Finite Group Databasebeta

← #13322276

Subgroups — #13322276

Order 1792.

884 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11743272C211yesmaximal, characteristic
2#11736458C211yesmaximal, characteristic
3#11736445C211yesmaximal, characteristic
4C2×C7×#332C211yesmaximal, characteristic, complemented
5#11729527C211yesmaximal, characteristic, complemented
6#11728192C211yesmaximal, characteristic, complemented
7#11728191C211yesmaximal, characteristic, complemented
8#11726181C212yesmaximal, complemented
9#11726178C212yesmaximal, complemented
10#11726173C212yesmaximal, complemented
11#11726172C212yesmaximal, complemented
12C2×C7×C4⋊Q8C2211yescharacteristic
13#90507—21no—
14#90503—21no—
15#90423—21no—
16#90423C412yes—
17#90422—22no—
18#90419C2212yes—
19#90419C2212yes—
20#90412—21no—
21#90412C412yes—
22#90204—22no—
23#90204C414yes—
24C4×#1157C2211yescharacteristic
25#90161C2211yescharacteristic
26C2×C7×C4⋊C8C2211yescharacteristic
27C2×C7×C4⋊C8C2211yescharacteristic
28#89882—21no—
29C8×C22⋊D7—22no—
30#89873—21no—
31#89697C2211yescharacteristic
32#89696C2211yescharacteristic
33#89612—22no—
34#89607C2212yes—
35#89606—21no—
36#89605C2212yes—
37#89605C2212yes—
38D7×C4⋊C8C2212yes—
39#89602—21no—
40C7×#332C2212yes—
41C7×#332C2212yes—
42#89342C2212yes—
43#89342C2212yes—
44#89281C2211yescharacteristic
45#89281C2211yescharacteristic
46#89277C2212yes—
47#89276C2211yescharacteristic
48#89276C2211yescharacteristic
49#89276C2212yes—
50#17725—71nomaximal, Sylow
51C22×C7×Q8—21no—
52C2×#1157D411yescharacteristic
53C22×C7×C8—21no—
54C22×C7×C8—21no—
55C7×C4⋊Q8—21no—
56C7×C4⋊Q8—21no—
57C7×C4⋊Q8C2×C412yes—
58C7×C4⋊Q8C2312yes—
59C2×C7×C4⋊C4—21no—
60C2×C7×C4⋊C4C2×C412yes—
61C2×C42×C7C2311yescharacteristic
62#6510—22no—
63#6509—22no—
64#6509—22no—
65Q8×Dic7—22no—
66Q8×Dic7—22no—
67Q8×Dic7—22no—
68Q8×Dic7—22no—
69#6507—22no—
70#6492—24no—
71C4×C22⋊D7C2×C412yes—
72C4×C22⋊D7D412yes—
73#6489—21no—
74#6489—24no—
75#6489D411yescharacteristic
76#6487—21no—
77#6487C2×C412yes—
78C2×#1136—21no—
79C2×C8×D7—22no—
80#6461—24no—
81#6461—24no—
82#6460—22no—
83#6460C2×C414yes—
84#6455—22no—
85#6455C2×C414yes—
86#6453—22no—
87#6453C2×C414yes—
88#6452—24no—
89#6452—24no—
90#6450—22no—
91#6450C2×C414yes—
92C4×D28C2×C411yescharacteristic
93C4×D28D411yescharacteristic
94#6435D412yes—
95C42×D7C2312yes—
96#6433—21no—
97#6432C2311yescharacteristic
98#6432C2311yescharacteristic
99C4×Dic14—21no—
100C4×Dic14C2×C412yes—
101C4×Dic14C2×C411yescharacteristic
102C4×Dic14D411yescharacteristic
103C7×C4⋊C8—21no—
104C7×C4⋊C8—21no—
105C7×C4⋊C8C2312yes—
106C7×C4⋊C8C2311yescharacteristic
107C7×C4⋊C8C2311yescharacteristic
108C22⋊(C7⋊C8)—21no—
109(C2×D7)⋊C8—22no—
110(C2×D7)⋊C8—22no—
111(C2×D7)⋊C8—22no—
