Finite Group Databasebeta

← #13284794

Subgroups — #13284794

Order 1792.

1030 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#400C211yesmaximal, characteristic
2#11729323C211yesmaximal, characteristic
3#11729319C212yesmaximal
4#11729318C211yesmaximal, characteristic
5#11727166C212yesmaximal
6#11727166C212yesmaximal
7#11727166C212yesmaximal
8#11727166C212yesmaximal
9#11727161C212yesmaximal
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C7×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic7C2212yes—
13C22×C4⋊Dic7C2212yes—
14C22×C4×Dic7C2211yescharacteristic
15C7×#400C418yescomplemented
16C2×C7×#95C2212yes—
17C2×C7×#95C2211yescharacteristic
18C2×C7×#95C2212yes—
19C2×C7⋊#95C2212yes—
20C2×C7⋊#95C2212yes—
21C2×C7⋊#95C2212yes—
22C2×C7⋊#95C2212yes—
23C2×C7⋊#95C2212yes—
24C2×C7⋊#95C2212yes—
25C2×C7⋊#95C2212yes—
26C2×C7⋊#95C2211yescharacteristic
27C2×C7⋊#95C2212yes—
28C2×C7⋊#95C2211yescharacteristic
29C2×C7⋊#95C2211yescharacteristic
30C2×C7⋊#95C2212yes—
31C2×C7⋊#95C2212yes—
32#14654—71nomaximal, Sylow
33C23×C4×C7C2311yescharacteristic
34C23×C4×C7C2312yes—
35C23×C4×C7C2312yes—
36C23×C4×C7C2311yescharacteristic
37C23×C4×C7C2311yescharacteristic
38C23×Dic7C2312yes—
39C23×Dic7C2312yes—
40C23×Dic7C2312yes—
41C23×Dic7C2312yes—
42C2×C7×C4⋊C4—41no—
43C2×C7×C4⋊C4—41no—
44C2×C7×C4⋊C4—41no—
45C2×C7×C4⋊C4—41no—
46C2×C7×C4⋊C4C2×C414yes—
47C2×C7×C4⋊C4C2×C414yes—
48C2×C4⋊Dic7—24no—
49C2×C4⋊Dic7—42no—
50C2×C4⋊Dic7—42no—
51C2×C4⋊Dic7—42no—
52C2×C4⋊Dic7—42no—
53C2×C4⋊Dic7—42no—
54C2×C4×Dic7—41no—
55C2×C4×Dic7—42no—
56C7×#95C2×C414yes—
57C7×#95C2×C418yes—
58C7×#95C2×C418yes—
59C7⋊#95—24no—
60C7⋊#95—24no—
61C7⋊#95—42no—
62C7⋊#95—42no—
63C7⋊#95—42no—
64C7⋊#95—42no—
65C7⋊#95—42no—
66C7⋊#95—41no—
67C7⋊#95—42no—
68C7⋊#95—42no—
69C7⋊#95—42no—
70C7⋊#95—41no—
71C7⋊#95—41no—
72C2×#400D711yescharacteristic
73#1445—71no—
74#1442—72no—
75#1442—72no—
76#1442—72no—
77#1442—72no—
78#1441—72no—
79#1436—72no—
80#1436—71no—
81C24×C7C2411yescharacteristic
82C22×C4×C7—22no—
83C22×C4×C7—22no—
84C22×C4×C7—22no—
85C22×C4×C7—22no—
86C22×C4×C7—22no—
87C22×C4×C7—22no—
88C22×C4×C7—22no—
89C22×C4×C7—22no—
90C22×C4×C7—22no—
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—22no—
94C22×C4×C7—21no—
95C22×C4×C7—21no—
96C22×C4×C7—22no—
97C22×C4×C7—21no—
98C22×C4×C7—21no—
99C22×C4×C7—22no—
100C22×C4×C7—22no—
101C22×C4×C7—22no—
102C22×C4×C7—22no—
103C22×C4×C7—22no—
104C22×C4×C7—22no—
105C22×C4×C7—22no—
106C22×C4×C7C22×C414yes—
107C22×C4×C7C22×C412yes—
108C22×C4×C7C22×C412yes—
109C22×C4×C7C22×C414yes—
110C22×C4×C7C22×C412yes—
111C22×Dic7—22no—
112C22×Dic7—22no—
113C22×Dic7—22no—
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#4114yes—
139C7×C4⋊C4—44no—
140C7×C4⋊C4—44no—
141C4⋊Dic7—48no—
142C4⋊Dic7—48no—
143C4×Dic7—44no—
144C22×C4⋊C4—72no—
