Finite Group Databasebeta

← #13272495

Subgroups — #13272495

Order 1792.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×SD32C211yesmaximal, characteristic, complemented
2C2×#89960C211yesmaximal, characteristic, complemented
3C2×#89929C211yesmaximal, characteristic
4C2×#89359C211yesmaximal, characteristic, complemented
5C2×#89357C211yesmaximal, characteristic, complemented
6C2×(C2×D7)⋊C16C211yesmaximal, characteristic, complemented
7#11725612C211yesmaximal, characteristic, complemented
8C22×C7×Q16C2211yescharacteristic
9C22×C7×D8C2211yescharacteristic
10C2×#6509—21no—
11C2×#6501—21no—
12C22×C8×D7C2211yescharacteristic
13C2×C7×SD32—22no—
14C2×C7×SD32—22no—
15C2×C7×SD32—22no—
16C22×C7×C16C2211yescharacteristic
17C2×#6409—21no—
18C2×#6406—21no—
19#89960—22no—
20#89960—22no—
21#89929—22no—
22#89929—22no—
23C2×#6392C2211yescharacteristic
24C2×#6392C2211yescharacteristic
25C22×C7⋊C16C2211yescharacteristic
26#89359—22no—
27#89357—22no—
28(C2×D7)⋊C16—22no—
29#13305—71nomaximal, Sylow
30C22×C7×Q8—21no—
31C22×C7×D4—21no—
32C22×C22⋊D7—41no—
33C22×C4×D7D411yescharacteristic
34C2×C7×Q16—21no—
35C2×C7×Q16—21no—
36C2×C7×Q16—21no—
37C2×C7×Q16—21no—
38C2×C7×Q16—21no—
39C2×C7×Q16D412yescomplemented
40C2×C7×D8—21no—
41C2×C7×D8—21no—
42C2×C7×D8—21no—
43C2×C7×D8—21no—
44C2×C7×D8—21no—
45C2×C7×D8D412yes—
46C22×C7×C8C2311yescharacteristic
47C2×C22⋊Dic7—41no—
48#6509—24no—
49#6509—42no—
50#6501—24no—
51#6501—42no—
52C2×(C2×D7)⋊C4—41no—
53C2×C4⋊Dic7—21no—
54C2×C4⋊Dic7—21no—
55C2×Dic7⋊C4—41no—
56C22×C7⋊C8D411yescharacteristic
57C2×C8×D7—21no—
58C2×C8×D7—21no—
59C2×C8×D7—21no—
60C2×C8×D7—21no—
61C2×C8×D7—21no—
62C2×C8×D7—21no—
63C7×SD32—28no—
64C2×C7×C16—21no—
65C2×C7×C16—21no—
66C2×C7×C16D412yescomplemented
67#6409—24no—
68#6406—24no—
69#6392—21no—
70#6392—21no—
71#6392D412yes—
72#6392D412yescomplemented
73C2×C7⋊C16—21no—
74C2×C7⋊C16—21no—
75C2×C7⋊C16—21no—
76C22×SD32D711yescharacteristic, complemented
77C2×#467—71no—
78C2×#466—71no—
79C2×#358—71no—
80C2×#357—71no—
81C2×C22⋊C16—71no—
82#1380—71no—
83C24×C7—41no—
84C23×D7D811yescharacteristic
85C2×C7×Q8—22no—
86C2×C7×Q8—41no—
87C2×C7×Q8—41no—
88C2×C7×Q8—41no—
89C2×C7×Q8—41no—
90C2×C7×Q8—41no—
91C2×C7×D4—22no—
92C2×C7×D4—41no—
93C2×C7×D4—41no—
94C2×C7×D4—41no—
95C2×C7×D4—41no—
96C2×C7×D4—41no—
97C22×C4×C7—41no—
98C22×C4×C7C2×D411yescharacteristic
99C2×C22⋊D7—44no—
100C2×C22⋊D7—82no—
101C2×C22⋊D7—82no—
102C22×Dic7—41no—
103C22×Dic7—41no—
104C22×Dic7D811yescharacteristic
105C2×C4×D7—21no—
106C2×C4×D7—21no—
107C2×C4×D7—21no—
108C2×C4×D7—21no—
109C2×C4×D7—21no—
110C2×C4×D7—21no—
111C7×Q16—22no—
112C7×Q16—22no—
113C7×Q16—41no—
114C7×Q16—41no—
115C7×D8—22no—
116C7×D8—22no—
117C7×D8—41no—
118C7×D8—41no—
119C2×C7×C8C2×D411yescharacteristic
120C2×C7×C8C2×D411yescharacteristic
121C2×C7×C8C2×D411yescharacteristic
122C2×C7×C8C2×D411yescharacteristic
123C2×C7×C8C2×D411yescharacteristic
124C2×C7×C8#4111yescharacteristic
125C22⋊Dic7—44no—
126(C2×D7)⋊C4—44no—
127C4⋊Dic7—22no—
128C4⋊Dic7—22no—
129C4⋊Dic7—41no—
130C4⋊Dic7—41no—
131Dic7⋊C4—44no—
132C2×C7⋊C8—21no—
133C2×C7⋊C8—21no—
134C2×C7⋊C8—21no—
135C8×D7—41no—
136C8×D7—41no—
137C8×D7—41no—
138C8×D7—41no—
139C7×C16—22no—
140C7⋊C16—41no—
141C22×Q16C2×D711yescharacteristic
142C22×D8C2×D711yescharacteristic
143C23×C8—71no—
