Finite Group Databasebeta

← C2×C7×#3370 #13238528

Subgroups — C2×C7×#3370 #13238528

Order 1792.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#559C211yesmaximal, characteristic, complemented
2C2×C7×#554C211yesmaximal, characteristic, complemented
3C7×#3370C2116yesmaximal, direct product factor
4C2×C7×#490C211yesmaximal, characteristic, complemented
5C2×C7×#489C211yesmaximal, characteristic, complemented
6C2×C7×#488C211yesmaximal, characteristic, complemented
7C2×C7×#479C211yesmaximal, characteristic, complemented
8C2×C7×#478C211yesmaximal, characteristic, complemented
9C2×C7×#474C211yesmaximal, characteristic, complemented
10C2×C7×#463C211yesmaximal, characteristic, complemented
11C2×C7×#463C211yesmaximal, characteristic, complemented
12C2×C7×#459C211yesmaximal, characteristic
13C2×C7×#446C211yesmaximal, characteristic, complemented
14C2×C7×#442C211yesmaximal, characteristic, complemented
15C2×C7×#440C211yesmaximal, characteristic, complemented
16C2×C4×C7×D8C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C22×C7×D8C2211yescharacteristic
20C7×#559—24no—
21C7×#559C2218yescomplemented
22C7×#554—24no—
23C7×#554C2218yescomplemented
24C2×C7×C4⋊Q8C2211yescharacteristic
25C2×C7×#127C2211yescharacteristic
26C2×C7×#125C2211yescharacteristic
27C2×C7×#125C2211yescharacteristic
28C2×C7×#124—21no—
29C2×C7×#124C2211yescharacteristic
30C2×C7×#124C2211yescharacteristic
31C2×C7×#123—21no—
32C2×C7×#123—21no—
33C2×C7×C22⋊Q8—21no—
34C2×C7×C22⋊Q8—21no—
35C2×C7×C22⋊Q8—21no—
36C2×C4×C7×Q8C2211yescharacteristic
37C2×C4×C7×Q8C2211yescharacteristic
38C2×C4×C7×D4—21no—
39C2×C4×C7×D4C2211yescharacteristic
40C2×C4×C7×D4C2211yescharacteristic
41C2×C4×C7×D4C2211yescharacteristic
42C2×C4×C7×D4C2211yescharacteristic
43C2×C4×C7×D4C2211yescharacteristic
44C22×C7×C4⋊C4—21no—
45C7×#490C2218yescomplemented
46C7×#489C2218yescomplemented
47C7×#488C2218yescomplemented
48C7×#479C2218yescomplemented
49C7×#478C2218yescomplemented
50C7×#474C2218yescomplemented
51C7×#463C2218yescomplemented
52C7×#463C2218yescomplemented
53C7×#459C2218yes—
54C7×#446C2218yescomplemented
55C7×#442C2218yescomplemented
56C7×#440C2218yescomplemented
57C4×C7×D8C2218yescomplemented
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×#102C2211yescharacteristic
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×#3370C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8D411yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×D4—21no—
82C22×C7×D4—21no—
83C22×C7×D4C2311yescharacteristic
84C22×C7×D4C2311yescharacteristic
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C23×C4×C7—21no—
89C23×C4×C7—21no—
90C23×C4×C7—21no—
91C2×C7×SD16—24no—
92C2×C7×SD16C2314yes—
93C2×C7×D8—24no—
94C2×C7×D8—24no—
95C2×C7×D8C2314yes—
96C2×C7×D8C2314yes—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C7×C4⋊Q8—22no—
102C7×C4⋊Q8C2314yes—
103C7×#127—22no—
104C7×#127C2314yes—
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—
116C7×C22⋊Q8—28no—
117C7×C22⋊Q8—28no—
118C7×C22⋊Q8—28no—
119C4×C7×Q8—22no—
120C4×C7×Q8D414yes—
121C4×C7×Q8C2314yes—
122C4×C7×Q8C2314yes—
123C4×C7×D4—28no—
124C4×C7×D4—22no—
125C4×C7×D4—22no—
126C4×C7×D4—22no—
127C4×C7×D4—22no—
128C4×C7×D4—22no—
129C4×C7×D4C2314yes—
130C4×C7×D4C2314yes—
