Finite Group Databasebeta

← C2×C7×#3258 #13238125

Subgroups — C2×C7×#3258 #13238125

Order 1792.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic
2C2×C7×#541C211yesmaximal, characteristic, complemented
3C7×#3258C2116yesmaximal, direct product factor
4C2×C7×#479C211yesmaximal, characteristic, complemented
5C2×C7×#477C211yesmaximal, characteristic, complemented
6C2×C7×#475C211yesmaximal, characteristic, complemented
7C2×C7×#478C211yesmaximal, characteristic, complemented
8C2×C7×#470C211yesmaximal, characteristic, complemented
9C2×C7×#468C211yesmaximal, characteristic
10C2×C7×#467C211yesmaximal, characteristic, complemented
11C2×C7×#465C211yesmaximal, characteristic
12C2×C7×#464C211yesmaximal, characteristic, complemented
13C2×C7×#464C211yesmaximal, characteristic, complemented
14C2×C7×#462C211yesmaximal, characteristic, complemented
15C2×C7×#461C211yesmaximal, characteristic, complemented
16C2×C7×#424C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C22×C7×M16C2211yescharacteristic
22C23×C7×C8C2211yescharacteristic
23C7×#542—24no—
24C7×#542C2218yes—
25C7×#541—24no—
26C7×#541C2218yescomplemented
27C2×C7×C4⋊Q8C2211yescharacteristic
28C2×C7×C4⋊Q8C2211yescharacteristic
29C2×C7×#126—21no—
30C2×C7×#126—21no—
31C2×C7×#126—21no—
32C2×C7×#125—21no—
33C2×C7×#125—21no—
34C2×C7×#125C2211yescharacteristic
35C2×C7×#124—21no—
36C2×C7×#124C2211yescharacteristic
37C2×C7×#123—21no—
38C2×C7×C22⋊Q8—21no—
39C2×C7×C22⋊Q8C2211yescharacteristic
40C2×C7×C22⋊Q8C2211yescharacteristic
41C2×C7×C22⋊Q8C2211yescharacteristic
42C2×C7×#121C2211yescharacteristic
43C2×C4×C7×Q8C2211yescharacteristic
44C2×C4×C7×Q8C2211yescharacteristic
45C2×C4×C7×Q8C2211yescharacteristic
46C2×C4×C7×D4C2211yescharacteristic
47C2×C7×#117C2211yescharacteristic
48C7×#479C2218yescomplemented
49C7×#478C2218yescomplemented
50C7×#477C2218yescomplemented
51C7×#475C2218yescomplemented
52C7×#470C2218yescomplemented
53C7×#468C2218yes—
54C7×#467C2218yescomplemented
55C7×#465C2218yes—
56C7×#464C2218yescomplemented
57C7×#464C2218yescomplemented
58C7×#462C2218yescomplemented
59C7×#461C2218yescomplemented
60C2×C7×#107C2211yescharacteristic
61C2×C7×#107C2211yescharacteristic
62C2×C7×#106C2211yescharacteristic
63C2×C7×#106C2211yescharacteristic
64C7×#424C2218yescomplemented
65C2×C7×C4⋊C8C2211yescharacteristic
66C2×C7×C4⋊C8C2211yescharacteristic
67C2×C7×C4⋊C8C2211yescharacteristic
68C2×C7×C4⋊C8C2211yescharacteristic
69C2×C7×#103C2211yescharacteristic
70C2×C7×#103C2211yescharacteristic
71C2×C7×#103C2211yescharacteristic
72C2×C7×#103C2211yescharacteristic
73C2×C7×#103C2211yescharacteristic
74C2×C7×#103C2211yescharacteristic
75C2×C7×#102C2211yescharacteristic
76C2×C7×#102C2211yescharacteristic
77C2×#3258C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×Q8C2311yescharacteristic
82C22×C7×D4—21no—
83C22×C7×D4C2311yescharacteristic
84C23×C4×C7—21no—
85C23×C4×C7C2311yescharacteristic
86C2×C7×Q16—42no—
87C2×C7×Q16—42no—
88C2×C7×Q16C2314yes—
89C2×C7×Q16C2314yes—
90C2×C7×SD16—42no—
91C2×C7×SD16—42no—
92C2×C7×SD16C2314yes—
93C2×C7×SD16C2314yes—
94C2×C7×M16—42no—
95C2×C7×M16C2314yes—
96C22×C7×C8—42no—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C22×C7×C8C2314yes—
102C7×C4⋊Q8—22no—
103C7×C4⋊Q8—22no—
104C7×C4⋊Q8C2314yes—
105C7×C4⋊Q8C2314yes—
106C7×#126—28no—
107C7×#126—28no—
108C7×#126—28no—
