Finite Group Databasebeta

← #13370353

Subgroups — #13370353

Order 1792.

1114 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90234C211yesmaximal, characteristic
2#11731324C212yesmaximal, complemented
3C7×#1799C211yesmaximal, characteristic
4C4×#6408C211yesmaximal, characteristic
5#11727782C212yesmaximal
6Dic7×#99C212yesmaximal
7#11727283C212yesmaximal, complemented
8#11726709C214yesmaximal, complemented
9C2×C4×C7×D4C2211yescharacteristic
10C2×D4×Dic7C2212yes—
11C22×C4⋊Dic7C411yescharacteristic, complemented
12C22×C4⋊Dic7C2211yescharacteristic
13C2×#6487C411yescharacteristic, complemented
14C2×#6487C2211yescharacteristic
15#90234—24no—
16#90234—22no—
17#90234—22no—
18C2×#6453C412yescomplemented
19C2×#6441C412yescomplemented
20C2×#6441C2212yes—
21C2×#6432C411yescharacteristic, complemented
22C2×C4×Dic14C411yescharacteristic, complemented
23C2×C7×#99C2212yes—
24C7×#380C2212yes—
25C2×#6408C2211yescharacteristic
26C2×#6408C2211yescharacteristic
27C4×C22⋊Dic7C2212yes—
28C4⋊C4×Dic7—22no—
29#89745—22no—
30#89714C2214yes—
31C22⋊C4×Dic7C2214yes—
32#89425—24no—
33C7×#342C2212yes—
34#89322C2214yes—
35#89322C2214yes—
36#89321C2212yes—
37#22513—71nomaximal, Sylow
38C22×C7×D4C2311yescharacteristic
39C23×C4×C7C2×C411yescharacteristic
40C23×C4×C7C2311yescharacteristic
41C23×Dic7C2×C412yes—
42C23×Dic7C2312yes—
43C22×Dic14C2×C411yescharacteristic
44C22×Dic14C2×C412yes—
45C4×C7×D4—22no—
46C4×C7×D4—22no—
47C2×C7×C4⋊C4—22no—
48C2×C7×C4⋊C4C2×C411yescharacteristic
49C2×C7×C22⋊C4C2×C411yescharacteristic
50C2×C7×C22⋊C4C2314yes—
51C2×C7×C22⋊C4C2311yescharacteristic
52C2×C42×C7C2×C411yescharacteristic
53C2×C22⋊Dic7C2×C412yes—
54C2×C22⋊Dic7C2312yes—
55C2×C22⋊Dic7C2312yes—
56C2×C22⋊Dic7C2312yes—
57D4×Dic7—24no—
58D4×Dic7—24no—
59C2×C4⋊Dic7—22no—
60C2×C4⋊Dic7—21no—
61C2×C4⋊Dic7—21no—
62C2×C4⋊Dic7C2×C412yes—
63C2×C4⋊Dic7C2×C411yescharacteristic
64C2×C4⋊Dic7C2×C412yes—
65C2×C4⋊Dic7C2×C411yescharacteristic
66C2×C4⋊Dic7C2×C411yescharacteristic
67C2×C4⋊Dic7C2×C412yes—
68C2×C4⋊Dic7D414yes—
69C2×C4⋊Dic7D412yes—
70C2×C4⋊Dic7D412yes—
71#6487—22no—
72#6487—22no—
73#6487—22no—
74#6487—22no—
75C2×Dic7⋊C4—24no—
76C2×Dic7⋊C4C2×C412yes—
77C2×Dic7⋊C4C2×C412yes—
78C2×Dic7⋊C4C2×C412yes—
79C2×C4×Dic7—22no—
80C2×C4×Dic7—24no—
81C2×C4×Dic7C2×C412yes—
82#6453—24no—
83#6453—24no—
84#6441—24no—
85#6441—24no—
86#6441—24no—
87#6441—24no—
88#6432—22no—
89#6432—22no—
90C4×Dic14—22no—
91C4×Dic14—21no—
92C4×Dic14—21no—
93C7×#99—24no—
94C7×#95—22no—
95#6408—22no—
96#6408Q814yescomplemented
97C7⋊#95—22no—
98C7⋊#95—24no—
99C7⋊#95—24no—
100C2×#554—71no—
101#2345—72no—
102#1996—72no—
103#1996—74no—
104#1799—72no—
105#1799D711yescharacteristic
106C4×#99—72no—
107C4×#99—71no—
108C24×C7C22×C411yescharacteristic
109C24×C7C2411yescharacteristic
