Finite Group Databasebeta

← #13280474

Subgroups — #13280474

Order 1792.

1610 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#126C211yesmaximal, characteristic
2C2×#89708C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
4#11729319C212yesmaximal, complemented
5#11729319C212yesmaximal, complemented
6#11729318C212yesmaximal, complemented
7#11729300C212yesmaximal
8#11729300C212yesmaximal
9#11729299C212yesmaximal
10C2×C7×#126—24no—
11C2×C7×#126—24no—
12C2×C7×#126C418yescomplemented
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2211yescharacteristic
16C22×C7×C22⋊C4C2211yescharacteristic
17C22×C7×C22⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×C22⋊Dic7C2214yes—
21C22×C4⋊Dic7C2212yes—
22C22×C4⋊Dic7C2212yes—
23C22×C4×Dic7C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2214yes—
28C2×C7⋊#95C2214yes—
29C2×C7⋊#95C2214yes—
30#89708—24no—
31C4×C4⋊Dic7—24no—
32#14291—71nomaximal, Sylow
33C25×C7C2311yescharacteristic
34C23×C4×C7C2311yescharacteristic
35C23×C4×C7C2311yescharacteristic
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2311yescharacteristic
39C23×C4×C7C2311yescharacteristic
40C23×Dic7C2314yes—
41C23×Dic7C2314yes—
42C7×#126—232no—
43C2×C7×C4⋊C4—22no—
44C2×C7×C4⋊C4—22no—
45C2×C7×C4⋊C4—22no—
46C2×C7×C4⋊C4—22no—
47C2×C7×C4⋊C4—22no—
48C2×C7×C4⋊C4—22no—
49C2×C7×C4⋊C4C2×C414yes—
50C2×C7×C4⋊C4C2×C414yes—
51C2×C7×C4⋊C4C2×C414yes—
52C2×C7×C22⋊C4—22no—
53C2×C7×C22⋊C4—22no—
54C2×C7×C22⋊C4—22no—
55C2×C7×C22⋊C4—22no—
56C2×C7×C22⋊C4—22no—
57C2×C7×C22⋊C4—22no—
58C2×C7×C22⋊C4C2×C414yes—
59C2×C7×C22⋊C4C2×C414yes—
60C2×C7×C22⋊C4C2×C414yes—
61C2×C42×C7C2×C414yes—
62C2×C42×C7D414yes—
63C2×C42×C7D414yes—
64C2×C22⋊Dic7—28no—
65C2×C22⋊Dic7—44no—
66C2×C22⋊Dic7—44no—
67C2×C4⋊Dic7—24no—
68C2×C4⋊Dic7—28no—
69C2×C4⋊Dic7—24no—
70C2×C4⋊Dic7—44no—
71C2×C4×Dic7—24no—
72C2×C4×Dic7—44no—
73C7⋊#95—24no—
74C7⋊#95—24no—
75C7⋊#95—24no—
76C7⋊#95—28no—
77C7⋊#95—44no—
78C7⋊#95—44no—
79C22×#126D711yescharacteristic
80C2×#382—71no—
81C2×C4×C4⋊C4—71no—
82#1441—72no—
83#1441—72no—
84#1439—72no—
85#1439—72no—
86#1437—72no—
87#1436—72no—
88C24×C7—21no—
89C24×C7—21no—
90C24×C7—24no—
91C24×C7—22no—
92C24×C7—22no—
93C24×C7—22no—
94C24×C7—22no—
95C24×C7C22×C412yes—
96C24×C7C2411yescharacteristic
97C22×C4×C7—24no—
98C22×C4×C7—22no—
99C22×C4×C7—22no—
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—21no—
103C22×C4×C7—21no—
104C22×C4×C7—21no—
105C22×C4×C7—21no—
106C22×C4×C7—21no—
107C22×C4×C7—21no—
108C22×C4×C7—24no—
109C22×C4×C7—22no—