145C22×C4⋊C4—72no—
146C22×C4⋊C4C2×D711yescharacteristic
147C22×C4⋊C4C2×D711yescharacteristic
148C22×C42—71no—
149#400Dic718yescomplemented
150C2×#95—72no—
151C2×#95—72no—
152C2×#95—72no—
153C2×#95—72no—
154C2×#95—72no—
155C2×#95—71no—
156C2×#95—72no—
157C2×#95—72no—
158C2×#95—72no—
159C2×#95—72no—
160C2×#95—72no—
161C2×#95—71no—
162C2×#95—71no—
163C2×#95C2×D712yes—
164C2×#95C2×D712yes—
165C2×#95C2×D711yescharacteristic
166C23×C7C23×C411yescharacteristic
167C23×C7C2×#4112yes—
168C23×C7H(5,𝔽2)11yescharacteristic
169C23×C7H(5,𝔽2)11yescharacteristic
170C23×C7H(5,𝔽2)12yes—
171C23×C7H(5,𝔽2)12yes—
172C23×C72−1+412yes—
173C23×C72−1+412yes—
174C23×C72−1+412yes—
175C2×C4×C7—22no—
176C2×C4×C7—24no—
177C2×C4×C7—22no—
178C2×C4×C7—22no—
179C2×C4×C7—22no—
180C2×C4×C7—24no—
181C2×C4×C7—22no—
182C2×C4×C7—24no—
183C2×C4×C7—24no—
184C2×C4×C7—24no—
185C2×C4×C7—24no—
186C2×C4×C7—24no—
187C2×C4×C7—24no—
188C2×C4×C7—42no—
189C2×C4×C7—42no—
190C2×C4×C7—42no—
191C2×C4×C7—42no—
192C2×C4×C7—42no—
193C2×C4×C7—42no—
194C2×C4×C7—41no—
195C2×C4×C7—41no—
196C2×C4×C7—42no—
197C2×C4×C7—42no—
198C2×C4×C7—42no—
199C2×C4×C7—42no—
200C2×C4×C7—42no—
201C2×C4×C7—41no—
202C2×C4×C7—41no—
203C2×C4×C7—42no—
204C2×Dic7—24no—
205C2×Dic7—24no—
206C2×Dic7—24no—
207C2×Dic7—42no—
208C2×Dic7—42no—
209C2×Dic7—42no—
210C2×Dic7—42no—
211C2×Dic7—42no—
212C2×Dic7—42no—
213C2×Dic7—42no—
214C2×Dic7—42no—
215C2×Dic7—42no—
216C2×Dic7—42no—
217C2×Dic7—42no—
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—
232C23×C4—72no—
233C23×C4—72no—
234C23×C4—72no—
235C23×C4—72no—
236C23×C4C22×D712yes—
237C23×C4C22×D712yes—
238C23×C4C22×D711yescharacteristic
239C23×C4C22×D711yescharacteristic
240C23×C4C22×D711yescharacteristic
241C2×C4⋊C4—41no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—41no—
244C2×C4⋊C4—41no—
245C2×C4⋊C4—144no—
246C2×C4⋊C4—282no—
247C2×C4⋊C4—282no—
248C2×C4⋊C4—282no—
249C2×C4⋊C4—282no—
250C2×C4⋊C4—282no—
251C2×C4⋊C4C2×Dic714yes—
252C2×C4⋊C4C2×Dic714yes—
253C2×C42—281no—
254C2×C42—282no—
255#95—144no—
256#95—144no—
257#95—282no—
258#95—281no—
259#95—281no—
260#95—281no—
261#95—282no—
262#95—282no—
263#95—282no—
264#95—282no—
265#95—282no—
266#95—282no—
267#95—282no—
268#95C2×Dic714yes—
269#95C2×Dic718yes—
270#95C2×Dic718yes—
271C22×C7C4×#4111yescharacteristic
272C22×C7#51811yescharacteristic
273C22×C7#51911yescharacteristic
274C22×C7#52012yes—
275C22×C7#52012yes—
276C22×C7#53812yes—
277C22×C7#53912yes—
278C22×C7#53912yes—
279C22×C7#54112yes—
280C22×C7#54212yes—
281C22×C7#54212yes—
282C22×C7#56011yescharacteristic
283C22×C7H(3,𝔽4)11yescharacteristic
284C22×C7#56212yes—
285C22×C7#56212yes—
286C22×C7#56212yes—
287C22×C7#56312yes—
288C22×C7#56312yes—
289C22×C7#56311yescharacteristic
290C22×C7#56311yescharacteristic
291C22×C7#56412yes—
292C4×C7—42no—
293C4×C7—44no—