110C2×C7×D4—22no—
111C2×C7×D4—22no—
112C2×C7×D4C2×Q812yes—
113C2×C7×D4#4112yes—
114C22×C4×C7—21no—
115C22×C4×C7—21no—
116C22×C4×C7—24no—
117C22×C4×C7—42no—
118C22×C4×C7—42no—
119C22×C4×C7C22×C411yescharacteristic
120C22×C4×C7C22×C411yescharacteristic
121C22×C4×C7C22×C411yescharacteristic
122C22×C4×C7C22×C411yescharacteristic
123C22×C4×C7C22×C411yescharacteristic
124C22×C4×C7C2×D412yes—
125C22×C4×C7C2×D412yes—
126C22×Dic7—22no—
127C22×Dic7—22no—
128C22×Dic7—22no—
129C22×Dic7—22no—
130C22×Dic7—82no—
131C22×Dic7—82no—
132C22×Dic7C22×C412yes—
133C22×Dic7C22×C412yes—
134C22×Dic7C22×C412yes—
135C22×Dic7C22×C412yes—
136C22×Dic7C2×D414yes—
137C22×Dic7C2×D414yes—
138C2×Dic14—21no—
139C2×Dic14—21no—
140C2×Dic14—24no—
141C2×Dic14—42no—
142C2×Dic14—82no—
143C7×C4⋊C4—22no—
144C7×C4⋊C4—44no—
145C7×C22⋊C4—22no—
146C7×C22⋊C4—22no—
147C7×C22⋊C4—24no—
148C7×C22⋊C4—24no—
149C42×C7—21no—
150C42×C7—21no—
151C22⋊Dic7—24no—
152C22⋊Dic7—22no—
153C22⋊Dic7—24no—
154C22⋊Dic7—22no—
155C22⋊Dic7—22no—
156C22⋊Dic7C2×Q814yes—
157C4⋊Dic7—21no—
158C4⋊Dic7—21no—
159C4⋊Dic7—24no—
160C4⋊Dic7—22no—
161C4⋊Dic7—22no—
162C4⋊Dic7C22⋊C412yes—
163C4⋊Dic7C22⋊C411yescharacteristic
164C4⋊Dic7C22⋊C411yescharacteristic
165C4⋊Dic7C22⋊C412yes—
166C4⋊Dic7C22⋊C412yes—
167C4⋊Dic7C22⋊C414yes—
168C4⋊Dic7C22⋊C414yes—
169Dic7⋊C4—24no—
170Dic7⋊C4—22no—
171Dic7⋊C4—22no—
172Dic7⋊C4—24no—
173Dic7⋊C4—84no—
174C4×Dic7—22no—
175C4×Dic7—22no—
176C4×Dic7—44no—
177C4×Dic7—84no—
178#554—142no—
179#554—144no—
180#554—142no—
181C2×C4⋊Q8—71no—
182C2×#125—72no—
183C2×C22⋊Q8—71no—
184C2×C22⋊Q8—71no—
185C2×C22⋊Q8—72no—
186C2×C22⋊Q8—72no—
187C2×C4×Q8—71no—
188C2×C4×D4—72no—
189C2×C4×D4C2×D711yescharacteristic
190C22×C4⋊C4—71no—
191C22×C4⋊C4—71no—
192C2×#99—71no—
193C2×#99—71no—
194C2×#99C2×D712yes—
195#389—142no—
196#387—144no—
197#380—74no—
198#380C2×D712yes—
199C4×C4⋊C4—142no—
200C4×C22⋊C4—72no—
201C4×C22⋊C4—74no—
202#342—74no—
203#342—72no—
204#342—74no—
205#342C2×D712yes—
206C23×C7—21no—
207C23×C7—21no—
208C23×C7—41no—
209C23×C7—41no—
210C23×C7—41no—
211C23×C7—41no—
212C23×C7C4×Q812yes—
213C23×C7C23×C411yescharacteristic
214C23×C7C22×D412yes—
215C23×C7C22×Q811yescharacteristic
216C23×C7C2×#4111yescharacteristic
217C23×C72−1+412yes—
218C7×D4—24no—
219C7×D4—24no—
220C2×C4×C7—21no—
221C2×C4×C7—21no—
222C2×C4×C7—24no—
223C2×C4×C7—22no—
224C2×C4×C7—21no—
225C2×C4×C7—21no—
226C2×C4×C7—41no—
227C2×C4×C7—42no—
228C2×C4×C7—42no—
229C2×C4×C7—42no—
230C2×C4×C7—41no—
231C2×C4×C7—41no—
232C2×C4×C7—44no—
233C2×C4×C7—44no—
234C2×C4×C7—44no—
235C2×C4×C7C2×C22⋊C412yes—
236C2×C4×C7C2×C22⋊C411yescharacteristic
237C2×C4×C7C2×C22⋊C411yescharacteristic
238C2×C4×C7C4×Q812yes—
239C2×Dic7—22no—
240C2×Dic7—22no—
241C2×Dic7—24no—
242C2×Dic7—44no—
243C2×Dic7—44no—
244C2×Dic7—42no—
245C2×Dic7—42no—