110C22×C4×C7—22no—
111C22×C4×C7—22no—
112C22×C4×C7—22no—
113C22×C4×C7C22×C412yes—
114C22×C4×C7C22×C412yes—
115C22×C4×C7C22×C412yes—
116C22×C4×C7C22×C412yes—
117C22×C4×C7C22×C412yes—
118C22×C4×C7C22×C412yes—
119C22×C4×C7C2×D412yes—
120C22×C4×C7C2×D412yes—
121C22×C4×C7C2×D412yes—
122C22×C4×C7C2×D412yes—
123C22×C4×C7C2×D412yes—
124C22×C4×C7C2×D412yes—
125C22×Dic7—24no—
126C22×Dic7—24no—
127C22×Dic7—24no—
128C22×Dic7—24no—
129C22×Dic7—24no—
130C22×Dic7—24no—
131C22×Dic7—24no—
132C22×Dic7—24no—
133C22×Dic7—24no—
134C22×Dic7—24no—
135C22×Dic7—24no—
136C22×Dic7—24no—
137C22×Dic7—24no—
138C22×Dic7#4118yes—
139C7×C4⋊C4—28no—
140C7×C4⋊C4—28no—
141C7×C4⋊C4—28no—
142C7×C22⋊C4—28no—
143C7×C22⋊C4—28no—
144C7×C22⋊C4—28no—
145C42×C7C22⋊C4116yescomplemented
146C22⋊Dic7—416no—
147C4⋊Dic7—216no—
148C4⋊Dic7—48no—
149C4×Dic7—48no—
150C2×#126—24no—
151C2×#126—24no—
152C2×#126Dic718yescomplemented
153C22×C4⋊C4—72no—
154C22×C4⋊C4—72no—
155C22×C4⋊C4C2×D711yescharacteristic
156C22×C4⋊C4C2×D711yescharacteristic
157C22×C4⋊C4C2×D711yescharacteristic
158C22×C22⋊C4—74no—
159C22×C22⋊C4C2×D711yescharacteristic
160C22×C22⋊C4C2×D711yescharacteristic
161C22×C22⋊C4C2×D711yescharacteristic
162C22×C42—72no—
163C22×C42C2×D711yescharacteristic
164#382—144no—
165C4×C4⋊C4—144no—
166C2×#95—72no—
167C2×#95—74no—
168C2×#95—72no—
169C2×#95—72no—
170C2×#95—74no—
171C2×#95—74no—
172C23×C7—22no—
173C23×C7—24no—
174C23×C7—24no—
175C23×C7—24no—
176C23×C7—42no—
177C23×C7—42no—
178C23×C7—41no—
179C23×C7—41no—
180C23×C7—41no—
181C23×C7—41no—
182C23×C7—42no—
183C23×C7—42no—
184C23×C7—44no—
185C23×C7—44no—
186C23×C7—44no—
187C23×C7—44no—
188C23×C7C23×C411yescharacteristic
189C23×C7C22×D411yescharacteristic
190C23×C7C22×D411yescharacteristic
191C23×C7C2×#4114yes—
192C23×C7H(5,𝔽2)12yes—
193C23×C7H(5,𝔽2)12yes—
194C23×C72−1+412yes—
195C23×C72−1+412yes—
196C2×C4×C7—24no—
197C2×C4×C7—24no—
198C2×C4×C7—24no—
199C2×C4×C7—24no—
200C2×C4×C7—24no—
201C2×C4×C7—22no—
202C2×C4×C7—22no—
203C2×C4×C7—22no—
204C2×C4×C7—22no—
205C2×C4×C7—24no—
206C2×C4×C7—24no—
207C2×C4×C7—22no—
208C2×C4×C7—22no—
209C2×C4×C7—22no—
210C2×C4×C7—24no—
211C2×C4×C7—24no—
212C2×C4×C7—24no—
213C2×C4×C7—42no—
214C2×C4×C7—42no—
215C2×C4×C7—41no—
216C2×C4×C7—41no—
217C2×C4×C7—41no—
218C2×C4×C7—41no—
219C2×C4×C7—42no—
220C2×C4×C7—42no—
221C2×C4×C7C2×C22⋊C414yes—
222C2×C4×C7C2×C22⋊C414yes—
223C2×C4×C7C2×C22⋊C414yes—
224C2×Dic7—28no—
225C2×Dic7—28no—
226C2×Dic7—28no—
227C2×Dic7—44no—
228C2×Dic7—44no—
229C2×Dic7—44no—
230C2×Dic7—44no—
