Finite Group Databasebeta

← C2×C7×#3337 #13238444

Subgroups — C2×C7×#3337 #13238444

Order 1792.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#553C211yesmaximal, characteristic
2C2×C7×#552C211yesmaximal, characteristic, complemented
3C7×#3337C2116yesmaximal, direct product factor
4C2×C7×#499C211yesmaximal, characteristic, complemented
5C2×C7×#484C211yesmaximal, characteristic, complemented
6C2×C7×#485C211yesmaximal, characteristic, complemented
7C2×C7×#482C211yesmaximal, characteristic, complemented
8C2×C7×#480C211yesmaximal, characteristic, complemented
9C2×C7×#479C211yesmaximal, characteristic, complemented
10C2×C7×#478C211yesmaximal, characteristic, complemented
11C2×C7×#465C211yesmaximal, characteristic, complemented
12C2×C7×#465C211yesmaximal, characteristic, complemented
13C2×C4×C7×SD16C211yesmaximal, characteristic, complemented
14C2×C7×C8×D4C211yesmaximal, characteristic, complemented
15C2×C7×#427C211yesmaximal, characteristic, complemented
16C22×C7×#106C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C23×C7×C8C2211yescharacteristic
20C7×#553—24no—
21C7×#553C2218yes—
22C7×#552—24no—
23C7×#552C2218yescomplemented
24C2×C7×#126—21no—
25C2×C7×#126—21no—
26C2×C7×#125—21no—
27C2×C7×#125C2211yescharacteristic
28C2×C7×#125C2211yescharacteristic
29C2×C7×#123—21no—
30C2×C7×#123—21no—
31C2×C7×C22⋊Q8C2211yescharacteristic
32C2×C7×C22⋊Q8C2211yescharacteristic
33C2×C7×#121—21no—
34C2×C7×#121C2211yescharacteristic
35C2×C7×#121C2211yescharacteristic
36C2×C4×C7×Q8C2211yescharacteristic
37C2×C4×C7×D4—21no—
38C2×C4×C7×D4C2211yescharacteristic
39C2×C4×C7×D4C2211yescharacteristic
40C2×C7×#117—21no—
41C2×C7×#117C2211yescharacteristic
42C2×C7×#117C2211yescharacteristic
43C22×C7×C4⋊C4C2211yescharacteristic
44C22×C7×C4⋊C4C2211yescharacteristic
45C7×#499C2218yescomplemented
46C7×#485C2218yescomplemented
47C7×#484C2218yescomplemented
48C7×#482C2218yescomplemented
49C7×#480C2218yescomplemented
50C7×#479C2218yescomplemented
51C7×#478C2218yescomplemented
52C7×#465C2218yescomplemented
53C7×#465C2218yescomplemented
54C4×C7×SD16C2218yescomplemented
55C7×C8×D4C2218yescomplemented
56C7×#427C2218yescomplemented
57C2×C7×#107C2211yescharacteristic
58C2×C7×#107C2211yescharacteristic
59C2×C7×#107C2211yescharacteristic
60C2×C7×#107C2211yescharacteristic
61C2×C7×#106C2211yescharacteristic
62C2×C7×#106C2211yescharacteristic
63C2×C7×#106C2211yescharacteristic
64C2×C7×#106C2211yescharacteristic
65C2×C7×#106C2211yescharacteristic
66C2×C7×#106C2218yescomplemented
67C2×C7×C4⋊C8C2211yescharacteristic
68C2×C7×#103C2211yescharacteristic
69C2×C7×#103C2211yescharacteristic
70C2×C7×#103C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×#102C2211yescharacteristic
74C2×C7×C22⋊C8C2211yescharacteristic
75C2×C7×C22⋊C8C2211yescharacteristic
76C2×C4×C7×C8C2211yescharacteristic
77C2×#3337C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4D411yescharacteristic
82C22×C7×D4C2311yescharacteristic
83C23×C4×C7—21no—
84C23×C4×C7—21no—
85C23×C4×C7—21no—
86C23×C4×C7C2311yescharacteristic
87C23×C4×C7C2311yescharacteristic
88C2×C7×SD16—24no—
89C2×C7×SD16C2314yes—
90C22×C7×C8—24no—
91C22×C7×C8—24no—
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C22×C7×C8C2314yes—
96C22×C7×C8C2314yes—
97C22×C7×C8C2311yescharacteristic
98C7×#126—28no—
99C7×#126—28no—
100C7×#125—28no—
101C7×#125—22no—
102C7×#125—22no—
103C7×#125C2314yes—