144C2×C22⋊Q8—141no—
145C2×#121—141no—
146C2×SD32—22no—
147C2×SD32—22no—
148C2×SD32—22no—
149C22×C16—71no—
150C22×C16C2×D711yescharacteristic
151#467—142no—
152#467—142no—
153#466—142no—
154#466—142no—
155C2×#107—71no—
156C2×#107—71no—
157C2×#103—141no—
158C2×#102—141no—
159#358—142no—
160#357—142no—
161C22⋊C16—142no—
162C23×C7—42no—
163C23×C7—81no—
164C23×C7—81no—
165C23×C7—81no—
166C23×C7—81no—
167C23×C7—81no—
168C23×C7—81no—
169C23×C7C2×D811yescharacteristic
170C22×D7—21no—
171C22×D7—21no—
172C22×D7—21no—
173C22×D7—21no—
174C22×D7—21no—
175C22×D7—21no—
176C22×D7SD3212yescomplemented
177C7×Q8—42no—
178C7×Q8—42no—
179C7×Q8—81no—
180C7×Q8—81no—
181C7×D4—42no—
182C7×D4—42no—
183C7×D4—81no—
184C7×D4—81no—
185C2×C4×C7—42no—
186C2×C4×C7—81no—
187C2×C4×C7—81no—
188C2×C4×C7#12011yescharacteristic
189C2×C4×C7#12011yescharacteristic
190C2×C4×C7#12111yescharacteristic
191C2×C4×C7#13511yescharacteristic
192C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
194C22⋊D7—88no—
195C2×Dic7—21no—
196C2×Dic7—21no—
197C2×Dic7—21no—
198C2×Dic7—42no—
199C2×Dic7—42no—
200C2×Dic7—81no—
201C2×Dic7—81no—
202C2×Dic7—81no—
203C2×Dic7—81no—
204C4×D7—41no—
205C4×D7—41no—
206C4×D7—41no—
207C4×D7—41no—
208C7×C8#12011yescharacteristic
209C7×C8#12111yescharacteristic
210C7×C8#12111yescharacteristic
211C7×C8#12711yescharacteristic
212C7⋊C8—41no—
213C22×Q8—21no—
214C22×D4—21no—
215C22×D4—281no—
216C23×C4—71no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16C22⋊D712yescomplemented
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8C22⋊D712yes—
229C22×C8—71no—
230C22×C8—141no—
231C22×C8—141no—
232C22×C8—141no—
233C22×C8—141no—
234C22×C8—141no—
235C22×C8—141no—
236C22×C8C22×D711yescharacteristic
237C22⋊Q8—144no—
238C22⋊Q8—282no—
239#121—144no—
240#121—282no—
241C2×C4⋊C4—141no—
242C2×C4⋊C4—141no—
243C2×C4⋊C4—281no—
244C2×C22⋊C4—281no—
245C2×C22⋊C4—281no—
246SD32—28no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—141no—
250C2×C16—141no—
251C2×C16—141no—
252C2×C16C22⋊D712yescomplemented
253#107—72no—
254#107—72no—
255#107—141no—
256#107—141no—
257#103—144no—
258#102—144no—
259C22×C7—82no—
260C22×C7—82no—
261C22×C7—82no—
262C22×C7—161no—
263C22×C7—161no—
264C22×C7—161no—
265C22×C7—161no—
266C22×C7#44711yescharacteristic
267C22×C7#44711yescharacteristic
268C22×C7#46611yescharacteristic
269C22×C7C2×SD3211yescharacteristic
270C22×C7#50811yescharacteristic
271C22×C7#50911yescharacteristic
272C22×C7#51011yescharacteristic
273C2×D7—22no—
274C2×D7—22no—
275C2×D7—22no—
276C2×D7—41no—
277C2×D7—41no—
278C2×D7—41no—
279C2×D7—41no—
280C4×C7—82no—
281C4×C7#39211yescharacteristic
282C4×C7#44911yescharacteristic
283C4×C7#44911yescharacteristic
284C4×C7#46911yescharacteristic
285Dic7—41no—
286Dic7—82no—
287Dic7—82no—
288C24—41no—
289C24—71no—
290C2×Q8—22no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—284no—
303C2×D4—562no—
304C2×D4—562no—
305C22×C4—41no—
306C22×C4—71no—
307C22×C4—141no—
308C22×C4—141no—
309C22×C4—141no—
310C22×C4—141no—
311C22×C4—141no—
312C22×C4—141no—
313C22×C4—281no—
314C22×C4—281no—
315C22×C4D4×D711yescharacteristic
316Q16—22no—
317Q16—22no—
318Q16—41no—
319Q16—41no—
320D8—22no—
321D8—22no—
322D8—41no—
323D8—41no—
324C2×C8—141no—
325C2×C8—141no—
326C2×C8—141no—
327C2×C8—281no—
328C2×C8—281no—