246C2×Dic7—42no—
247C2×Dic7—42no—
248C2×Dic7—42no—
249C2×Dic7—42no—
250C2×Dic7—42no—
251C2×Dic7—42no—
252C2×Dic7—42no—
253C2×Dic7—82no—
254C2×Dic7—82no—
255C2×Dic7C2×C22⋊C412yes—
256C2×Dic7C2×C22⋊C412yes—
257C2×Dic7C2×C22⋊C414yes—
258Dic14—42no—
259Dic14—42no—
260Dic14—84no—
261C22×Q8—71no—
262C22×Q8—72no—
263C22×D4C22×D711yescharacteristic
264C23×C4—72no—
265C23×C4—72no—
266C23×C4C4×D711yescharacteristic
267C23×C4C22×D711yescharacteristic
268C4⋊Q8—142no—
269C4⋊Q8—142no—
270#125—144no—
271#125—144no—
272C22⋊Q8—144no—
273C22⋊Q8—144no—
274C22⋊Q8—144no—
275C22⋊Q8—144no—
276C22⋊Q8—142no—
277C22⋊Q8—142no—
278C22⋊Q8—142no—
279C22⋊Q8—142no—
280C4×Q8—142no—
281C4×Q8—141no—
282C4×Q8—141no—
283C4×D4—22no—
284C4×D4—22no—
285C4×D4—144no—
286C4×D4—144no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—71no—
289C2×C4⋊C4—72no—
290C2×C4⋊C4—71no—
291C2×C4⋊C4—72no—
292C2×C4⋊C4—74no—
293C2×C4⋊C4—72no—
294C2×C4⋊C4—72no—
295C2×C4⋊C4—71no—
296C2×C4⋊C4—72no—
297C2×C4⋊C4—72no—
298C2×C4⋊C4—72no—
299C2×C4⋊C4—72no—
300C2×C4⋊C4—142no—
301C2×C4⋊C4—141no—
302C2×C4⋊C4—141no—
303C2×C4⋊C4—144no—
304C2×C4⋊C4C4×D711yescharacteristic
305C2×C22⋊C4—72no—
306C2×C22⋊C4—72no—
307C2×C22⋊C4—72no—
308C2×C22⋊C4—72no—
309C2×C22⋊C4C4×D711yescharacteristic
310C2×C22⋊C4C22×D714yes—
311C2×C22⋊C4C22×D711yescharacteristic
312C2×C42—72no—
313C2×C42—142no—
314C2×C42—144no—
315C2×C42C4×D711yescharacteristic
316#99—24no—
317#99—74no—
318#99—142no—
319#95—22no—
320#95—144no—
321#95—144no—
322#95—142no—
323C22×C7—22no—
324C22×C7—21no—
325C22×C7—22no—
326C22×C7—21no—
327C22×C7—22no—
328C22×C7—41no—
329C22×C7—41no—
330C22×C7—42no—
331C22×C7—42no—
332C22×C7—42no—
333C22×C7—41no—
334C22×C7—41no—
335C22×C7C22×C22⋊C411yescharacteristic
336C22×C7C2×C4×Q811yescharacteristic
337C22×C7#51911yescharacteristic
338C22×C7#54812yes—
339C22×C7D4×Q812yes—
340C4×C7—22no—
341C4×C7—21no—
342C4×C7—22no—
343C4×C7—41no—
344C4×C7—41no—
345C4×C7—84no—
346C4×C7#41012yes—
347Dic7—24no—
348Dic7—22no—
349Dic7—22no—
350Dic7—44no—
351Dic7—42no—
352Dic7—42no—
353Dic7—82no—
354C24C2×C4×D711yescharacteristic
355C24C23×D711yescharacteristic
356C2×Q8—144no—
357C2×Q8—141no—
358C2×Q8—141no—
359C2×Q8—282no—
360C2×Q8—562no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4#115912yes—
364C2×D4Q8×D712yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—24no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—72no—
371C22×C4—72no—
372C22×C4—74no—
373C22×C4—74no—
374C22×C4—72no—
375C22×C4—72no—
376C22×C4—142no—
377C22×C4—142no—
378C22×C4—142no—
379C22×C4—142no—
380C22×C4—562no—
381C22×C4—562no—
382C22×C4C2×C4×D711yescharacteristic
383C22×C4C2×C4×D711yescharacteristic
384C22×C4C2×C4×D711yescharacteristic
385C22×C4C2×C4×D711yescharacteristic
386C22×C4C2×C4×D711yescharacteristic
