Finite Group Databasebeta

← C2×C7×#3371 #13238530

Subgroups — C2×C7×#3371 #13238530

Order 1792.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#559C211yesmaximal, characteristic
2C2×C7×#557C211yesmaximal, characteristic, complemented
3C7×#3371C2116yesmaximal, direct product factor
4C2×C7×#490C211yesmaximal, characteristic
5C2×C7×#489C211yesmaximal, characteristic, complemented
6C2×C7×#488C211yesmaximal, characteristic, complemented
7C2×C7×#479C211yesmaximal, characteristic, complemented
8C2×C7×#478C211yesmaximal, characteristic, complemented
9C2×C7×#476C211yesmaximal, characteristic, complemented
10C2×C7×#464C211yesmaximal, characteristic, complemented
11C2×C7×#464C211yesmaximal, characteristic, complemented
12C2×C7×#460C211yesmaximal, characteristic
13C2×C7×#446C211yesmaximal, characteristic, complemented
14C2×C7×#441C211yesmaximal, characteristic, complemented
15C2×C7×#440C211yesmaximal, characteristic, complemented
16C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C22×C7×SD16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C7×#559—24no—
21C7×#559C2218yes—
22C7×#557—24no—
23C7×#557C2218yescomplemented
24C2×C7×C4⋊Q8—21no—
25C2×C7×C4⋊Q8C2211yescharacteristic
26C2×C7×#127C2211yescharacteristic
27C2×C7×#125—21no—
28C2×C7×#125—21no—
29C2×C7×#125C2211yescharacteristic
30C2×C7×#125C2211yescharacteristic
31C2×C7×#124—21no—
32C2×C7×#124C2211yescharacteristic
33C2×C7×#124C2211yescharacteristic
34C2×C7×#123—21no—
35C2×C7×#123—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×D4—21no—
43C2×C4×C7×D4C2211yescharacteristic
44C2×C4×C7×D4C2211yescharacteristic
45C7×#490C2218yes—
46C7×#489C2218yescomplemented
47C7×#488C2218yescomplemented
48C7×#479C2218yescomplemented
49C7×#478C2218yescomplemented
50C7×#476C2218yescomplemented
51C7×#464C2218yescomplemented
52C7×#464C2218yescomplemented
53C7×#460C2218yes—
54C7×#446C2218yescomplemented
55C7×#441C2218yescomplemented
56C7×#440C2218yescomplemented
57C4×C7×SD16C2218yescomplemented
58C2×C7×#107C2211yescharacteristic
59C2×C7×#106C2211yescharacteristic
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×#102C2211yescharacteristic
69C2×C7×#102C2211yescharacteristic
70C2×C7×#102C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×#102C2211yescharacteristic
74C2×C7×#97C2211yescharacteristic
75C2×C7×#97C2211yescharacteristic
76C2×C4×C7×C8C2211yescharacteristic
77C2×#3371C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8D411yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×Q8C2311yescharacteristic
82C22×C7×D4—21no—
83C22×C7×D4—21no—
84C22×C7×D4C2311yescharacteristic
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C2×C7×Q16—24no—
89C2×C7×Q16C2314yes—
90C2×C7×SD16—24no—
91C2×C7×SD16—24no—
92C2×C7×SD16C2314yes—
93C2×C7×SD16C2314yes—
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C7×C4⋊Q8—28no—
99C7×C4⋊Q8—22no—
100C7×C4⋊Q8C2314yes—
101C7×#127—22no—
102C7×#127C2314yes—
103C7×#125—28no—
104C7×#125—28no—
105C7×#125—22no—
106C7×#125—22no—
107C7×#125C2314yes—
108C7×#125C2314yes—
109C7×#124—28no—
110C7×#124—22no—
111C7×#124—22no—
112C7×#124C2314yes—
113C7×#124C2314yes—
114C7×#123—28no—
115C7×#123—28no—