104C7×#125C2314yes—
105C7×#123—28no—
106C7×#123—28no—
107C7×C22⋊Q8—22no—
108C7×C22⋊Q8—22no—
109C7×C22⋊Q8C2314yes—
110C7×C22⋊Q8C2314yes—
111C7×#121—28no—
112C7×#121—22no—
113C7×#121—22no—
114C7×#121C2314yes—
115C7×#121C2314yes—
116C4×C7×Q8—22no—
117C4×C7×Q8C2314yes—
118C4×C7×D4—28no—
119C4×C7×D4—22no—
120C4×C7×D4D414yes—
121C4×C7×D4C2314yes—
122C4×C7×D4C2314yes—
123C7×#117—22no—
124C7×#117—22no—
125C7×#117—28no—
126C7×#117C2314yes—
127C7×#117C2314yes—
128C2×C7×C4⋊C4—21no—
129C2×C7×C4⋊C4—21no—
130C2×C7×C4⋊C4—22no—
131C2×C7×C4⋊C4—22no—
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⋊C4D411yescharacteristic
140C2×C7×C4⋊C4C2314yes—
141C2×C7×C4⋊C4C2314yes—
142C2×C7×C4⋊C4C2311yescharacteristic
143C2×C7×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
156C2×C7×C22⋊C4D411yescharacteristic
157C2×C42×C7—21no—
158C2×C42×C7—21no—
159C2×C42×C7—21no—
160C2×C42×C7C2311yescharacteristic
161C7×#107C2314yes—
162C7×#107C2314yes—
163C7×#107C2314yes—
164C7×#107C2314yes—
165C7×#106C2314yes—
166C7×#106C2314yes—
167C7×#106C2314yes—
168C7×#106C2314yes—
169C7×#106C2314yes—
170C7×C4⋊C8C2314yes—
171C7×#103C2314yes—
172C7×#103C2314yes—
173C7×#103C2314yes—
174C7×#102C2314yes—
175C7×#102C2314yes—
176C7×#102C2314yes—
177C7×C22⋊C8C2314yes—
178C7×C22⋊C8C2314yes—
179C4×C7×C8C2314yes—
180C2×#553C2×C711yescharacteristic
181C2×#552C2×C711yescharacteristic, complemented
182#3337C2×C7116yesdirect product factor
183C2×#499C2×C711yescharacteristic, complemented
184C2×#484C2×C711yescharacteristic, complemented
185C2×#485C2×C711yescharacteristic, complemented
186C2×#482C2×C711yescharacteristic, complemented
187C2×#480C2×C711yescharacteristic, complemented
188C2×#479C2×C711yescharacteristic, complemented
189C2×#478C2×C711yescharacteristic, complemented
190C2×#465C2×C711yescharacteristic, complemented
191C2×#465C2×C711yescharacteristic, complemented
192C2×C4×SD16C2×C711yescharacteristic, complemented
193C2×C8×D4C2×C711yescharacteristic, complemented
194C2×#427C2×C711yescharacteristic, complemented
195C22×#106C2×C711yescharacteristic, complemented
196C24×C7—21no—
197C24×C7C2×D411yescharacteristic
198C24×C7C2×D411yescharacteristic
199C2×C7×Q8—21no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8C2412yes—
203C2×C7×D4—24no—
204C2×C7×D4—24no—
205C2×C7×D4—24no—
206C2×C7×D4—21no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—44no—
210C2×C7×D4—82no—
211C2×C7×D4C2×D414yes—
212C2×C7×D4C2412yes—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—24no—
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—21no—
225C22×C4×C7—24no—
226C22×C4×C7—24no—
227C22×C4×C7—44no—
228C22×C4×C7—82no—
229C22×C4×C7—82no—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2412yes—
237C22×C4×C7C2412yes—
238C22×C4×C7C2411yescharacteristic
239C7×SD16—28no—
240C2×C7×C8—22no—
241C2×C7×C8—22no—
242C2×C7×C8—22no—
243C2×C7×C8—28no—
244C2×C7×C8—28no—
245C2×C7×C8#4114yes—
246C2×C7×C8C2412yes—
247C2×C7×C8C2412yes—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
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—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4C2×D414yes—
266C7×C4⋊C4C2412yes—
267C7×C4⋊C4C2412yes—
268C7×C4⋊C4C2412yes—
269C7×C4⋊C4C2412yes—
270C7×C4⋊C4C2412yes—
271C7×C4⋊C4C2412yes—
272C7×C22⋊C4—24no—
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⋊C4C2×D414yes—
280C7×C22⋊C4C2×D414yes—
281C42×C7—24no—
282C42×C7—24no—