329C2×C8—281no—
330C2×C8—281no—
331C2×C8D4×D711yescharacteristic
332C2×C8D4×D711yescharacteristic
333C2×C8#115911yescharacteristic
334C2×C8C2×C22⋊D711yescharacteristic
335C2×C8C2×C22⋊D711yescharacteristic
336C2×C8C2×C22⋊D711yescharacteristic
337C4⋊C4—142no—
338C4⋊C4—142no—
339C4⋊C4—284no—
340C4⋊C4—281no—
341C4⋊C4—281no—
342C22⋊C4—284no—
343C22⋊C4—284no—
344C16—22no—
345C16—281no—
346C2×C7—162no—
347C2×C7#199911yescharacteristic
348C2×C7#218511yescharacteristic
349C2×C7#218611yescharacteristic
350C2×C7#218711yescharacteristic
351C2×C7#218911yescharacteristic
352C2×C7#221711yescharacteristic
353C2×C7#222011yescharacteristic
354D7—42no—
355C23—42no—
356C23—72no—
357C23—81no—
358C23—81no—
359C23—81no—
360C23—81no—
361C23—81no—
362C23—81no—
363C23—141no—
364C23—141no—
365C23—141no—
366C23—141no—
367C23—141no—
368C23—141no—
369C23D7×D811yescharacteristic
370Q8—42no—
371Q8—42no—
372Q8—81no—
373Q8—81no—
374D4—42no—
375D4—42no—
376D4—81no—
377D4—81no—
378D4—568no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—141no—
383C2×C4—141no—
384C2×C4—141no—
385C2×C4—281no—
386C2×C4—281no—
387C2×C4—281no—
388C2×C4—281no—
389C2×C4—282no—
390C2×C4—282no—
391C2×C4—561no—
392C2×C4—561no—
393C2×C4—561no—
394C2×C4—561no—
395C2×C4#647411yescharacteristic
396C2×C4#647411yescharacteristic
397C2×C4#647511yescharacteristic
398C2×C4#650011yescharacteristic
399C2×C4#650011yescharacteristic
400C2×C4#650111yescharacteristic
401C8—281no—
402C8#650211yescharacteristic
403C8#650211yescharacteristic
404C8#650311yescharacteristic
405C8#651611yescharacteristic
406C7#1330511yescharacteristic, complemented, Sylow
407C22—82no—
408C22—82no—
409C22—82no—
410C22—142no—
411C22—142no—
412C22—142no—
413C22—161no—
414C22—161no—
415C22—161no—
416C22—161no—
417C22—281no—
418C22—281no—
419C22—281no—
420C22—281no—
421C22D7×SD3211yescharacteristic
422C22#8968611yescharacteristic
423C22#8968711yescharacteristic
424C22#8968811yescharacteristic
425C22#8992811yescharacteristic
426C22#8992811yescharacteristic
427C22#8992911yescharacteristic
428C4—82no—
429C4—281no—
430C4—562no—
431C4—562no—
432C4#8993011yescharacteristic
433C4#8993011yescharacteristic
434C4#8993111yescharacteristic
435C4#8999511yescharacteristic
436C2—162no—
437C2—282no—
438C2#1172923711yescharacteristic
439C2#1172923811yescharacteristic
440C2#1172923911yescharacteristic
441C2#1172924011yescharacteristic
442C2#1172924111yescharacteristic
443C2#1172924211yescharacteristic
444C2#1172979711yescharacteristic
subgroupG/H
centerC23D7×D8
commutator, cosocleC22×C7×C8C23
FrattiniC22×C8C22×D7
FittingC22×C7×SD32C2
socleC23×C7C2×D8
prime radicalC2×#89929C2
hypercenterC22×SD32D7
hypocenterC7#13305
LCSG ▷ C22×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C22×C7×SD32C2semidirect
2. C2×#89960C2semidirect
4. C2×#89359C2semidirect
5. C2×#89357C2semidirect
6. C2×(C2×D7)⋊C16C2semidirect
7. #11725612C2semidirect
39. C2×C7×Q16D4semidirect
66. C2×C7×C16D4semidirect
72. #6392D4semidirect
76. C22×SD32D7semidirect
176. C22×D7SD32semidirect
222. C2×Q16C22⋊D7semidirect
252. C2×C16C22⋊D7semidirect
406. C7#13305semidirect

Maximal subgroups

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

subgroupindex
C22×C7×SD322
C2×#899602
C2×#899292
C2×#893592
C2×#893572
C2×(C2×D7)⋊C162
#117256122
#133057