116C4×C7×Q8—28no—
117C4×C7×Q8—22no—
118C4×C7×Q8—22no—
119C4×C7×Q8—22no—
120C4×C7×Q8—22no—
121C4×C7×Q8D414yes—
122C4×C7×Q8C2314yes—
123C4×C7×Q8C2314yes—
124C4×C7×Q8C2314yes—
125C4×C7×Q8C2314yes—
126C4×C7×Q8C2314yes—
127C4×C7×D4—28no—
128C4×C7×D4—22no—
129C4×C7×D4—22no—
130C4×C7×D4C2314yes—
131C4×C7×D4C2314yes—
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×C7×C22⋊C4—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×#106C2314yes—
163C7×#106C2314yes—
164C7×C4⋊C8C2314yes—
165C7×C4⋊C8C2314yes—
166C7×C4⋊C8C2314yes—
167C7×#103C2314yes—
168C7×#103C2314yes—
169C7×#103C2314yes—
170C7×#103C2314yes—
171C7×#102C2314yes—
172C7×#102C2314yes—
173C7×#102C2314yes—
174C7×#102C2314yes—
175C7×#102C2314yes—
176C7×#102C2314yes—
177C7×#97C2314yes—
178C7×#97C2314yes—
179C4×C7×C8C2314yes—
180C2×#559C2×C711yescharacteristic
181C2×#557C2×C711yescharacteristic, complemented
182#3371C2×C7116yesdirect product factor
183C2×#490C2×C711yescharacteristic
184C2×#489C2×C711yescharacteristic, complemented
185C2×#488C2×C711yescharacteristic, complemented
186C2×#479C2×C711yescharacteristic, complemented
187C2×#478C2×C711yescharacteristic, complemented
188C2×#476C2×C711yescharacteristic, complemented
189C2×#464C2×C711yescharacteristic, complemented
190C2×#464C2×C711yescharacteristic, complemented
191C2×#460C2×C711yescharacteristic
192C2×#446C2×C711yescharacteristic, complemented
193C2×#441C2×C711yescharacteristic, complemented
194C2×#440C2×C711yescharacteristic, complemented
195C2×C4×SD16C2×C711yescharacteristic, complemented
196C24×C7—21no—
197C24×C7—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—42no—
205C2×C7×Q8—44no—
206C2×C7×Q8C2×D414yes—
207C2×C7×Q8#4114yes—
208C2×C7×Q8C2412yes—
209C2×C7×Q8C2412yes—
210C2×C7×D4—21no—
211C2×C7×D4—21no—
212C2×C7×D4—24no—
213C2×C7×D4—24no—
214C2×C7×D4—22no—
215C2×C7×D4—22no—
216C2×C7×D4—22no—
217C2×C7×D4—22no—
218C2×C7×D4—44no—
219C2×C7×D4—82no—
220C2×C7×D4C2412yes—
221C2×C7×D4C2412yes—
222C22×C4×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—24no—
229C22×C4×C7—24no—
230C22×C4×C7—82no—
231C22×C4×C7—82no—
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2411yescharacteristic
239C7×Q16—28no—
240C7×SD16—28no—
241C7×SD16—28no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8C2412yes—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
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—24no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—21no—
261C7×C4⋊C4—21no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4C2×D414yes—
264C7×C4⋊C4C2×D414yes—
265C7×C4⋊C4C2×D414yes—
266C7×C4⋊C4C2412yes—
267C7×C4⋊C4C2412yes—
268C7×C4⋊C4C2412yes—
269C7×C4⋊C4C2412yes—
270C7×C22⋊C4—24no—
271C7×C22⋊C4—24no—
272C7×C22⋊C4—24no—
273C7×C22⋊C4—24no—
274C7×C22⋊C4—24no—
275C7×C22⋊C4—24no—
276C42×C7—24no—
277C42×C7—24no—
278C42×C7—24no—
279C42×C7—24no—
280C42×C7C2×D412yes—
281C42×C7C2×D412yes—
282C42×C7C2×D412yes—
283C42×C7C2412yes—
284C42×C7C2412yes—
285C42×C7C2412yes—
286C22×Q16C22×C711yescharacteristic
287C22×SD16C22×C711yescharacteristic
288C22×SD16C22×C711yescharacteristic
289#559—24no—
290#559C22×C718yes—
291#557—24no—