283C42×C7—24no—
284C42×C7C2×D412yes—
285C42×C7C2412yes—
286C22×SD16C22×C711yescharacteristic
287C23×C8C22×C711yescharacteristic
288C23×C8C22×C711yescharacteristic
289#553—24no—
290#553C22×C718yes—
291#552—24no—
292#552C22×C718yescomplemented
293C2×#126—21no—
294C2×#126—21no—
295C2×#125—21no—
296C2×#125C22×C711yescharacteristic
297C2×#125C22×C711yescharacteristic
298C2×#123—21no—
299C2×#123—21no—
300C2×C22⋊Q8C22×C711yescharacteristic
301C2×C22⋊Q8C22×C711yescharacteristic
302C2×#121—21no—
303C2×#121C22×C711yescharacteristic
304C2×#121C22×C711yescharacteristic
305C2×C4×Q8C22×C711yescharacteristic
306C2×C4×D4—21no—
307C2×C4×D4C22×C711yescharacteristic
308C2×C4×D4C22×C711yescharacteristic
309C2×#117—21no—
310C2×#117C22×C711yescharacteristic
311C2×#117C22×C711yescharacteristic
312C22×C4⋊C4C22×C711yescharacteristic
313C22×C4⋊C4C22×C711yescharacteristic
314#499C22×C718yescomplemented
315#485C22×C718yescomplemented
316#484C22×C718yescomplemented
317#482C22×C718yescomplemented
318#480C22×C718yescomplemented
319#479C22×C718yescomplemented
320#478C22×C718yescomplemented
321#465C22×C718yescomplemented
322#465C22×C718yescomplemented
323C4×SD16C22×C718yescomplemented
324C8×D4C22×C718yescomplemented
325#427C22×C718yescomplemented
326C2×#107C22×C711yescharacteristic
327C2×#107C22×C711yescharacteristic
328C2×#107C22×C711yescharacteristic
329C2×#107C22×C711yescharacteristic
330C2×#106C22×C711yescharacteristic
331C2×#106C22×C711yescharacteristic
332C2×#106C22×C711yescharacteristic
333C2×#106C22×C711yescharacteristic
334C2×#106C22×C711yescharacteristic
335C2×#106C22×C718yescomplemented
336C2×C4⋊C8C22×C711yescharacteristic
337C2×#103C22×C711yescharacteristic
338C2×#103C22×C711yescharacteristic
339C2×#103C22×C711yescharacteristic
340C2×#102C22×C711yescharacteristic
341C2×#102C22×C711yescharacteristic
342C2×#102C22×C711yescharacteristic
343C2×C22⋊C8C22×C711yescharacteristic
344C2×C22⋊C8C22×C711yescharacteristic
345C2×C4×C8C22×C711yescharacteristic
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—42no—
353C23×C7—42no—
354C23×C7—42no—
355C23×C7#13514yes—
356C23×C7C22×D412yes—
357C23×C7C22×D412yes—
358C23×C7C22×D411yescharacteristic
359C7×Q8—22no—
360C7×Q8—22no—
361C7×Q8—42no—
362C7×D4—28no—
363C7×D4—22no—
364C7×D4—22no—
365C7×D4—48no—
366C7×D4—42no—
367C7×D4—84no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—24no—
373C2×C4×C7—24no—
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—22no—
385C2×C4×C7—42no—
386C2×C4×C7—48no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—84no—
394C2×C4×C7—84no—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D412yes—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D411yescharacteristic
400C2×C4×C7C2×#4112yes—
401C2×C4×C72−1+412yes—
402C2×C4×C7C2511yescharacteristic
403C7×C8—22no—
404C7×C8—22no—
405C7×C8—22no—
406C7×C8C2×#4114yes—
407C22×Q8C23×C711yescharacteristic
408C22×D4—21no—
409C22×D4—21no—
410C22×D4C7×D411yescharacteristic
411C22×D4C23×C711yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4C23×C711yescharacteristic
416C23×C4C23×C711yescharacteristic
417C2×SD16—24no—
418C2×SD16C23×C714yes—
419C22×C8—24no—
420C22×C8—24no—
421C22×C8C23×C711yescharacteristic
422C22×C8C23×C711yescharacteristic
423C22×C8C23×C714yes—
424C22×C8C23×C714yes—
425C22×C8C23×C711yescharacteristic
426C22×C8C23×C711yescharacteristic
427#126—28no—
428#126—28no—
429#125—28no—