109C7×#125—28no—
110C7×#125—28no—
111C7×#125—22no—
112C7×#125C2314yes—
113C7×#124—28no—
114C7×#124—22no—
115C7×#124C2314yes—
116C7×#123—28no—
117C7×C22⋊Q8—22no—
118C7×C22⋊Q8—22no—
119C7×C22⋊Q8—22no—
120C7×C22⋊Q8—28no—
121C7×C22⋊Q8C2314yes—
122C7×C22⋊Q8C2314yes—
123C7×C22⋊Q8C2314yes—
124C7×#121—22no—
125C7×#121C2314yes—
126C4×C7×Q8—22no—
127C4×C7×Q8—22no—
128C4×C7×Q8—22no—
129C4×C7×Q8C2314yes—
130C4×C7×Q8C2314yes—
131C4×C7×Q8C2314yes—
132C4×C7×D4—22no—
133C4×C7×D4C2314yes—
134C7×#117D414yes—
135C7×#117C2314yes—
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⋊C4—21no—
142C2×C7×C4⋊C4—21no—
143C2×C7×C4⋊C4—21no—
144C2×C7×C4⋊C4—21no—
145C2×C7×C4⋊C4—21no—
146C2×C7×C4⋊C4—21no—
147C2×C7×C4⋊C4D411yescharacteristic
148C2×C7×C4⋊C4D411yescharacteristic
149C2×C7×C4⋊C4C2311yescharacteristic
150C2×C7×C4⋊C4C2311yescharacteristic
151C2×C7×C4⋊C4C2311yescharacteristic
152C2×C7×C4⋊C4C2311yescharacteristic
153C2×C7×C22⋊C4—21no—
154C2×C7×C22⋊C4—21no—
155C2×C7×C22⋊C4—21no—
156C2×C7×C22⋊C4—21no—
157C2×C7×C22⋊C4—21no—
158C2×C7×C22⋊C4—21no—
159C2×C7×C22⋊C4—21no—
160C2×C7×C22⋊C4D411yescharacteristic
161C2×C7×C22⋊C4D411yescharacteristic
162C2×C42×C7—21no—
163C2×C42×C7—21no—
164C2×C42×C7—21no—
165C2×C42×C7C2311yescharacteristic
166C2×C42×C7C2311yescharacteristic
167C7×#107C2314yes—
168C7×#107C2314yes—
169C7×#106C2314yes—
170C7×#106C2314yes—
171C7×C4⋊C8C2314yes—
172C7×C4⋊C8C2314yes—
173C7×C4⋊C8C2314yes—
174C7×C4⋊C8C2314yes—
175C7×#103C2314yes—
176C7×#103C2314yes—
177C7×#103C2314yes—
178C7×#103C2314yes—
179C7×#103C2314yes—
180C7×#103C2314yes—
181C7×#102C2314yes—
182C7×#102C2314yes—
183C2×#542C2×C711yescharacteristic
184C2×#541C2×C711yescharacteristic, complemented
185#3258C2×C7116yesdirect product factor
186C2×#479C2×C711yescharacteristic, complemented
187C2×#477C2×C711yescharacteristic, complemented
188C2×#475C2×C711yescharacteristic, complemented
189C2×#478C2×C711yescharacteristic, complemented
190C2×#470C2×C711yescharacteristic, complemented
191C2×#468C2×C711yescharacteristic
192C2×#467C2×C711yescharacteristic, complemented
193C2×#465C2×C711yescharacteristic
194C2×#464C2×C711yescharacteristic, complemented
195C2×#464C2×C711yescharacteristic, complemented
196C2×#462C2×C711yescharacteristic, complemented
197C2×#461C2×C711yescharacteristic, complemented
198C2×#424C2×C711yescharacteristic, complemented
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—21no—
204C2×C7×Q8—24no—
205C2×C7×Q8—22no—
206C2×C7×Q8—22no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8—82no—
212C2×C7×Q8C2412yes—
213C2×C7×Q8C2412yes—
214C2×C7×Q8C2412yes—
215C2×C7×D4—24no—
216C2×C7×D4—21no—
217C2×C7×D4—22no—
218C2×C7×D4—22no—
219C2×C7×D4—82no—
220C2×C7×D4C2412yes—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—24no—
231C22×C4×C7—82no—
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D411yescharacteristic
237C22×C4×C7C2×D411yescharacteristic
238C22×C4×C7C2412yes—
239C22×C4×C7C2411yescharacteristic
240C7×Q16—44no—
241C7×Q16—44no—
242C7×SD16—44no—
243C7×SD16—44no—
244C7×M16—44no—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8—44no—
250C2×C7×C8C2412yes—
251C2×C7×C8C2412yes—
252C2×C7×C8C2412yes—
253C2×C7×C8C2412yes—
254C7×C4⋊C4—24no—
255C7×C4⋊C4—24no—
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—24no—
263C7×C4⋊C4—24no—