292#557C22×C718yescomplemented
293C2×C4⋊Q8—21no—
294C2×C4⋊Q8C22×C711yescharacteristic
295C2×#127C22×C711yescharacteristic
296C2×#125—21no—
297C2×#125—21no—
298C2×#125C22×C711yescharacteristic
299C2×#125C22×C711yescharacteristic
300C2×#124—21no—
301C2×#124C22×C711yescharacteristic
302C2×#124C22×C711yescharacteristic
303C2×#123—21no—
304C2×#123—21no—
305C2×C4×Q8—21no—
306C2×C4×Q8C22×C711yescharacteristic
307C2×C4×Q8C22×C711yescharacteristic
308C2×C4×Q8C22×C711yescharacteristic
309C2×C4×Q8C22×C711yescharacteristic
310C2×C4×Q8C22×C711yescharacteristic
311C2×C4×D4—21no—
312C2×C4×D4C22×C711yescharacteristic
313C2×C4×D4C22×C711yescharacteristic
314#490C22×C718yes—
315#489C22×C718yescomplemented
316#488C22×C718yescomplemented
317#479C22×C718yescomplemented
318#478C22×C718yescomplemented
319#476C22×C718yescomplemented
320#464C22×C718yescomplemented
321#464C22×C718yescomplemented
322#460C22×C718yes—
323#446C22×C718yescomplemented
324#441C22×C718yescomplemented
325#440C22×C718yescomplemented
326C4×SD16C22×C718yescomplemented
327C2×#107C22×C711yescharacteristic
328C2×#106C22×C711yescharacteristic
329C2×#106C22×C711yescharacteristic
330C2×C4⋊C8C22×C711yescharacteristic
331C2×C4⋊C8C22×C711yescharacteristic
332C2×C4⋊C8C22×C711yescharacteristic
333C2×#103C22×C711yescharacteristic
334C2×#103C22×C711yescharacteristic
335C2×#103C22×C711yescharacteristic
336C2×#103C22×C711yescharacteristic
337C2×#102C22×C711yescharacteristic
338C2×#102C22×C711yescharacteristic
339C2×#102C22×C711yescharacteristic
340C2×#102C22×C711yescharacteristic
341C2×#102C22×C711yescharacteristic
342C2×#102C22×C711yescharacteristic
343C2×#97C22×C711yescharacteristic
344C2×#97C22×C711yescharacteristic
345C2×C4×C8C22×C711yescharacteristic
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—42no—
349C23×C7—42no—
350C23×C7—42no—
351C23×C7—42no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7C22×D411yescharacteristic
355C7×Q8—24no—
356C7×Q8—22no—
357C7×Q8—22no—
358C7×Q8—22no—
359C7×Q8—44no—
360C7×Q8—48no—
361C7×Q8—42no—
362C7×Q8C2×#4114yes—
363C7×D4—22no—
364C7×D4—22no—
365C7×D4—22no—
366C7×D4—22no—
367C7×D4—48no—
368C7×D4—42no—
369C7×D4—42no—
370C7×D4—84no—
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—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—84no—
390C2×C4×C7—84no—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D412yes—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D411yescharacteristic
398C2×C4×C7C2×#4112yes—
399C2×C4×C72−1+412yes—
400C2×C4×C7C2511yescharacteristic
401C7×C8—22no—
402C7×C8—22no—
403C7×C8—22no—
404C7×C8—22no—
405C22×Q8—21no—
406C22×Q8C7×D411yescharacteristic
407C22×Q8C23×C711yescharacteristic
408C22×Q8C23×C711yescharacteristic
409C22×D4—21no—
410C22×D4—21no—
411C22×D4C23×C711yescharacteristic
412C22×D4C23×C711yescharacteristic
413C23×C4—21no—
414C23×C4—21no—
415C2×Q16—24no—
416C2×Q16C23×C714yes—
417C2×SD16—24no—
418C2×SD16—24no—
419C2×SD16C23×C714yes—
420C2×SD16C23×C714yes—
421C22×C8C23×C711yescharacteristic
422C22×C8C23×C711yescharacteristic
423C22×C8C23×C711yescharacteristic
424C22×C8C23×C711yescharacteristic
425C4⋊Q8—28no—
426C4⋊Q8—22no—
427C4⋊Q8C23×C714yes—