131C4×C7×D4C2314yes—
132C4×C7×D4C2314yes—
133C4×C7×D4C2314yes—
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—28no—
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×C7×C22⋊C4—21no—
155C2×C7×C22⋊C4—21no—
156C2×C7×C22⋊C4—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×#102C2314yes—
171C7×#102C2314yes—
172C7×#102C2314yes—
173C7×#102C2314yes—
174C7×#102C2314yes—
175C7×#102C2314yes—
176C7×#102C2314yes—
177C7×#97C2314yes—
178C7×#97C2314yes—
179C4×C7×C8C2314yes—
180C2×#559C2×C711yescharacteristic, complemented
181C2×#554C2×C711yescharacteristic, complemented
182#3370C2×C7116yesdirect product factor
183C2×#490C2×C711yescharacteristic, complemented
184C2×#489C2×C711yescharacteristic, complemented
185C2×#488C2×C711yescharacteristic, complemented
186C2×#479C2×C711yescharacteristic, complemented
187C2×#478C2×C711yescharacteristic, complemented
188C2×#474C2×C711yescharacteristic, complemented
189C2×#463C2×C711yescharacteristic, complemented
190C2×#463C2×C711yescharacteristic, complemented
191C2×#459C2×C711yescharacteristic
192C2×#446C2×C711yescharacteristic, complemented
193C2×#442C2×C711yescharacteristic, complemented
194C2×#440C2×C711yescharacteristic, complemented
195C2×C4×D8C2×C711yescharacteristic, complemented
196C24×C7—21no—
197C24×C7—21no—
198C24×C7—21no—
199C2×C7×Q8—21no—
200C2×C7×Q8—24no—
201C2×C7×Q8—22no—
202C2×C7×Q8—22no—
203C2×C7×Q8—42no—
204C2×C7×Q8—82no—
205C2×C7×Q8C2×D414yes—
206C2×C7×Q8C2412yes—
207C2×C7×D4—21no—
208C2×C7×D4—21no—
209C2×C7×D4—21no—
210C2×C7×D4—24no—
211C2×C7×D4—24no—
212C2×C7×D4—22no—
213C2×C7×D4—22no—
214C2×C7×D4—22no—
215C2×C7×D4—22no—
216C2×C7×D4—22no—
217C2×C7×D4—44no—
218C2×C7×D4—82no—
219C2×C7×D4#4114yes—
220C2×C7×D4C2412yes—
221C2×C7×D4C2412yes—
222C2×C7×D4C2412yes—
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—24no—
231C22×C4×C7—24no—
232C22×C4×C7—24no—
233C22×C4×C7—44no—
234C22×C4×C7—82no—
235C22×C4×C7—82no—
236C22×C4×C7—82no—
237C22×C4×C7—82no—
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2×D411yescharacteristic
240C22×C4×C7C2×D411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2×D411yescharacteristic
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2411yescharacteristic
245C7×SD16—28no—
246C7×D8—28no—
247C7×D8—28no—
248C2×C7×C8—22no—
249C2×C7×C8—22no—
250C2×C7×C8—22no—
251C2×C7×C8—22no—
252C2×C7×C8C2412yes—
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C2×C7×C8C2412yes—
256C7×C4⋊C4—24no—
257C7×C4⋊C4—24no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—24no—
260C7×C4⋊C4—24no—
261C7×C4⋊C4—24no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4C2×D414yes—
267C7×C4⋊C4C2×D414yes—
268C7×C4⋊C4C2×D414yes—
269C7×C4⋊C4C2412yes—
270C7×C4⋊C4C2412yes—
271C7×C4⋊C4C2412yes—
272C7×C4⋊C4C2412yes—
273C7×C22⋊C4—24no—
274C7×C22⋊C4—24no—
275C7×C22⋊C4—24no—
276C7×C22⋊C4—24no—
277C7×C22⋊C4—24no—
278C7×C22⋊C4—24no—
279C7×C22⋊C4—24no—
280C7×C22⋊C4—24no—
281C7×C22⋊C4—24no—
282C42×C7—24no—
283C42×C7C2×D412yes—
284C42×C7C2×D412yes—
285C42×C7C2×D412yes—
286C42×C7C2412yes—
287C42×C7C2412yes—
288C42×C7C2412yes—
289C22×SD16C22×C711yescharacteristic
290C22×D8C22×C711yescharacteristic
291C22×D8C22×C711yescharacteristic
292#559—24no—
293#559C22×C718yescomplemented
294#554—24no—
295#554C22×C718yescomplemented