112#6389—22no—
113Dic7⋊C8—22no—
114C8×Dic7—22no—
115C8×Dic7—22no—
116C4⋊(C7⋊C8)—21no—
117C4⋊(C7⋊C8)C2311yescharacteristic
118C4⋊(C7⋊C8)C2311yescharacteristic
119C4⋊(C7⋊C8)C2312yes—
120C4×C7⋊C8—21no—
121#3509—71no—
122#2988—71no—
123#2925—71no—
124#1554—72no—
125#1552—72no—
126#1550—71no—
127#1546—71no—
128#1544—72no—
129#1542—71no—
130#1542—72no—
131C2×#332D711yescharacteristic, complemented
132C2×C7×Q8—22no—
133C2×C7×Q8—22no—
134C2×C7×Q8—42no—
135C2×C7×Q8—42no—
136C22×C4×C7—22no—
137C22×C4×C7C22×C411yescharacteristic
138C22×C4×C7C2×D411yescharacteristic
139C22×C4×C7C2×D411yescharacteristic
140C2×C22⋊D7C22⋊C412yes—
141#1157—22no—
142#1157—22no—
143C2×D28C22⋊C411yescharacteristic
144C2×C4×D7C22×C412yes—
145C2×C4×D7C2×D412yes—
146C2×C4×D7C2×D412yes—
147C2×Dic14—21no—
148C2×Dic14C22⋊C411yescharacteristic
149C2×Dic14C22×C412yes—
150C2×C7×C8—22no—
151C2×C7×C8—21no—
152C2×C7×C8—21no—
153C2×C7×C8—42no—
154C2×C7×C8—81no—
155C7×C4⋊C4—22no—
156C7×C4⋊C4—22no—
157C7×C4⋊C4—22no—
158C7×C4⋊C4C22×C414yes—
159C42×C7C22×C411yescharacteristic
160C42×C7C2×D411yescharacteristic
161C42×C7C2×D411yescharacteristic
162C42×C7C2411yescharacteristic
163C22⋊Dic7—22no—
164C22⋊Dic7C22⋊C412yes—
165(C2×D7)⋊C4—24no—
166(C2×D7)⋊C4—24no—
167(C2×D7)⋊C4C22⋊C412yes—
168(C2×D7)⋊C4C22⋊C412yes—
169C4⋊Dic7—21no—
170C4⋊Dic7—21no—
171C4⋊Dic7—21no—
172C4⋊Dic7—24no—
173C4⋊Dic7—24no—
174C4⋊Dic7C22⋊C411yescharacteristic
175C4⋊Dic7C22⋊C411yescharacteristic
176C4⋊Dic7C22×C412yes—
177Dic7⋊C4—22no—
178Dic7⋊C4—22no—
179Dic7⋊C4—24no—
180Dic7⋊C4—24no—
181Dic7⋊C4C22⋊C412yes—
182Dic7⋊C4C22⋊C412yes—
183C4×Dic7—22no—
184C4×Dic7—24no—
185C4×Dic7—24no—
186C4×Dic7C22×C412yes—
187C4×Dic7C2×D412yes—
188C4×Dic7C2×D412yes—
189#1136—42no—
190C2×C7⋊C8—21no—
191C2×C7⋊C8—21no—
192C2×C7⋊C8—22no—
193C8×D7—82no—
194#557—72no—
195#557—141no—
196#556—72no—
197#556—141no—
198#552—74no—
199#552—142no—
200#541—142no—
201#536—141no—
202#533—72no—
203#533—72no—
204#533—71no—
205C2×C4⋊Q8C2×D711yescharacteristic
206#519—141no—
207C4×#41—71no—
208C8×Q8—141no—
209C8×D4—141no—
210C8×D4—142no—
211#433—142no—
212#432—72no—
213#431—71no—
214#431—72no—
215#431—72no—
216#423—71no—
217C2×C4⋊C8—72no—
218C2×C4⋊C8C2×D711yescharacteristic
219C2×C4⋊C8C2×D711yescharacteristic
220#408—141no—
221#405—141no—
222#333—71no—
223#333—72no—
224#333—71no—
225#332—72no—
226#332—72no—
227#332—71no—
228#332—71no—
229#332—72no—
230#332C2×D712yes—
231#332C2×D712yes—
232C23×C7C2×C22⋊C411yescharacteristic
233C22×D7C2×C22⋊C412yes—
234C7×Q8—42no—
235C7×Q8—42no—
236C7×Q8—44no—
237C2×C4×C7—21no—
238C2×C4×C7—21no—
239C2×C4×C7—24no—
240C2×C4×C7—41no—
241C2×C4×C7—44no—
242C2×C4×C7C2×C22⋊C411yescharacteristic
243C2×C4×C7C2×C22⋊C411yescharacteristic
