Finite Group Databasebeta

← #13282007

Subgroups — #13282007

Order 1792.

1246 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#384C211yesmaximal, characteristic
2C2×#89753C212yesmaximal
3#11729323C212yesmaximal
4#11729319C212yesmaximal
5#11729319C212yesmaximal
6#11729318C212yesmaximal
7#11729318C212yesmaximal
8#11729288C211yesmaximal, characteristic
9#11729288C211yesmaximal, characteristic
10C22×C7×C4⋊C4C2212yes—
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C7×C4⋊C4C2212yes—
13C22×C7×C4⋊C4C2211yescharacteristic
14C22×C42×C7C2211yescharacteristic
15C22×C4⋊Dic7C2212yes—
16C22×C4×Dic7C2212yes—
17C7×#384C418yescomplemented
18C2×C7⋊#95C2212yes—
19C2×C7⋊#95C2212yes—
20C2×C7⋊#95C2212yes—
21C2×C7⋊#95C2211yescharacteristic
22C2×C7⋊#95C2211yescharacteristic
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2212yes—
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2212yes—
29C2×C7⋊#95C2212yes—
30C2×C7⋊#95C2211yescharacteristic
31C2×C7⋊#95C2211yescharacteristic
32#89753—28no—
33#14425—71nomaximal, Sylow
34C23×C4×C7C2312yes—
35C23×C4×C7C2312yes—
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2311yescharacteristic
39C23×Dic7C2312yes—
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C23×Dic7C2312yes—
43C2×C7×C4⋊C4—24no—
44C2×C7×C4⋊C4—24no—
45C2×C7×C4⋊C4—42no—
46C2×C7×C4⋊C4—42no—
47C2×C7×C4⋊C4—42no—
48C2×C7×C4⋊C4—42no—
49C2×C7×C4⋊C4C2×C418yes—
50C2×C7×C4⋊C4C2×C414yes—
51C2×C7×C4⋊C4C2×C414yes—
52C2×C7×C4⋊C4C2×C418yes—
53C2×C42×C7—24no—
54C2×C42×C7C2×C414yes—
55C2×C4⋊Dic7—24no—
56C2×C4⋊Dic7—42no—
57C2×C4⋊Dic7—42no—
58C2×C4×Dic7—24no—
59C2×C4×Dic7—42no—
60C2×C4×Dic7—42no—
61C7⋊#95—24no—
62C7⋊#95—24no—
63C7⋊#95—24no—
64C7⋊#95—22no—
65C7⋊#95—24no—
66C7⋊#95—22no—
67C7⋊#95—24no—
68C7⋊#95—24no—
69C7⋊#95—42no—
70C7⋊#95—42no—
71C7⋊#95—42no—
72C7⋊#95—42no—
73C7⋊#95D414yes—
74C7⋊#95Q814yes—
75C2×#387—72no—
76C2×#384D711yescharacteristic
77#1445—72no—
78#1441—72no—
79#1441—72no—
80#1436—72no—
81#1436—72no—
82#1434—71no—
83#1434—71no—
84C24×C7C2411yescharacteristic
85C22×C4×C7—22no—
86C22×C4×C7—22no—
87C22×C4×C7—22no—
88C22×C4×C7—22no—
89C22×C4×C7—21no—
90C22×C4×C7—21no—
91C22×C4×C7—22no—
92C22×C4×C7—22no—
93C22×C4×C7—22no—
94C22×C4×C7—22no—
95C22×C4×C7—22no—
96C22×C4×C7—22no—
97C22×C4×C7—22no—
98C22×C4×C7—22no—
99C22×C4×C7—22no—
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—22no—
103C22×C4×C7—22no—
104C22×C4×C7C22×C414yes—
105C22×C4×C7C22×C414yes—
106C22×C4×C7C22×C412yes—
107C22×C4×C7C22×C412yes—
108C22×C4×C7C22×C412yes—
109C22×C4×C7C2×D412yes—