296C2×C4⋊Q8C22×C711yescharacteristic
297C2×#127C22×C711yescharacteristic
298C2×#125C22×C711yescharacteristic
299C2×#125C22×C711yescharacteristic
300C2×#124—21no—
301C2×#124C22×C711yescharacteristic
302C2×#124C22×C711yescharacteristic
303C2×#123—21no—
304C2×#123—21no—
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8—21no—
307C2×C22⋊Q8—21no—
308C2×C4×Q8C22×C711yescharacteristic
309C2×C4×Q8C22×C711yescharacteristic
310C2×C4×D4—21no—
311C2×C4×D4C22×C711yescharacteristic
312C2×C4×D4C22×C711yescharacteristic
313C2×C4×D4C22×C711yescharacteristic
314C2×C4×D4C22×C711yescharacteristic
315C2×C4×D4C22×C711yescharacteristic
316C22×C4⋊C4—21no—
317#490C22×C718yescomplemented
318#489C22×C718yescomplemented
319#488C22×C718yescomplemented
320#479C22×C718yescomplemented
321#478C22×C718yescomplemented
322#474C22×C718yescomplemented
323#463C22×C718yescomplemented
324#463C22×C718yescomplemented
325#459C22×C718yes—
326#446C22×C718yescomplemented
327#442C22×C718yescomplemented
328#440C22×C718yescomplemented
329C4×D8C22×C718yescomplemented
330C2×#107C22×C711yescharacteristic
331C2×#107C22×C711yescharacteristic
332C2×#106C22×C711yescharacteristic
333C2×C4⋊C8C22×C711yescharacteristic
334C2×C4⋊C8C22×C711yescharacteristic
335C2×C4⋊C8C22×C711yescharacteristic
336C2×#103C22×C711yescharacteristic
337C2×#103C22×C711yescharacteristic
338C2×#103C22×C711yescharacteristic
339C2×#102C22×C711yescharacteristic
340C2×#102C22×C711yescharacteristic
341C2×#102C22×C711yescharacteristic
342C2×#102C22×C711yescharacteristic
343C2×#102C22×C711yescharacteristic
344C2×#102C22×C711yescharacteristic
345C2×#102C22×C711yescharacteristic
346C2×#97C22×C711yescharacteristic
347C2×#97C22×C711yescharacteristic
348C2×C4×C8C22×C711yescharacteristic
349C23×C7—24no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7C22×D411yescharacteristic
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—44no—
365C7×Q8—42no—
366C7×Q8—84no—
367C7×D4—24no—
368C7×D4—22no—
369C7×D4—22no—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—22no—
373C7×D4—48no—
374C7×D4—42no—
375C7×D4—42no—
376C7×D4—84no—
377C7×D4C2×#4114yes—
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—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—48no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—84no—
396C2×C4×C7—84no—
397C2×C4×C7—84no—
398C2×C4×C7—84no—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×D412yes—
402C2×C4×C7C22×D412yes—
403C2×C4×C7C22×D412yes—
404C2×C4×C7C22×D412yes—
405C2×C4×C7C22×D411yescharacteristic
406C2×C4×C7C2×#4112yes—
407C2×C4×C72−1+412yes—
408C2×C4×C7C2511yescharacteristic
409C7×C8—22no—
410C7×C8—22no—
411C7×C8—22no—
412C7×C8—22no—
413C22×Q8—21no—
414C22×Q8C7×D411yescharacteristic
415C22×Q8C23×C711yescharacteristic
416C22×D4—21no—
417C22×D4—21no—
418C22×D4C23×C711yescharacteristic
419C22×D4C23×C711yescharacteristic
420C22×D4C23×C711yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—21no—
425C23×C4—21no—
426C2×SD16—24no—
427C2×SD16C23×C714yes—
428C2×D8—24no—
429C2×D8—24no—
430C2×D8C23×C714yes—
431C2×D8C23×C714yes—
432C22×C8C23×C711yescharacteristic
433C22×C8C23×C711yescharacteristic
434C22×C8C23×C711yescharacteristic
435C22×C8C23×C711yescharacteristic
436C4⋊Q8—22no—
437C4⋊Q8C23×C714yes—
438#127—22no—
