42no—
362C2×C4×C7—24no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—48no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D412yes—
388C2×C4×C7C22×D412yes—
389C2×C4×C7C22×D411yescharacteristic
390C2×C4×C7C2×#4112yes—
391C2×C4×C72−1+412yes—
392C2×C4×C7C2511yescharacteristic
393C7×C8—22no—
394C7×C8—22no—
395C7×C8—22no—
396C7×C8—22no—
397C22×Q8—21no—
398C22×Q8C7×D411yescharacteristic
399C22×Q8C23×C711yescharacteristic
400C22×Q8C23×C711yescharacteristic
401C22×Q8C23×C711yescharacteristic
402C22×D4C23×C711yescharacteristic
403C23×C4—21no—
404C2×Q16—24no—
405C2×Q16—24no—
406C2×Q16C23×C714yes—
407C2×Q16C23×C714yes—
408C2×SD16—24no—
409C2×SD16C23×C714yes—
410C22×C8C23×C711yescharacteristic
411C22×C8C23×C711yescharacteristic
412C22×C8C23×C711yescharacteristic
413C22×C8C23×C711yescharacteristic
414C4⋊Q8—28no—
415C4⋊Q8—22no—
416C4⋊Q8—22no—
417C4⋊Q8C23×C714yes—
418C4⋊Q8C23×C714yes—
419#126—28no—
420#126—28no—
421#125—28no—
422#125—28no—
423#125—22no—
424#125—22no—
425#125C23×C714yes—
426#125C23×C714yes—
427#124—22no—
428#124—22no—
429#124C23×C714yes—
430#124C23×C714yes—
431C22⋊Q8—28no—
432C4×Q8—28no—
433C4×Q8—22no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×Q8C7×D414yes—
439C4×Q8C23×C714yes—
440C4×Q8C23×C714yes—
441C4×Q8C23×C714yes—
442C4×Q8C23×C714yes—
443C4×Q8C23×C714yes—
444C4×Q8C23×C714yes—
445C4×D4—22no—
446C4×D4C23×C714yes—
447#117—28no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
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⋊C4C7×D411yescharacteristic
463C2×C4⋊C4C23×C711yescharacteristic
464C2×C4⋊C4C23×C711yescharacteristic
465C2×C4⋊C4C23×C711yescharacteristic
466C2×C4⋊C4C23×C711yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42C23×C711yescharacteristic
478C2×C42C23×C711yescharacteristic
479C2×C42C23×C711yescharacteristic
480#107C23×C714yes—
481#107C23×C714yes—
482#106C23×C714yes—
483C4⋊C8C23×C714yes—
484C4⋊C8C23×C714yes—
485C4⋊C8C23×C714yes—
486#103C23×C714yes—
487#103C23×C714yes—
488#103C23×C714yes—
489#103C23×C714yes—
490#103C23×C714yes—
491#103C23×C714yes—
492#103C23×C714yes—
493#102C23×C714yes—
494#102C23×C714yes—
495#102C23×C714yes—
496#97C23×C714yes—
497#97C23×C714yes—
498C4×C8C23×C714yes—
499C22×C7—42no—
500C22×C7—42no—
501C22×C7—42no—
502C22×C7—84no—
503C22×C7#54812yes—
504C22×C7#57512yes—
505C22×C7#57812yes—
506C22×C7C23×D411yescharacteristic
507C4×C7—24no—
508C4×C7—22no—
509C4×C7—22no—
510C4×C7—22no—
511C4×C7—22no—
512C4×C7—22no—
513C4×C7—22no—
514C4×C7—42no—
515C4×C7—42no—
516C4×C7—42no—
517C4×C7—42no—
518C4×C7—42no—
519C4×C7—42no—
520C4×C7#54812yes—
521C4×C7C22×#4111yescharacteristic
522C4×C7C2×2−1+411yescharacteristic
523C24—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—24no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8C2×C7×D414yes—
536C2×Q8C7×#4114yes—
537C2×Q8C24×C712yes—
538C2×Q8C24×C712yes—
539C2×Q8C24×C712yes—
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4C24×C712yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—44no—
553C22×C4C2×C7×D411yescharacteristic
554C22×C4C2×C7×D411yescharacteristic
555C22×C4C2×C7×D411yescharacteristic
556C22×C4C2×C7×D411yescharacteristic
557C22×C4C2×C7×D411yescharacteristic
558C22×C4C2×C7×D411yescharacteristic
559C22×C4C24×C711yescharacteristic
560Q16—28no—
561Q16—28no—