244C2×C4×C7C2×C22⋊C411yescharacteristic
245C2×C4×C7#13512yes—
246C2×C4×C7#13512yes—
247C2×C4×C7C23×C411yescharacteristic
248C2×C4×C7C22×D411yescharacteristic
249C2×C4×C7C22×D411yescharacteristic
250C22⋊D7—24no—
251C2×Dic7—22no—
252C2×Dic7—22no—
253C2×Dic7C2×C22⋊C412yes—
254C2×Dic7C2×C22⋊C412yes—
255C2×Dic7C2×C22⋊C412yes—
256D28—22no—
257C4×D7—22no—
258C4×D7—22no—
259C4×D7—22no—
260C4×D7—22no—
261C4×D7—42no—
262Dic14—22no—
263Dic14—41no—
264Dic14—41no—
265Dic14—42no—
266C7×C8—41no—
267C7×C8—41no—
268C7×C8—42no—
269C7⋊C8—42no—
270C7⋊C8—41no—
271C7⋊C8—41no—
272C2×#41—71no—
273C22×Q8—21no—
274C2×M16—141no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—142no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—71no—
281C4⋊Q8—71no—
282C4⋊Q8—142no—
283C4⋊Q8C4×D712yes—
284C4⋊Q8C22×D712yes—
285#126—144no—
286#126—144no—
287#125—74no—
288#125—142no—
289#125—144no—
290#125—144no—
291#125—141no—
292#124—142no—
293#123—144no—
294C22⋊Q8—72no—
295C22⋊Q8—74no—
296C22⋊Q8—142no—
297C22⋊Q8—142no—
298C22⋊Q8—142no—
299C22⋊Q8—141no—
300C4×Q8—71no—
301C4×Q8—71no—
302C4×Q8—74no—
303C4×Q8—72no—
304C4×Q8—142no—
305C4×Q8—142no—
306C4×Q8—142no—
307C4×Q8—142no—
308C4×Q8—142no—
309C4×Q8—141no—
310C4×D4—72no—
311C4×D4—72no—
312C4×D4—71no—
313C4×D4—71no—
314#117—71no—
315#117—72no—
316#117—74no—
317#117—144no—
318#117—142no—
319#117—141no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4C4×D712yes—
322C2×C42—72no—
323C2×C42C22×D711yescharacteristic
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8—71no—
327C4⋊C8—72no—
328C4⋊C8—71no—
329C4⋊C8—142no—
330C4⋊C8—141no—
331C4⋊C8C22×D712yes—
332C4⋊C8C22×D711yescharacteristic
333C4⋊C8C22×D711yescharacteristic
334C22⋊C8—142no—
335C22⋊C8—142no—
336C22⋊C8—142no—
337C22⋊C8—141no—
338#97—142no—
339C4×C8—142no—
340C4×C8—142no—
341C4×C8—141no—
342C22×C7—21no—
343C22×C7—21no—
344C22×C7#41612yes—
345C22×C7C22×C22⋊C411yescharacteristic
346C2×D7—22no—
347C2×D7—22no—
348C2×D7—22no—
349C4×C7—21no—
350C4×C7—21no—
351C4×C7—21no—
352C4×C7—44no—
353C4×C7#41612yes—
354C4×C7C2×#13511yescharacteristic
355C4×C7C2×#13511yescharacteristic
356C4×C7#57711yescharacteristic
357C4×C7#57811yescharacteristic
358Dic7—22no—
359Dic7—22no—
360Dic7—22no—
361Dic7—42no—
362Dic7—42no—
363#41—142no—
364#41—142no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—71no—
370C2×Q8—72no—
371C2×Q8—141no—
372C2×D4—72no—
373C2×D4—71no—
374C22×C4—22no—
375C22×C4—72no—
376C22×C4—72no—
377C22×C4—72no—
378C22×C4C2×C4×D711yescharacteristic
379C22×C4D4×D711yescharacteristic
380C22×C4D4×D711yescharacteristic
381M16—282no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—42no—
386C2×C8—81no—
387C2×C8—141no—
388C2×C8—142no—
389C2×C8—141no—
390C2×C8—562no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—72no—