439#127C23×C714yes—
440#125—22no—
441#125—22no—
442#125C23×C714yes—
443#125C23×C714yes—
444#124—28no—
445#124—22no—
446#124—22no—
447#124C23×C714yes—
448#124C23×C714yes—
449#123—28no—
450#123—28no—
451C22⋊Q8—28no—
452C22⋊Q8—28no—
453C22⋊Q8—28no—
454C4×Q8—22no—
455C4×Q8C7×D414yes—
456C4×Q8C23×C714yes—
457C4×Q8C23×C714yes—
458C4×D4—28no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4C23×C714yes—
465C4×D4C23×C714yes—
466C4×D4C23×C714yes—
467C4×D4C23×C714yes—
468C4×D4C23×C714yes—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—28no—
476C2×C4⋊C4C7×D411yescharacteristic
477C2×C4⋊C4C7×D411yescharacteristic
478C2×C4⋊C4C7×D411yescharacteristic
479C2×C4⋊C4C23×C711yescharacteristic
480C2×C4⋊C4C23×C711yescharacteristic
481C2×C4⋊C4C23×C711yescharacteristic
482C2×C4⋊C4C23×C711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—21no—
493C2×C42C23×C711yescharacteristic
494C2×C42C23×C711yescharacteristic
495C2×C42C23×C711yescharacteristic
496#107C23×C714yes—
497#107C23×C714yes—
498#106C23×C714yes—
499C4⋊C8C23×C714yes—
500C4⋊C8C23×C714yes—
501C4⋊C8C23×C714yes—
502#103C23×C714yes—
503#103C23×C714yes—
504#103C23×C714yes—
505#102C23×C714yes—
506#102C23×C714yes—
507#102C23×C714yes—
508#102C23×C714yes—
509#102C23×C714yes—
510#102C23×C714yes—
511#102C23×C714yes—
512#97C23×C714yes—
513#97C23×C714yes—
514C4×C8C23×C714yes—
515C22×C7—24no—
516C22×C7—48no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—42no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—84no—
526C22×C7—84no—
527C22×C7#54812yes—
528C22×C7#57512yes—
529C22×C7#57612yes—
530C22×C7C23×D411yescharacteristic
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—22no—
536C4×C7—22no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7#54812yes—
543C4×C7C22×#4111yescharacteristic
544C4×C7C2×2−1+411yescharacteristic
545C24—21no—
546C24—21no—
547C24—21no—
548C2×Q8—21no—
549C2×Q8—24no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—42no—
553C2×Q8—82no—
554C2×Q8C2×C7×D414yes—
555C2×Q8C24×C712yes—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—82no—
568C2×D4C7×#4114yes—
569C2×D4C24×C712yes—
570C2×D4C24×C712yes—
571C2×D4C24×C712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—44no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—82no—
587C22×C4C2×C7×D411yescharacteristic
588C22×C4C2×C7×D411yescharacteristic
589C22×C4C2×C7×D411yescharacteristic
590C22×C4C2×C7×D411yescharacteristic
591C22×C4C2×C7×D411yescharacteristic
592C22×C4C2×C7×D411yescharacteristic
593C22×C4C24×C711yescharacteristic
594SD16—28no—
595D8—28no—
596D8—28no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8C24×C712yes—
602C2×C8C24×C712yes—
603C2×C8C24×C712yes—
604C2×C8C24×C712yes—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4C2×C7×D414yes—
616C4⋊C4C2×C7×D414yes—
617C4⋊C4C2×C7×D414yes—
618C4⋊C4C24×C712yes—
619C4⋊C4C24×C712yes—
620C4⋊C4C24×C712yes—
621C4⋊C4C24×C712yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C42—24no—
632C42C2×C7×D412yes—
633C42C2×C7×D412yes—
634C42C2×C7×D412yes—
635C42C24×C712yes—
636C42C24×C712yes—
637C42C24×C712yes—
638C2×C7—44no—
639C2×C7—82no—
640C2×C7—82no—
641C2×C7#337014yesdirect product factor
642C2×C7C2×#54811yescharacteristic
643C2×C7C2×#57511yescharacteristic