264C7×C4⋊C4—24no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—21no—
267C7×C4⋊C4—21no—
268C7×C4⋊C4—21no—
269C7×C4⋊C4C2×D414yes—
270C7×C4⋊C4C2×D414yes—
271C7×C4⋊C4C2412yes—
272C7×C4⋊C4C2412yes—
273C7×C4⋊C4C2412yes—
274C7×C4⋊C4C2412yes—
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—
282C7×C22⋊C4C2×D414yes—
283C7×C22⋊C4C2×D414yes—
284C42×C7—24no—
285C42×C7—24no—
286C42×C7—24no—
287C42×C7C2×D412yes—
288C42×C7C2×D412yes—
289C42×C7C2412yes—
290C42×C7C2412yes—
291C22×Q16C22×C711yescharacteristic
292C22×Q16C22×C711yescharacteristic
293C22×SD16C22×C711yescharacteristic
294C22×SD16C22×C711yescharacteristic
295C22×M16C22×C711yescharacteristic
296C23×C8C22×C711yescharacteristic
297#542—24no—
298#542C22×C718yes—
299#541—24no—
300#541C22×C718yescomplemented
301C2×C4⋊Q8C22×C711yescharacteristic
302C2×C4⋊Q8C22×C711yescharacteristic
303C2×#126—21no—
304C2×#126—21no—
305C2×#126—21no—
306C2×#125—21no—
307C2×#125—21no—
308C2×#125C22×C711yescharacteristic
309C2×#124—21no—
310C2×#124C22×C711yescharacteristic
311C2×#123—21no—
312C2×C22⋊Q8—21no—
313C2×C22⋊Q8C22×C711yescharacteristic
314C2×C22⋊Q8C22×C711yescharacteristic
315C2×C22⋊Q8C22×C711yescharacteristic
316C2×#121C22×C711yescharacteristic
317C2×C4×Q8C22×C711yescharacteristic
318C2×C4×Q8C22×C711yescharacteristic
319C2×C4×Q8C22×C711yescharacteristic
320C2×C4×D4C22×C711yescharacteristic
321C2×#117C22×C711yescharacteristic
322#479C22×C718yescomplemented
323#478C22×C718yescomplemented
324#477C22×C718yescomplemented
325#475C22×C718yescomplemented
326#470C22×C718yescomplemented
327#468C22×C718yes—
328#467C22×C718yescomplemented
329#465C22×C718yes—
330#464C22×C718yescomplemented
331#464C22×C718yescomplemented
332#462C22×C718yescomplemented
333#461C22×C718yescomplemented
334C2×#107C22×C711yescharacteristic
335C2×#107C22×C711yescharacteristic
336C2×#106C22×C711yescharacteristic
337C2×#106C22×C711yescharacteristic
338#424C22×C718yescomplemented
339C2×C4⋊C8C22×C711yescharacteristic
340C2×C4⋊C8C22×C711yescharacteristic
341C2×C4⋊C8C22×C711yescharacteristic
342C2×C4⋊C8C22×C711yescharacteristic
343C2×#103C22×C711yescharacteristic
344C2×#103C22×C711yescharacteristic
345C2×#103C22×C711yescharacteristic
346C2×#103C22×C711yescharacteristic
347C2×#103C22×C711yescharacteristic
348C2×#103C22×C711yescharacteristic
349C2×#102C22×C711yescharacteristic
350C2×#102C22×C711yescharacteristic
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—42no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7C22×D412yes—
359C23×C7C22×D411yescharacteristic
360C7×Q8—22no—
361C7×Q8—22no—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—22no—
366C7×Q8—42no—
367C7×Q8—42no—
368C7×Q8—42no—
369C7×Q8—84no—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—42no—
373C7×D4—84no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—24no—
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—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—84no—
397C2×C4×C7C22×D412yes—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×D412yes—
402C2×C4×C7C22×D411yescharacteristic
403C2×C4×C7H(5,𝔽2)12yes—
404C2×C4×C72−1+412yes—
405C2×C4×C7C2511yescharacteristic
406C7×C8—22no—
407C7×C8—22no—
408C7×C8—22no—
409C7×C8—22no—
410C22×Q8—21no—
411C22×Q8C23×C711yescharacteristic
412C22×Q8C23×C711yescharacteristic
413C22×Q8C23×C711yescharacteristic
414C22×D4—21no—