430#125—22no—
431#125—22no—
432#125C23×C714yes—
433#125C23×C714yes—
434#123—28no—
435#123—28no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8C23×C714yes—
439C22⋊Q8C23×C714yes—
440#121—28no—
441#121—22no—
442#121—22no—
443#121C23×C714yes—
444#121C23×C714yes—
445C4×Q8—22no—
446C4×Q8C23×C714yes—
447C4×D4—28no—
448C4×D4—22no—
449C4×D4C7×D414yes—
450C4×D4C23×C714yes—
451C4×D4C23×C714yes—
452#117—22no—
453#117—22no—
454#117—28no—
455#117C23×C714yes—
456#117C23×C714yes—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
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⋊C4C23×C711yescharacteristic
470C2×C4⋊C4C23×C711yescharacteristic
471C2×C4⋊C4C23×C711yescharacteristic
472C2×C4⋊C4C23×C711yescharacteristic
473C2×C4⋊C4C23×C714yes—
474C2×C4⋊C4C23×C714yes—
475C2×C4⋊C4C23×C711yescharacteristic
476C2×C4⋊C4C23×C711yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4C7×D411yescharacteristic
485C2×C22⋊C4C7×D411yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42C23×C711yescharacteristic
490#107C23×C714yes—
491#107C23×C714yes—
492#107C23×C714yes—
493#107C23×C714yes—
494#106C23×C714yes—
495#106C23×C714yes—
496#106C23×C714yes—
497#106C23×C714yes—
498#106C23×C714yes—
499C4⋊C8C23×C714yes—
500#103C23×C714yes—
501#103C23×C714yes—
502#103C23×C714yes—
503#102C23×C714yes—
504#102C23×C714yes—
505#102C23×C714yes—
506C22⋊C8C23×C714yes—
507C22⋊C8C23×C714yes—
508C4×C8C23×C714yes—
509C22×C7—28no—
510C22×C7—22no—
511C22×C7—22no—
512C22×C7—22no—
513C22×C7—22no—
514C22×C7—22no—
515C22×C7—44no—
516C22×C7—42no—
517C22×C7—42no—
518C22×C7—42no—
519C22×C7—84no—
520C22×C7#54712yes—
521C22×C7C2×#13514yes—
522C22×C7C2×#13512yes—
523C22×C7#57712yes—
524C22×C7C23×D411yescharacteristic
525C4×C7—22no—
526C4×C7—22no—
527C4×C7—22no—
528C4×C7—22no—
529C4×C7—42no—
530C4×C7—42no—
531C4×C7—42no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#54712yes—
537C4×C7C22×#4111yescharacteristic
538C4×C7C2×2−1+411yescharacteristic
539C24—21no—
540C24C2×C7×D411yescharacteristic
541C24C2×C7×D411yescharacteristic
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8C24×C712yes—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—44no—
553C2×D4—82no—
554C2×D4C2×C7×D414yes—
555C2×D4C24×C712yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—44no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4C2×C7×D411yescharacteristic
574C22×C4C2×C7×D411yescharacteristic
575C22×C4C2×C7×D411yescharacteristic
576C22×C4C2×C7×D411yescharacteristic
577C22×C4C2×C7×D412yes—
578C22×C4C2×C7×D412yes—
579C22×C4C24×C712yes—
580C22×C4C24×C712yes—
581C22×C4C24×C711yescharacteristic
582SD16—28no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—28no—
587C2×C8—28no—
588C2×C8C7×#4114yes—
589C2×C8C24×C712yes—
590C2×C8C24×C712yes—
591C2×C8C24×C712yes—
592C2×C8C24×C712yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
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—21no—
607C4⋊C4—21no—
608C4⋊C4C2×C7×D414yes—
609C4⋊C4C24×C712yes—
610C4⋊C4C24×C712yes—
611C4⋊C4C24×C712yes—
612C4⋊C4C24×C712yes—
613C4⋊C4C24×C712yes—
614C4⋊C4C24×C712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4C2×C7×D414yes—
623C22⋊C4C2×C7×D414yes—
624C42—24no—
625C42—24no—
626C42—24no—
627C42C2×C7×D412yes—
628C42C24×C712yes—
629C2×C7—24no—
630C2×C7—42no—
631C2×C7—82no—
632C2×C7#333714yesdirect product factor
633C2×C7C2×#54711yescharacteristic
634C2×C7C22×#13511yescharacteristic