395C4⋊C4—72no—
396C4⋊C4—71no—
397C4⋊C4—71no—
398C4⋊C4—72no—
399C4⋊C4—144no—
400C4⋊C4—144no—
401C4⋊C4—144no—
402C4⋊C4—144no—
403C4⋊C4—142no—
404C4⋊C4—142no—
405C4⋊C4—141no—
406C4⋊C4—141no—
407C4⋊C4—141no—
408C4⋊C4C2×C4×D714yes—
409C22⋊C4—72no—
410C22⋊C4—72no—
411C22⋊C4—72no—
412C22⋊C4—144no—
413C22⋊C4—144no—
414C22⋊C4—142no—
415C42—72no—
416C42—72no—
417C42—72no—
418C42—144no—
419C42—144no—
420C42—142no—
421C42C2×C4×D711yescharacteristic
422C42D4×D711yescharacteristic
423C42D4×D711yescharacteristic
424C42C23×D711yescharacteristic
425C2×C7—22no—
426C2×C7#288911yescharacteristic
427C2×C7C2×#41611yescharacteristic
428C2×C7#289811yescharacteristic
429D7—42no—
430C23—72no—
431C23D7×C22⋊C411yescharacteristic
432Q8—42no—
433Q8—42no—
434Q8—44no—
435Q8—142no—
436Q8—282no—
437Q8—281no—
438Q8—281no—
439D4—144no—
440D4—142no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—41no—
445C2×C4—44no—
446C2×C4—72no—
447C2×C4—72no—
448C2×C4—72no—
449C2×C4—142no—
450C2×C4—142no—
451C2×C4—142no—
452C2×C4—142no—
453C2×C4—142no—
454C2×C4—142no—
455C2×C4—282no—
456C2×C4D7×C22⋊C411yescharacteristic
457C2×C4D7×C22⋊C411yescharacteristic
458C2×C4D7×C22⋊C411yescharacteristic
459C2×C4#647512yes—
460C2×C4#647912yes—
461C2×C4C22×C4×D711yescharacteristic
462C2×C4C2×D4×D711yescharacteristic
463C2×C4C2×D4×D711yescharacteristic
464C8—41no—
465C8—41no—
466C8—42no—
467C8—282no—
468C8—281no—
469C8—281no—
470C7#1772511yescharacteristic, complemented, Sylow
471C22—21no—
472C22—21no—
473C22—142no—
474C22—142no—
475C22—142no—
476C22#8954412yes—
477C22C2×D7×C22⋊C411yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—142no—
483C4—142no—
484C4—142no—
485C4—282no—
486C4—282no—
487C4#8954412yes—
488C4C2×#647511yescharacteristic
489C4C2×#647911yescharacteristic
490C4#9045311yescharacteristic
491C4#9045711yescharacteristic
492C2—22no—
493C2—282no—
494C2#1173615111yescharacteristic
495C2C2×#8954411yescharacteristic
496C2#1173623511yescharacteristic
subgroupG/H
centerC22C2×D7×C22⋊C4
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC2×C7×#332C2
socleC22×C7C22×C22⋊C4
prime radicalC2×#1157D4
cosocleC42×C7C24
hypercenterC2×#332D7
hypocenterC7#17725
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
4. C2×C7×#332C2semidirect
5. #11729527C2semidirect
6. #11728192C2semidirect
7. #11728191C2semidirect
8. #11726181C2semidirect
9. #11726178C2semidirect
10. #11726173C2semidirect
11. #11726172C2semidirect
131. C2×#332D7semidirect
470. C7#17725semidirect

Maximal subgroups

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

subgroupindex
#117432722
#117364582
#117364452
C2×C7×#3322
#117295272
#117281922
#117281912
#117261812
#117261782
#117261732
#117261722
#177257