415C22×D4C23×C711yescharacteristic
416C23×C4—21no—
417C23×C4C23×C711yescharacteristic
418C2×Q16—42no—
419C2×Q16—42no—
420C2×Q16C23×C714yes—
421C2×Q16C23×C714yes—
422C2×SD16—42no—
423C2×SD16—42no—
424C2×SD16C23×C714yes—
425C2×SD16C23×C714yes—
426C2×M16—42no—
427C2×M16C23×C714yes—
428C22×C8—42no—
429C22×C8C23×C711yescharacteristic
430C22×C8C23×C711yescharacteristic
431C22×C8C23×C711yescharacteristic
432C22×C8C23×C711yescharacteristic
433C22×C8C23×C714yes—
434C4⋊Q8—22no—
435C4⋊Q8—22no—
436C4⋊Q8C23×C714yes—
437C4⋊Q8C23×C714yes—
438#126—28no—
439#126—28no—
440#126—28no—
441#125—28no—
442#125—28no—
443#125—22no—
444#125C23×C714yes—
445#124—28no—
446#124—22no—
447#124C23×C714yes—
448#123—28no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—28no—
453C22⋊Q8C23×C714yes—
454C22⋊Q8C23×C714yes—
455C22⋊Q8C23×C714yes—
456#121—22no—
457#121C23×C714yes—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8C23×C714yes—
462C4×Q8C23×C714yes—
463C4×Q8C23×C714yes—
464C4×D4—22no—
465C4×D4C23×C714yes—
466#117C7×D414yes—
467#117C23×C714yes—
468C2×C4⋊C4—21no—
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—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4C7×D411yescharacteristic
480C2×C4⋊C4C7×D411yescharacteristic
481C2×C4⋊C4C23×C711yescharacteristic
482C2×C4⋊C4C23×C711yescharacteristic
483C2×C4⋊C4C23×C711yescharacteristic
484C2×C4⋊C4C23×C711yescharacteristic
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×C22⋊C4C7×D411yescharacteristic
493C2×C22⋊C4C7×D411yescharacteristic
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—21no—
497C2×C42C23×C711yescharacteristic
498C2×C42C23×C711yescharacteristic
499#107C23×C714yes—
500#107C23×C714yes—
501#106C23×C714yes—
502#106C23×C714yes—
503C4⋊C8C23×C714yes—
504C4⋊C8C23×C714yes—
505C4⋊C8C23×C714yes—
506C4⋊C8C23×C714yes—
507#103C23×C714yes—
508#103C23×C714yes—
509#103C23×C714yes—
510#103C23×C714yes—
511#103C23×C714yes—
512#103C23×C714yes—
513#102C23×C714yes—
514#102C23×C714yes—
515C22×C7—22no—
516C22×C7—22no—
517C22×C7—22no—
518C22×C7—44no—
519C22×C7—42no—
520C22×C7—42no—
521C22×C7—42no—
522C22×C7—84no—
523C22×C7#53712yes—
524C22×C7#57712yes—
525C22×C7#57812yes—
526C22×C7C23×D411yescharacteristic
527C4×C7—22no—
528C4×C7—22no—
529C4×C7—22no—
530C4×C7—22no—
531C4×C7—22no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7#53712yes—
540C4×C7C2×H(5,𝔽2)11yescharacteristic
541C4×C7C2×2−1+411yescharacteristic
542C24—21no—
543C24C2×C7×D411yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—24no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—82no—
555C2×Q8C24×C712yes—
556C2×Q8C24×C712yes—
557C2×Q8C24×C712yes—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—82no—
563C2×D4C24×C712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—82no—
575C22×C4C2×C7×D411yescharacteristic
576C22×C4C2×C7×D411yescharacteristic
577C22×C4C2×C7×D411yescharacteristic
578C22×C4C2×C7×D411yescharacteristic
579C22×C4C2×C7×D411yescharacteristic
580C22×C4C2×C7×D412yes—
581C22×C4C24×C712yes—
582C22×C4C24×C711yescharacteristic
583Q16—44no—
584Q16—44no—
585SD16—44no—
586SD16—44no—
587M16—44no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—44no—
593C2×C8C24×C712yes—
594C2×C8C24×C712yes—
595C2×C8C24×C712yes—
596C2×C8C24×C712yes—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4C2×C7×D414yes—
613C4⋊C4C2×C7×D414yes—