428#127—22no—
429#127C23×C714yes—
430#125—28no—
431#125—28no—
432#125—22no—
433#125—22no—
434#125C23×C714yes—
435#125C23×C714yes—
436#124—28no—
437#124—22no—
438#124—22no—
439#124C23×C714yes—
440#124C23×C714yes—
441#123—28no—
442#123—28no—
443C4×Q8—28no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8C7×D414yes—
449C4×Q8C23×C714yes—
450C4×Q8C23×C714yes—
451C4×Q8C23×C714yes—
452C4×Q8C23×C714yes—
453C4×Q8C23×C714yes—
454C4×D4—28no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4C23×C714yes—
458C4×D4C23×C714yes—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4C7×D411yescharacteristic
469C2×C4⋊C4C7×D411yescharacteristic
470C2×C4⋊C4C7×D411yescharacteristic
471C2×C4⋊C4C23×C711yescharacteristic
472C2×C4⋊C4C23×C711yescharacteristic
473C2×C4⋊C4C23×C711yescharacteristic
474C2×C4⋊C4C23×C711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42C23×C711yescharacteristic
486C2×C42C23×C711yescharacteristic
487C2×C42C23×C711yescharacteristic
488#107C23×C714yes—
489#106C23×C714yes—
490#106C23×C714yes—
491C4⋊C8C23×C714yes—
492C4⋊C8C23×C714yes—
493C4⋊C8C23×C714yes—
494#103C23×C714yes—
495#103C23×C714yes—
496#103C23×C714yes—
497#103C23×C714yes—
498#102C23×C714yes—
499#102C23×C714yes—
500#102C23×C714yes—
501#102C23×C714yes—
502#102C23×C714yes—
503#102C23×C714yes—
504#97C23×C714yes—
505#97C23×C714yes—
506C4×C8C23×C714yes—
507C22×C7—42no—
508C22×C7—42no—
509C22×C7—42no—
510C22×C7—42no—
511C22×C7—42no—
512C22×C7—42no—
513C22×C7—84no—
514C22×C7—84no—
515C22×C7#54812yes—
516C22×C7#57512yes—
517C22×C7#57712yes—
518C22×C7C23×D411yescharacteristic
519C4×C7—24no—
520C4×C7—22no—
521C4×C7—22no—
522C4×C7—22no—
523C4×C7—22no—
524C4×C7—22no—
525C4×C7—22no—
526C4×C7—42no—
527C4×C7—42no—
528C4×C7—42no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7#54812yes—
532C4×C7C22×#4111yescharacteristic
533C4×C7C2×2−1+411yescharacteristic
534C24—21no—
535C24—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—24no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—42no—
543C2×Q8—44no—
544C2×Q8C2×C7×D414yes—
545C2×Q8C7×#4114yes—
546C2×Q8C24×C712yes—
547C2×Q8C24×C712yes—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—44no—
557C2×D4—82no—
558C2×D4C24×C712yes—
559C2×D4C24×C712yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4C2×C7×D411yescharacteristic
571C22×C4C2×C7×D411yescharacteristic
572C22×C4C2×C7×D411yescharacteristic
573C22×C4C2×C7×D411yescharacteristic
574C22×C4C2×C7×D411yescharacteristic
575C22×C4C2×C7×D411yescharacteristic
576C22×C4C24×C711yescharacteristic
577Q16—28no—
578SD16—28no—
579SD16—28no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8C24×C712yes—
585C2×C8C24×C712yes—
586C2×C8C24×C712yes—
587C2×C8C24×C712yes—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4C2×C7×D414yes—
602C4⋊C4C2×C7×D414yes—
603C4⋊C4C2×C7×D414yes—
604C4⋊C4C24×C712yes—
605C4⋊C4C24×C712yes—
606C4⋊C4C24×C712yes—
607C4⋊C4C24×C712yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C42—24no—
615C42—24no—
616C42—24no—
617C42—24no—
618C42C2×C7×D412yes—
619C42C2×C7×D412yes—
620C42C2×C7×D412yes—
621C42C24×C712yes—
622C42C24×C712yes—
623C42C24×C712yes—
624C2×C7—82no—
625C2×C7—82no—