644C2×C7C2×#57611yescharacteristic
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C22×C7×D411yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—44no—
661Q8—42no—
662Q8—84no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—24no—
669D4—48no—
670D4—42no—
671D4—42no—
672D4—84no—
673D4C2×C7×#4114yes—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—84no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4C22×C7×D412yes—
696C2×C4C22×C7×D412yes—
697C2×C4C22×C7×D412yes—
698C2×C4C22×C7×D412yes—
699C2×C4C22×C7×D412yes—
700C2×C4C22×C7×D412yes—
701C2×C4C22×C7×D411yescharacteristic
702C2×C4C2×C7×#4112yes—
703C2×C4C7×2−1+412yes—
704C2×C4C25×C711yescharacteristic
705C8—22no—
706C8—22no—
707C8—22no—
708C8—22no—
709C7C2×#337011yescharacteristic, direct product factor, Sylow
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22—84no—
722C22C7×#54812yes—
723C22C7×#57512yes—
724C22C7×#57612yes—
725C22C23×C7×D411yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4C7×#54812yes—
738C4C22×C7×#4111yescharacteristic
739C4C2×C7×2−1+411yescharacteristic
740C2—44no—
741C2—82no—
742C2—82no—
743C2C7×#337014yesdirect product factor
744C2C2×C7×#54811yescharacteristic
745C2C2×C7×#57511yescharacteristic
746C2C2×C7×#57611yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC2×C7×#459C2
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×#559C2semidirect
2. C2×C7×#554C2semidirect
3. C7×#3370C2direct (N × H)
4. C2×C7×#490C2semidirect
5. C2×C7×#489C2semidirect
6. C2×C7×#488C2semidirect
7. C2×C7×#479C2semidirect
8. C2×C7×#478C2semidirect
9. C2×C7×#474C2semidirect
10. C2×C7×#463C2semidirect
11. C2×C7×#463C2semidirect
13. C2×C7×#446C2semidirect
14. C2×C7×#442C2semidirect
15. C2×C7×#440C2semidirect
16. C2×C4×C7×D8C2semidirect
21. C7×#559C22semidirect
23. C7×#554C22semidirect
45. C7×#490C22semidirect
46. C7×#489C22semidirect
47. C7×#488C22semidirect
48. C7×#479C22semidirect
49. C7×#478C22semidirect
50. C7×#474C22semidirect
51. C7×#463C22semidirect
52. C7×#463C22semidirect
54. C7×#446C22semidirect
55. C7×#442C22semidirect
56. C7×#440C22semidirect
57. C4×C7×D8C22semidirect
77. C2×#3370C7direct (N × H)
180. C2×#559C2×C7semidirect
181. C2×#554C2×C7semidirect
182. #3370C2×C7direct (N × H)
183. C2×#490C2×C7semidirect
184. C2×#489C2×C7semidirect
185. C2×#488C2×C7semidirect
186. C2×#479C2×C7semidirect
187. C2×#478C2×C7semidirect
188. C2×#474C2×C7semidirect
189. C2×#463C2×C7semidirect
190. C2×#463C2×C7semidirect
192. C2×#446C2×C7semidirect
193. C2×#442C2×C7semidirect
194. C2×#440C2×C7semidirect
195. C2×C4×D8C2×C7semidirect
293. #559C22×C7semidirect
295. #554C22×C7semidirect
317. #490C22×C7semidirect
318. #489C22×C7semidirect
319. #488C22×C7semidirect
320. #479C22×C7semidirect
321. #478C22×C7semidirect
322. #474C22×C7semidirect
323. #463C22×C7semidirect
324. #463C22×C7semidirect
326. #446C22×C7semidirect
327. #442C22×C7semidirect
328. #440C22×C7semidirect
329. C4×D8C22×C7semidirect
641. C2×C7#3370direct (N × H)
709. C7C2×#3370direct (N × H)
743. C2C7×#3370direct (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×#5542
C7×#33702
C2×C7×#4902
C2×C7×#4892
C2×C7×#4882
C2×C7×#4792
C2×C7×#4782
C2×C7×#4742
C2×C7×#4632
C2×C7×#4592
C2×C7×#4462
C2×C7×#4422
C2×C7×#4402
C2×C4×C7×D82
C2×#33707