231C2×Dic7—44no—
232C2×Dic7—44no—
233C2×Dic7—44no—
234C2×Dic7—44no—
235C2×Dic7—44no—
236C2×Dic7—44no—
237C2×Dic7—44no—
238C25C22×D711yescharacteristic
239C23×C4—74no—
240C23×C4—74no—
241C23×C4C22×D711yescharacteristic
242C23×C4C22×D711yescharacteristic
243C23×C4C22×D711yescharacteristic
244C23×C4C22×D711yescharacteristic
245C23×C4C22×D711yescharacteristic
246C23×C4C22×D711yescharacteristic
247#126—232no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—148no—
255C2×C4⋊C4—144no—
256C2×C4⋊C4—144no—
257C2×C4⋊C4—284no—
258C2×C4⋊C4C2×Dic714yes—
259C2×C4⋊C4C2×Dic714yes—
260C2×C4⋊C4C2×Dic714yes—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—148no—
268C2×C22⋊C4—284no—
269C2×C22⋊C4—284no—
270C2×C22⋊C4C2×Dic714yes—
271C2×C22⋊C4C2×Dic714yes—
272C2×C22⋊C4C2×Dic714yes—
273C2×C42—144no—
274C2×C42—284no—
275C2×C42C2×Dic714yes—
276C2×C42C22⋊D714yes—
277C2×C42C22⋊D714yes—
278#95—148no—
279#95—144no—
280#95—144no—
281#95—144no—
282#95—284no—
283#95—284no—
284C22×C7—42no—
285C22×C7—42no—
286C22×C7—48no—
287C22×C7—42no—
288C22×C7—82no—
289C22×C7—82no—
290C22×C7—82no—
291C22×C7—82no—
292C22×C7C22×C22⋊C411yescharacteristic
293C22×C7C4×#4112yes—
294C22×C7#52012yes—
295C22×C7#52012yes—
296C22×C7#52512yes—
297C22×C7#53212yes—
298C22×C7#53511yescharacteristic
299C22×C7#53511yescharacteristic
300C22×C7#53611yescharacteristic
301C22×C7#53611yescharacteristic
302C22×C7#53712yes—
303C22×C7#53712yes—
304C22×C7#53814yes—
305C22×C7#53914yes—
306C22×C7#54114yes—
307C22×C7#54214yes—
308C4×C7—24no—
309C4×C7—24no—
310C4×C7—24no—
311C4×C7—42no—
312C4×C7—42no—
313C4×C7—42no—
314Dic7—48no—
315Dic7—84no—
316C24—24no—
317C24—22no—
318C24—22no—
319C24—22no—
320C24—22no—
321C24—21no—
322C24—21no—
323C24C22×Dic712yes—
324C24C23×D711yescharacteristic
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—78no—
342C22×C4—144no—
343C22×C4—144no—
344C22×C4—144no—
345C22×C4—144no—
346C22×C4—144no—
347C22×C4—144no—
348C22×C4—144no—
349C22×C4—144no—
350C22×C4—144no—
351C22×C4—144no—
352C22×C4—144no—
353C22×C4—144no—
354C22×C4—144no—
355C22×C4C22×Dic712yes—
356C22×C4C22×Dic712yes—
357C22×C4C22×Dic712yes—
358C22×C4C22×Dic712yes—
359C22×C4C22×Dic712yes—
360C22×C4C22×Dic712yes—
361C22×C4C2×C22⋊D712yes—
362C22×C4C2×C22⋊D712yes—
363C22×C4C2×C22⋊D712yes—
364C22×C4C2×C22⋊D712yes—
365C22×C4C2×C22⋊D712yes—
366C22×C4C2×C22⋊D712yes—
367C4⋊C4—28no—
368C4⋊C4—28no—
369C4⋊C4—28no—
370C4⋊C4—1416no—
371C4⋊C4—288no—
372C22⋊C4—28no—
373C22⋊C4—28no—
374C22⋊C4—28no—
375C22⋊C4—2816no—
376C42—288no—