387C22×C4D4×D712yes—
388C22×C4D4×D712yes—
389C4⋊C4—22no—
390C4⋊C4—44no—
391C4⋊C4—72no—
392C4⋊C4—71no—
393C4⋊C4—71no—
394C4⋊C4—74no—
395C4⋊C4—74no—
396C4⋊C4—72no—
397C4⋊C4—72no—
398C4⋊C4—142no—
399C4⋊C4—142no—
400C4⋊C4—144no—
401C4⋊C4—142no—
402C4⋊C4—142no—
403C4⋊C4—144no—
404C4⋊C4—144no—
405C4⋊C4—141no—
406C4⋊C4—141no—
407C4⋊C4—564no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—74no—
413C22⋊C4—144no—
414C22⋊C4—144no—
415C22⋊C4—142no—
416C22⋊C4—142no—
417C22⋊C4—142no—
418C42—21no—
419C42—21no—
420C42—142no—
421C42—142no—
422C42—284no—
423C42—564no—
424C2×C7—22no—
425C2×C7—22no—
426C2×C7—21no—
427C2×C7—21no—
428C2×C7—42no—
429C2×C7Q8×C22⋊C411yescharacteristic
430C2×C7C2×#41011yescharacteristic
431C2×C7#288311yescharacteristic
432C23—21no—
433C23—21no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23#645012yes—
439C23C22×C4×D711yescharacteristic
440C23C2×D4×D712yes—
441C23C2×#115911yescharacteristic
442C23C2×Q8×D711yescharacteristic
443C23#655412yes—
444Q8—282no—
445Q8—282no—
446Q8—564no—
447D4—24no—
448D4—24no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—72no—
465C2×C4—72no—
466C2×C4—74no—
467C2×C4—142no—
468C2×C4—142no—
469C2×C4—144no—
470C2×C4—284no—
471C2×C4—284no—
472C2×C4—282no—
473C2×C4—282no—
474C2×C4—282no—
475C2×C4—282no—
476C2×C4—282no—
477C2×C4—282no—
478C2×C4—282no—
479C2×C4—282no—
480C2×C4—282no—
481C2×C4—562no—
482C2×C4—562no—
483C2×C4D7×C22⋊C411yescharacteristic
484C2×C4D7×C22⋊C412yes—
485C2×C4D7×C22⋊C411yescharacteristic
486C2×C4#645012yes—
487C7#2251311yescharacteristic, complemented, Sylow
488C22—22no—
489C22—21no—
490C22—22no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—41no—
499C22—41no—
500C22C2×D7×C22⋊C411yescharacteristic
501C22C2×#645011yescharacteristic
502C22#9020711yescharacteristic
503C22#9028912yes—
504C22#9032312yes—
505C4—21no—
506C4—22no—
507C4—22no—
508C4—41no—
509C4—41no—
510C4—84no—
511C4—142no—
512C4—142no—
513C4—144no—
514C4—284no—
515C4—282no—
516C4—282no—
517C4—562no—
518C4#8951212yes—
519C2—22no—
520C2—22no—
521C2—21no—
522C2—21no—
523C2—42no—
524C2#1173132111yescharacteristic
525C2C2×#8951211yescharacteristic
526C2#1173613911yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC7×#1799C2
socleC22×C7C22×C22⋊C4
prime radicalC22×C7×D4C23
cosocleC24×C7C24
hypercenter#1799D7
hypocenterC7#22513
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #11731324C2semidirect
7. #11727283C2semidirect
8. #11726709C2semidirect
11. C22×C4⋊Dic7C4semidirect
13. C2×#6487C4semidirect
18. C2×#6453C4semidirect
19. C2×#6441C4semidirect
21. C2×#6432C4semidirect
22. C2×C4×Dic14C4semidirect
96. #6408Q8semidirect
487. C7#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#902342
#117313242
C7×#17992
C4×#64082
#117277822
Dic7×#992
#117272832
#117267092
#225137