110C22×C4×C7C2×Q812yes—
111C22×C4×C7#4114yes—
112C22×C4×C7#4112yes—
113C22×C4×C7#4112yes—
114C22×Dic7—22no—
115C22×Dic7—22no—
116C22×Dic7—22no—
117C22×Dic7—22no—
118C22×Dic7—22no—
119C22×Dic7—22no—
120C22×Dic7—22no—
121C22×Dic7—22no—
122C22×Dic7—22no—
123C22×Dic7—22no—
124C22×Dic7—22no—
125C22×Dic7—22no—
126C22×Dic7—22no—
127C22×Dic7—22no—
128C22×Dic7—22no—
129C22×Dic7—22no—
130C22×Dic7—22no—
131C22×Dic7—22no—
132C22×Dic7—22no—
133C22×Dic7—22no—
134C22×Dic7—22no—
135C22×Dic7—22no—
136C22×Dic7—22no—
137C22×Dic7—22no—
138C22×Dic7—22no—
139C22×Dic7—22no—
140C22×Dic7C2×D414yes—
141C22×Dic7C2×Q814yes—
142C7×C4⋊C4—216no—
143C7×C4⋊C4—44no—
144C7×C4⋊C4—44no—
145C7×C4⋊C4—48no—
146C42×C7—28no—
147C4⋊Dic7—48no—
148C4×Dic7—48no—
149C22×C4⋊C4—72no—
150C22×C4⋊C4C2×D712yes—
151C22×C4⋊C4C2×D711yescharacteristic
152C22×C4⋊C4C2×D712yes—
153C22×C4⋊C4C2×D711yescharacteristic
154C22×C42—72no—
155C22×C42C2×D711yescharacteristic
156#387—148no—
157#384Dic718yescomplemented
158C2×#95—71no—
159C2×#95—71no—
160C2×#95—72no—
161C2×#95—72no—
162C2×#95—72no—
163C2×#95—71no—
164C2×#95—71no—
165C2×#95—72no—
166C2×#95—72no—
167C2×#95—72no—
168C2×#95—72no—
169C2×#95—72no—
170C2×#95—72no—
171C2×#95—72no—
172C23×C7C23×C411yescharacteristic
173C23×C7C22×D411yescharacteristic
174C23×C7C22×Q811yescharacteristic
175C23×C7C2×#4112yes—
176C23×C7C2×#4111yescharacteristic
177C23×C7C2×#4111yescharacteristic
178C23×C7H(5,𝔽2)12yes—
179C23×C7H(5,𝔽2)12yes—
180C23×C72−1+411yescharacteristic
181C23×C72−1+411yescharacteristic
182C23×C72−1+412yes—
183C2×C4×C7—22no—
184C2×C4×C7—22no—
185C2×C4×C7—22no—
186C2×C4×C7—22no—
187C2×C4×C7—22no—
188C2×C4×C7—22no—
189C2×C4×C7—24no—
190C2×C4×C7—24no—
191C2×C4×C7—24no—
192C2×C4×C7—24no—
193C2×C4×C7—24no—
194C2×C4×C7—24no—
195C2×C4×C7—24no—
196C2×C4×C7—24no—
197C2×C4×C7—24no—
198C2×C4×C7—24no—
199C2×C4×C7—24no—
200C2×C4×C7—24no—
201C2×C4×C7—42no—
202C2×C4×C7—42no—
203C2×C4×C7—42no—
204C2×C4×C7—42no—
205C2×C4×C7—42no—
206C2×C4×C7—42no—
207C2×C4×C7—42no—
208C2×C4×C7—42no—
209C2×C4×C7#11714yes—
210C2×C4×C7C4×D414yes—
211C2×C4×C7C4×Q814yes—
212C2×Dic7—24no—
213C2×Dic7—24no—
214C2×Dic7—24no—
215C2×Dic7—24no—
216C2×Dic7—24no—
217C2×Dic7—24no—
218C2×Dic7—42no—
219C2×Dic7—42no—
220C2×Dic7—42no—
221C2×Dic7—42no—
222C2×Dic7—42no—
223C2×Dic7—42no—
224C2×Dic7—42no—
225C2×Dic7—42no—
226C2×Dic7—42no—
227C2×Dic7—42no—
228C2×Dic7—42no—
229C2×Dic7—42no—
230C2×Dic7—42no—
231C2×Dic7—42no—
232C2×Dic7—42no—
233C2×Dic7—42no—
234C2×Dic7—42no—
235C2×Dic7—42no—
236C2×Dic7—42no—
237C2×Dic7—42no—
238C2×Dic7—42no—