294C4×C7—42no—
295C4×C7—42no—
296C4×C7—44no—
297Dic7—44no—
298Dic7—82no—
299Dic7—82no—
300Dic7—82no—
301C24C23×D711yescharacteristic
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—74no—
327C22×C4—142no—
328C22×C4—142no—
329C22×C4—142no—
330C22×C4—142no—
331C22×C4—142no—
332C22×C4—142no—
333C22×C4—142no—
334C22×C4—142no—
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×C4C22×Dic714yes—
355C22×C4C22×Dic712yes—
356C22×C4C22×Dic714yes—
357C22×C4C22×Dic712yes—
358C22×C4C22×Dic712yes—
359C4⋊C4—44no—
360C4⋊C4—44no—
361C4⋊C4—288no—
362C4⋊C4—288no—
363C42—284no—
364C2×C7#233211yescharacteristic
365C2×C7#233412yes—
366C2×C7#237611yescharacteristic
367C2×C7#237911yescharacteristic
368C2×C7#238212yes—
369C2×C7#282712yes—
370C2×C7#283212yes—
371C2×C7#283912yes—
372C2×C7#283912yes—
373C23#654811yescharacteristic
374C23#654811yescharacteristic
375C23#655112yes—
376C23D7×#4112yes—
377C23#655312yes—
378C23#655312yes—
379C23#655412yes—
380C23#655412yes—
381C23C23×Dic711yescharacteristic
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—144no—
412C2×C4—144no—
413C2×C4—144no—
414C2×C4—282no—
415C2×C4—282no—
416C2×C4—282no—
417C2×C4—282no—
418C2×C4—282no—
419C2×C4—282no—
420C2×C4—282no—
421C2×C4—282no—
422C2×C4—282no—
423C2×C4—282no—
424C2×C4—282no—
425C2×C4—282no—
426C2×C4—282no—
427C2×C4—282no—
428C2×C4—282no—
429C2×C4—282no—
430C2×C4—282no—
431C2×C4—282no—
432C2×C4—282no—
433C2×C4—282no—
434C2×C4—282no—
435C2×C4—282no—
436C2×C4—282no—
437C2×C4—282no—
438C2×C4—282no—
439C7#1465411yescharacteristic, complemented, Sylow
440C22#9032912yes—
441C22#9033112yes—
442C22#9034211yescharacteristic
443C22#9035711yescharacteristic
444C22#9035812yes—
445C22#9036311yescharacteristic
446C22#9037411yescharacteristic
447C22#9037512yes—
448C22C7⋊#56412yes—
449C22#9039012yes—
450C22#9039012yes—
451C22#9039112yes—
452C22#9039212yes—
453C22#9039512yes—
454C22#9039812yes—
455C22#9040112yes—
456C22#9048911yescharacteristic
457C22#9050311yescharacteristic
458C22#41×Dic711yescharacteristic
459C22#9051812yes—
460C22#9051812yes—
461C4—42no—
462C4—44no—
463C4—42no—
464C4—42no—
465C4—44no—
466C4—284no—
467C4—562no—
468C4—562no—
469C4—562no—
470C2#1173576712yes—
471C2#1173577912yes—
472C2#1173578112yes—
473C2#1173585012yes—
474C2#1174019111yescharacteristic
475C2#1174028511yescharacteristic
476C2#1174040211yescharacteristic
477C2#1174047212yes—
478C2#1174051912yes—
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#400C2
socle, prime radical, cosocleC24×C7C24
hypercenterC2×#400D7
hypocenterC7#14654
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
15. C7×#400C4semidirect
149. #400Dic7semidirect
439. C7#14654semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#4002
#117293232
#117293192
#117293182
#117271662
#117271612
#146547