614C4⋊C4C24×C712yes—
615C4⋊C4C24×C712yes—
616C4⋊C4C24×C712yes—
617C4⋊C4C24×C712yes—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4C2×C7×D414yes—
626C22⋊C4C2×C7×D414yes—
627C42—24no—
628C42—24no—
629C42—24no—
630C42C2×C7×D412yes—
631C42C2×C7×D412yes—
632C42C24×C712yes—
633C42C24×C712yes—
634C2×C7—42no—
635C2×C7—82no—
636C2×C7#325814yesdirect product factor
637C2×C7C2×#53711yescharacteristic
638C2×C7C2×#57711yescharacteristic
639C2×C7C2×#57811yescharacteristic
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×C7×D412yes—
648C23C22×C7×D411yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—84no—
659D4—22no—
660D4—22no—
661D4—42no—
662D4—84no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—84no—
686C2×C4C22×C7×D412yes—
687C2×C4C22×C7×D412yes—
688C2×C4C22×C7×D412yes—
689C2×C4C22×C7×D412yes—
690C2×C4C22×C7×D412yes—
691C2×C4C22×C7×D411yescharacteristic
692C2×C4C7×H(5,𝔽2)12yes—
693C2×C4C7×2−1+412yes—
694C2×C4C25×C711yescharacteristic
695C8—22no—
696C8—22no—
697C8—22no—
698C8—22no—
699C7C2×#325811yescharacteristic, direct product factor, Sylow
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—84no—
708C22C7×#53712yes—
709C22C7×#57712yes—
710C22C7×#57812yes—
711C22C23×C7×D411yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4C7×#53712yes—
725C4C2×C7×H(5,𝔽2)11yescharacteristic
726C4C2×C7×2−1+411yescharacteristic
727C2—42no—
728C2—82no—
729C2C7×#325814yesdirect product factor
730C2C2×C7×#53711yescharacteristic
731C2C2×C7×#57711yescharacteristic
732C2C2×C7×#57811yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC2×C7×#121C22
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
2. C2×C7×#541C2semidirect
3. C7×#3258C2direct (N × H)
4. C2×C7×#479C2semidirect
5. C2×C7×#477C2semidirect
6. C2×C7×#475C2semidirect
7. C2×C7×#478C2semidirect
8. C2×C7×#470C2semidirect
10. C2×C7×#467C2semidirect
12. C2×C7×#464C2semidirect
13. C2×C7×#464C2semidirect
14. C2×C7×#462C2semidirect
15. C2×C7×#461C2semidirect
16. C2×C7×#424C2semidirect
26. C7×#541C22semidirect
48. C7×#479C22semidirect
49. C7×#478C22semidirect
50. C7×#477C22semidirect
51. C7×#475C22semidirect
52. C7×#470C22semidirect
54. C7×#467C22semidirect
56. C7×#464C22semidirect
57. C7×#464C22semidirect
58. C7×#462C22semidirect
59. C7×#461C22semidirect
64. C7×#424C22semidirect
77. C2×#3258C7direct (N × H)
184. C2×#541C2×C7semidirect
185. #3258C2×C7direct (N × H)
186. C2×#479C2×C7semidirect
187. C2×#477C2×C7semidirect
188. C2×#475C2×C7semidirect
189. C2×#478C2×C7semidirect
190. C2×#470C2×C7semidirect
192. C2×#467C2×C7semidirect
194. C2×#464C2×C7semidirect
195. C2×#464C2×C7semidirect
196. C2×#462C2×C7semidirect
197. C2×#461C2×C7semidirect
198. C2×#424C2×C7semidirect
300. #541C22×C7semidirect
322. #479C22×C7semidirect
323. #478C22×C7semidirect
324. #477C22×C7semidirect
325. #475C22×C7semidirect
326. #470C22×C7semidirect
328. #467C22×C7semidirect
330. #464C22×C7semidirect
331. #464C22×C7semidirect
332. #462C22×C7semidirect
333. #461C22×C7semidirect
338. #424C22×C7semidirect
636. C2×C7#3258direct (N × H)
699. C7C2×#3258direct (N × H)
729. C2C7×#3258direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
C2×C7×#5412
C7×#32582
C2×C7×#4792
C2×C7×#4772
C2×C7×#4752
C2×C7×#4782
C2×C7×#4702
C2×C7×#4682
C2×C7×#4672
C2×C7×#4652
C2×C7×#4642
C2×C7×#4622
C2×C7×#4612
C2×C7×#4242
C2×#32587