239C2×Dic7—42no—
240C23×C4—72no—
241C23×C4—72no—
242C23×C4—72no—
243C23×C4—72no—
244C23×C4C22×D712yes—
245C23×C4C22×D712yes—
246C23×C4C22×D711yescharacteristic
247C23×C4C22×D711yescharacteristic
248C23×C4C22×D711yescharacteristic
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4—42no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—144no—
256C2×C4⋊C4—282no—
257C2×C4⋊C4—282no—
258C2×C4⋊C4C2×Dic718yes—
259C2×C4⋊C4C2×Dic714yes—
260C2×C4⋊C4C2×Dic714yes—
261C2×C4⋊C4C2×Dic718yes—
262C2×C42—24no—
263C2×C42—144no—
264C2×C42—282no—
265C2×C42—282no—
266C2×C42C2×Dic714yes—
267#95—74no—
268#95—74no—
269#95—144no—
270#95—144no—
271#95—144no—
272#95—144no—
273#95—144no—
274#95—142no—
275#95—144no—
276#95—142no—
277#95—282no—
278#95—282no—
279#95—282no—
280#95—282no—
281C22×C7C2×#11711yescharacteristic
282C22×C7C2×C4×D411yescharacteristic
283C22×C7C2×C4×Q811yescharacteristic
284C22×C7#51811yescharacteristic
285C22×C7#51811yescharacteristic
286C22×C7#51911yescharacteristic
287C22×C7#51911yescharacteristic
288C22×C7#53512yes—
289C22×C7#53912yes—
290C22×C7#53912yes—
291C22×C7#54012yes—
292C22×C7#54212yes—
293C22×C7#54412yes—
294C22×C7#54711yescharacteristic
295C22×C7#54712yes—
296C22×C7D4×Q811yescharacteristic
297C22×C7#55212yes—
298C22×C7#55312yes—
299C22×C7#55412yes—
300C22×C7#55611yescharacteristic
301C22×C7#55711yescharacteristic
302C22×C7#56312yes—
303C22×C7#56312yes—
304C4×C7—24no—
305C4×C7—24no—
306C4×C7—24no—
307C4×C7—44no—
308C4×C7—44no—
309Dic7—44no—
310Dic7—44no—
311Dic7—82no—
312Dic7—82no—
313C24C23×D711yescharacteristic
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—74no—
334C22×C4—74no—
335C22×C4—142no—
336C22×C4—142no—
337C22×C4—142no—
338C22×C4—142no—
339C22×C4—142no—
340C22×C4—142no—
341C22×C4—142no—
342C22×C4—142no—
343C22×C4—142no—
344C22×C4—142no—
345C22×C4—142no—
346C22×C4—142no—
347C22×C4—142no—
348C22×C4—142no—
349C22×C4—142no—
350C22×C4—142no—
351C22×C4—142no—
352C22×C4—142no—
353C22×C4—142no—
354C22×C4—142no—
355C22×C4—142no—
356C22×C4—142no—
357C22×C4—142no—
358C22×C4—142no—
359C22×C4—142no—
360C22×C4—142no—
361C22×C4#115714yes—
362C22×C4D4×D712yes—
363C22×C4#115912yes—
364C22×C4Q8×D712yes—
365C22×C4#116112yes—
366C22×C4C22×Dic714yes—
367C22×C4C22×Dic714yes—
368C22×C4C22×Dic712yes—
369C22×C4C22×Dic712yes—
370C22×C4C22×Dic712yes—
371C4⋊C4—216no—
372C4⋊C4—44no—
373C4⋊C4—44no—
374C4⋊C4—48no—
375C4⋊C4—288no—
376C42—28no—
377C42—288no—
378C2×C7#231311yescharacteristic
379C2×C7#232811yescharacteristic
380C2×C7#233111yescharacteristic