377C42C22⋊Dic7116yescomplemented
378C2×C7—82no—
379C2×C7#229711yescharacteristic
380C2×C7#231111yescharacteristic
381C2×C7#231111yescharacteristic
382C2×C7#233414yes—
383C2×C7#263612yes—
384C2×C7#263712yes—
385C2×C7#266212yes—
386C2×C7#266412yes—
387C23—24no—
388C23—24no—
389C23—24no—
390C23—22no—
391C23—44no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—41no—
396C23—41no—
397C23—42no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23D7×#4114yes—
404C23#655312yes—
405C23#655312yes—
406C23#655412yes—
407C23#655412yes—
408C23C23×Dic711yescharacteristic
409C23C22×C22⋊D711yescharacteristic
410C23C22×C22⋊D711yescharacteristic
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—148no—
437C2×C4—148no—
438C2×C4—148no—
439C2×C4—284no—
440C2×C4—284no—
441C2×C4—284no—
442C2×C4—284no—
443C2×C4—284no—
444C2×C4—284no—
445C2×C4—284no—
446C2×C4—284no—
447C2×C4—284no—
448C2×C4—284no—
449C2×C4—284no—
450C2×C4C2×C22⋊Dic714yes—
451C2×C4C2×C22⋊Dic714yes—
452C2×C4C2×C22⋊Dic714yes—
453C7#1429111yescharacteristic, complemented, Sylow
454C22—42no—
455C22—42no—
456C22—42no—
457C22—48no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—82no—
462C22#9039214yes—
463C22#9039514yes—
464C22#9039814yes—
465C22#9040114yes—
466C22#9051611yescharacteristic
467C22#9051611yescharacteristic
468C22#41×Dic712yes—
469C22#9051812yes—
470C22#9051812yes—
471C22#9051912yes—
472C22#9052111yescharacteristic
473C22#9052111yescharacteristic
474C22#9052312yes—
475C22#9052412yes—
476C22#9052412yes—
477C22C22×C22⋊Dic711yescharacteristic
478C4—24no—
479C4—24no—
480C4—24no—
481C4—42no—
482C4—42no—
483C4—42no—
484C4—288no—
485C4—564no—
486C2—82no—
487C2#1174051914yes—
488C2#1174053412yes—
489C2#1174053512yes—
490C2#1174055712yes—
491C2#1174055812yes—
492C2#1174153111yescharacteristic
493C2#1174153211yescharacteristic
494C2#1174153211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC22×C7×#126C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22×#126D7
hypocenterC7#14291
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
2. C2×#89708C2semidirect
3. C2×C4×C4⋊Dic7C2semidirect
4. #11729319C2semidirect
5. #11729319C2semidirect
6. #11729318C2semidirect
12. C2×C7×#126C4semidirect
145. C42×C7C22⋊C4semidirect
152. C2×#126Dic7semidirect
377. C42C22⋊Dic7semidirect
453. C7#14291semidirect

Maximal subgroups

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

subgroupindex
C22×C7×#1262
C2×#897082
C2×C4×C4⋊Dic72
#117293192
#117293182
#117293002
#117292992
#142917