626C2×C7#337114yesdirect product factor
627C2×C7C2×#54811yescharacteristic
628C2×C7C2×#57511yescharacteristic
629C2×C7C2×#57711yescharacteristic
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C22×C7×D411yescharacteristic
639Q8—22no—
640Q8—24no—
641Q8—22no—
642Q8—22no—
643Q8—44no—
644Q8—48no—
645Q8—42no—
646Q8C2×C7×#4114yes—
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—42no—
653D4—42no—
654D4—84no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—84no—
674C2×C4—84no—
675C2×C4C22×C7×D412yes—
676C2×C4C22×C7×D412yes—
677C2×C4C22×C7×D412yes—
678C2×C4C22×C7×D412yes—
679C2×C4C22×C7×D412yes—
680C2×C4C22×C7×D412yes—
681C2×C4C22×C7×D411yescharacteristic
682C2×C4C2×C7×#4112yes—
683C2×C4C7×2−1+412yes—
684C2×C4C25×C711yescharacteristic
685C8—22no—
686C8—22no—
687C8—22no—
688C8—22no—
689C7C2×#337111yescharacteristic, direct product factor, Sylow
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—84no—
697C22—84no—
698C22C7×#54812yes—
699C22C7×#57512yes—
700C22C7×#57712yes—
701C22C23×C7×D411yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4C7×#54812yes—
715C4C22×C7×#4111yescharacteristic
716C4C2×C7×2−1+411yescharacteristic
717C2—82no—
718C2—82no—
719C2C7×#337114yesdirect product factor
720C2C2×C7×#54811yescharacteristic
721C2C2×C7×#57511yescharacteristic
722C2C2×C7×#57711yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC2×C7×#127C22
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
2. C2×C7×#557C2semidirect
3. C7×#3371C2direct (N × H)
5. C2×C7×#489C2semidirect
6. C2×C7×#488C2semidirect
7. C2×C7×#479C2semidirect
8. C2×C7×#478C2semidirect
9. C2×C7×#476C2semidirect
10. C2×C7×#464C2semidirect
11. C2×C7×#464C2semidirect
13. C2×C7×#446C2semidirect
14. C2×C7×#441C2semidirect
15. C2×C7×#440C2semidirect
16. C2×C4×C7×SD16C2semidirect
23. C7×#557C22semidirect
46. C7×#489C22semidirect
47. C7×#488C22semidirect
48. C7×#479C22semidirect
49. C7×#478C22semidirect
50. C7×#476C22semidirect
51. C7×#464C22semidirect
52. C7×#464C22semidirect
54. C7×#446C22semidirect
55. C7×#441C22semidirect
56. C7×#440C22semidirect
57. C4×C7×SD16C22semidirect
77. C2×#3371C7direct (N × H)
181. C2×#557C2×C7semidirect
182. #3371C2×C7direct (N × H)
184. C2×#489C2×C7semidirect
185. C2×#488C2×C7semidirect
186. C2×#479C2×C7semidirect
187. C2×#478C2×C7semidirect
188. C2×#476C2×C7semidirect
189. C2×#464C2×C7semidirect
190. C2×#464C2×C7semidirect
192. C2×#446C2×C7semidirect
193. C2×#441C2×C7semidirect
194. C2×#440C2×C7semidirect
195. C2×C4×SD16C2×C7semidirect
292. #557C22×C7semidirect
315. #489C22×C7semidirect
316. #488C22×C7semidirect
317. #479C22×C7semidirect
318. #478C22×C7semidirect
319. #476C22×C7semidirect
320. #464C22×C7semidirect
321. #464C22×C7semidirect
323. #446C22×C7semidirect
324. #441C22×C7semidirect
325. #440C22×C7semidirect
326. C4×SD16C22×C7semidirect
626. C2×C7#3371direct (N × H)
689. C7C2×#3371direct (N × H)
719. C2C7×#3371direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5592
C2×C7×#5572
C7×#33712
C2×C7×#4902
C2×C7×#4892
C2×C7×#4882
C2×C7×#4792
C2×C7×#4782
C2×C7×#4762
C2×C7×#4642
C2×C7×#4602
C2×C7×#4462
C2×C7×#4412
C2×C7×#4402
C2×C4×C7×SD162
C2×#33717