635C2×C7C2×#57711yescharacteristic
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23C7×#13514yes—
646C23C22×C7×D412yes—
647C23C22×C7×D412yes—
648C23C22×C7×D411yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—42no—
652D4—28no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—42no—
657D4—84no—
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—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—48no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4—84no—
685C2×C4C22×C7×D412yes—
686C2×C4C22×C7×D412yes—
687C2×C4C22×C7×D412yes—
688C2×C4C22×C7×D412yes—
689C2×C4C22×C7×D411yescharacteristic
690C2×C4C2×C7×#4112yes—
691C2×C4C7×2−1+412yes—
692C2×C4C25×C711yescharacteristic
693C8—22no—
694C8—22no—
695C8—22no—
696C8C2×C7×#4114yes—
697C7C2×#333711yescharacteristic, direct product factor, Sylow
698C22—22no—
699C22—22no—
700C22—28no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—84no—
709C22C7×#54712yes—
710C22C2×C7×#13514yes—
711C22C2×C7×#13512yes—
712C22C7×#57712yes—
713C22C23×C7×D411yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4C7×#54712yes—
726C4C22×C7×#4111yescharacteristic
727C4C2×C7×2−1+411yescharacteristic
728C2—24no—
729C2—42no—
730C2—82no—
731C2C7×#333714yesdirect product factor
732C2C2×C7×#54711yescharacteristic
733C2C22×C7×#13511yescharacteristic
734C2C2×C7×#57711yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC2×C7×#553C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C7×#552C2semidirect
3. C7×#3337C2direct (N × H)
4. C2×C7×#499C2semidirect
5. C2×C7×#484C2semidirect
6. C2×C7×#485C2semidirect
7. C2×C7×#482C2semidirect
8. C2×C7×#480C2semidirect
9. C2×C7×#479C2semidirect
10. C2×C7×#478C2semidirect
11. C2×C7×#465C2semidirect
12. C2×C7×#465C2semidirect
13. C2×C4×C7×SD16C2semidirect
14. C2×C7×C8×D4C2semidirect
15. C2×C7×#427C2semidirect
16. C22×C7×#106C2semidirect
23. C7×#552C22semidirect
45. C7×#499C22semidirect
46. C7×#485C22semidirect
47. C7×#484C22semidirect
48. C7×#482C22semidirect
49. C7×#480C22semidirect
50. C7×#479C22semidirect
51. C7×#478C22semidirect
52. C7×#465C22semidirect
53. C7×#465C22semidirect
54. C4×C7×SD16C22semidirect
55. C7×C8×D4C22semidirect
56. C7×#427C22semidirect
66. C2×C7×#106C22semidirect
77. C2×#3337C7direct (N × H)
181. C2×#552C2×C7semidirect
182. #3337C2×C7direct (N × H)
183. C2×#499C2×C7semidirect
184. C2×#484C2×C7semidirect
185. C2×#485C2×C7semidirect
186. C2×#482C2×C7semidirect
187. C2×#480C2×C7semidirect
188. C2×#479C2×C7semidirect
189. C2×#478C2×C7semidirect
190. C2×#465C2×C7semidirect
191. C2×#465C2×C7semidirect
192. C2×C4×SD16C2×C7semidirect
193. C2×C8×D4C2×C7semidirect
194. C2×#427C2×C7semidirect
195. C22×#106C2×C7semidirect
292. #552C22×C7semidirect
314. #499C22×C7semidirect
315. #485C22×C7semidirect
316. #484C22×C7semidirect
317. #482C22×C7semidirect
318. #480C22×C7semidirect
319. #479C22×C7semidirect
320. #478C22×C7semidirect
321. #465C22×C7semidirect
322. #465C22×C7semidirect
323. C4×SD16C22×C7semidirect
324. C8×D4C22×C7semidirect
325. #427C22×C7semidirect
335. C2×#106C22×C7semidirect
632. C2×C7#3337direct (N × H)
697. C7C2×#3337direct (N × H)
731. C2C7×#3337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5532
C2×C7×#5522
C7×#33372
C2×C7×#4992
C2×C7×#4842
C2×C7×#4852
C2×C7×#4822
C2×C7×#4802
C2×C7×#4792
C2×C7×#4782
C2×C7×#4652
C2×C4×C7×SD162
C2×C7×C8×D42
C2×C7×#4272
C22×C7×#1062
C2×#33377