381C2×C7#234411yescharacteristic
382C2×C7#234511yescharacteristic
383C2×C7#236511yescharacteristic
384C2×C7#238111yescharacteristic
385C2×C7#271812yes—
386C2×C7#272012yes—
387C2×C7#279112yes—
388C2×C7#279312yes—
389C23C2×#115712yes—
390C23C2×D4×D711yescharacteristic
391C23C2×#115911yescharacteristic
392C23#654812yes—
393C23#654812yes—
394C23C2×Q8×D711yescharacteristic
395C23C2×#116111yescharacteristic
396C23#655111yescharacteristic
397C23#655111yescharacteristic
398C23#655112yes—
399C23C23×Dic711yescharacteristic
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—144no—
427C2×C4—144no—
428C2×C4—144no—
429C2×C4—144no—
430C2×C4—144no—
431C2×C4—144no—
432C2×C4—282no—
433C2×C4—282no—
434C2×C4—282no—
435C2×C4—282no—
436C2×C4—282no—
437C2×C4—282no—
438C2×C4—282no—
439C2×C4—282no—
440C2×C4—282no—
441C2×C4—282no—
442C2×C4—282no—
443C2×C4—282no—
444C2×C4—282no—
445C2×C4—282no—
446C2×C4—282no—
447C2×C4—282no—
448C2×C4—282no—
449C2×C4—282no—
450C2×C4—282no—
451C2×C4—282no—
452C2×C4—282no—
453C2×C4—282no—
454C2×C4#648914yes—
455C2×C4D4×Dic714yes—
456C2×C4Q8×Dic714yes—
457C7#1442511yescharacteristic, complemented, Sylow
458C22#9019812yes—
459C22#9020212yes—
460C22#9020412yes—
461C22#9020512yes—
462C22#9020612yes—
463C22#9020612yes—
464C22#9040612yes—
465C22#9041012yes—
466C22#9041211yescharacteristic
467C22#9041711yescharacteristic
468C22#9041811yescharacteristic
469C22#9042012yes—
470C22#9042311yescharacteristic
471C22#9042412yes—
472C22#9042612yes—
473C22#9042612yes—
474C22C2×#648911yescharacteristic
475C22C2×D4×Dic711yescharacteristic
476C22#9048911yescharacteristic
477C22#9048911yescharacteristic
478C22C2×Q8×Dic711yescharacteristic
479C22#9050311yescharacteristic
480C22#9050311yescharacteristic
481C4—24no—
482C4—24no—
483C4—24no—
484C4—44no—
485C4—44no—
486C4—284no—
487C4—284no—
488C4—562no—
489C4—562no—
490C2#1173179212yes—
491C2#1173179412yes—
492C2#1173179612yes—
493C2#1173181712yes—
494C2#1173960011yescharacteristic
495C2#1173960411yescharacteristic
496C2#1173960511yescharacteristic
497C2#1174061711yescharacteristic
498C2#1174067311yescharacteristic
499C2#1174067411yescharacteristic
500C2#1174067611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#384C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#384D7
hypocenterC7#14425
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
17. C7×#384C4semidirect
157. #384Dic7semidirect
457. C7#14425semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3842
C2×#897532
#117293232
#117293192
#117293182
#117292882
#144257