562SD16—28no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8C24×C712yes—
568C2×C8C24×C712yes—
569C2×C8C24×C712yes—
570C2×C8C24×C712yes—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4C2×C7×D414yes—
588C4⋊C4C2×C7×D414yes—
589C4⋊C4C2×C7×D414yes—
590C4⋊C4C24×C712yes—
591C4⋊C4C24×C712yes—
592C4⋊C4C24×C712yes—
593C4⋊C4C24×C712yes—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C42—24no—
600C42—24no—
601C42—24no—
602C42—24no—
603C42—24no—
604C42C2×C7×D412yes—
605C42C2×C7×D412yes—
606C42C2×C7×D412yes—
607C42C24×C712yes—
608C42C24×C712yes—
609C42C24×C712yes—
610C2×C7—82no—
611C2×C7#337714yesdirect product factor
612C2×C7C2×#54811yescharacteristic
613C2×C7C2×#57511yescharacteristic
614C2×C7C2×#57811yescharacteristic
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C22×C7×D411yescharacteristic
620Q8—22no—
621Q8—24no—
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—44no—
627Q8—48no—
628Q8—42no—
629Q8—42no—
630Q8C2×C7×#4114yes—
631D4—22no—
632D4—22no—
633D4—42no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—48no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4C22×C7×D412yes—
656C2×C4C22×C7×D412yes—
657C2×C4C22×C7×D412yes—
658C2×C4C22×C7×D412yes—
659C2×C4C22×C7×D412yes—
660C2×C4C22×C7×D412yes—
661C2×C4C22×C7×D411yescharacteristic
662C2×C4C2×C7×#4112yes—
663C2×C4C7×2−1+412yes—
664C2×C4C25×C711yescharacteristic
665C8—22no—
666C8—22no—
667C8—22no—
668C8—22no—
669C7C2×#337711yescharacteristic, direct product factor, Sylow
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22C7×#54812yes—
675C22C7×#57512yes—
676C22C7×#57812yes—
677C22C23×C7×D411yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—24no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4C7×#54812yes—
692C4C22×C7×#4111yescharacteristic
693C4C2×C7×2−1+411yescharacteristic
694C2—82no—
695C2C7×#337714yesdirect product factor
696C2C2×C7×#54811yescharacteristic
697C2C2×C7×#57511yescharacteristic
698C2C2×C7×#57811yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC22×C7×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#557C2semidirect
3. C7×#3377C2direct (N × H)
4. C2×C7×#491C2semidirect
7. C2×C7×#479C2semidirect
8. C2×C7×#477C2semidirect
12. C2×C7×#462C2semidirect
13. C2×C7×#446C2semidirect
14. C2×C7×#441C2semidirect
16. C2×C4×C7×Q16C2semidirect
21. C7×#557C22semidirect
45. C7×#491C22semidirect
48. C7×#479C22semidirect
50. C7×#477C22semidirect
53. C7×#462C22semidirect
54. C7×#446C22semidirect
55. C7×#441C22semidirect
57. C4×C7×Q16C22semidirect
77. C2×#3377C7direct (N × H)
180. C2×#557C2×C7semidirect
182. #3377C2×C7direct (N × H)
183. C2×#491C2×C7semidirect
186. C2×#479C2×C7semidirect
187. C2×#477C2×C7semidirect
191. C2×#462C2×C7semidirect
192. C2×#446C2×C7semidirect
193. C2×#441C2×C7semidirect
195. C2×C4×Q16C2×C7semidirect
287. #557C22×C7semidirect
311. #491C22×C7semidirect
314. #479C22×C7semidirect
316. #477C22×C7semidirect
319. #462C22×C7semidirect
320. #446C22×C7semidirect
321. #441C22×C7semidirect
323. C4×Q16C22×C7semidirect
611. C2×C7#3377direct (N × H)
669. C7C2×#3377direct (N × H)
695. C2C7×#3377direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5572
C2×C7×#5562
C7×#33772
C2×C7×#4912
C2×C7×#4892
C2×C7×#4882
C2×C7×#4792
C2×C7×#4772
C2×C7×#4782
C2×C7×#4642
C2×C7×#4622
C2×C7×#4462
C2×C7×#4412
C2×C7×#4402
C2×C4×C7×Q162
C2×#33777