Finite Group Databasebeta

← #13272499

Subgroups — #13272499

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
1C2×#89929C211yesmaximal, characteristic
2C22×#6401C211yesmaximal, characteristic, complemented
3C2×#89659C211yesmaximal, characteristic, complemented
4C2×C7×#357C211yesmaximal, characteristic, complemented
5C2×#89298C211yesmaximal, characteristic, complemented
6C2×(C2×D7)⋊C16C211yesmaximal, characteristic, complemented
7#11725528C211yesmaximal, characteristic, complemented
8C22×C7×D8C2211yescharacteristic
9C2×#6501—21no—
10C22×Dic28C2211yescharacteristic
11C22×C8×D7C2211yescharacteristic
12C2×#6460—21no—
13C22×C7×C16C2211yescharacteristic
14C2×C7×#107C2211yescharacteristic
15C2×#6406—21no—
16#89929—22no—
17#89929—22no—
18C2×#6401—22no—
19C2×#6401—22no—
20C2×#6401—22no—
21C2×#6392C2211yescharacteristic
22C22×C7⋊C16C2211yescharacteristic
23C2×#6384—21no—
24#89659—22no—
25#89659—22no—
26C7×#357—22no—
27(C2×D7)⋊C16—22no—
28#89298—22no—
29#13305—71nomaximal, Sylow
30C22×C7×D4—21no—
31C22×C22⋊D7—41no—
32C22×C4×D7D411yescharacteristic
33C22×Dic14—21no—
34C2×C7×D8—21no—
35C2×C7×D8—21no—
36C2×C7×D8—21no—
37C2×C7×D8—21no—
38C2×C7×D8—21no—
39C2×C7×D8D412yes—
40C22×C7×C8C2311yescharacteristic
41C2×C7×C4⋊C4—21no—
42C2×C22⋊Dic7—41no—
43#6501—24no—
44#6501—42no—
45C2×(C2×D7)⋊C4—41no—
46C2×C4⋊Dic7—21no—
47C2×C4⋊Dic7—41no—
48C22×C7⋊C8D411yescharacteristic
49C2×Dic28—21no—
50C2×Dic28—21no—
51C2×Dic28—21no—
52C2×Dic28—21no—
53C2×Dic28—21no—
54C2×Dic28D412yescomplemented
55C2×C8×D7—21no—
56C2×C8×D7—21no—
57C2×C8×D7—21no—
58C2×C8×D7—21no—
59C2×C8×D7—21no—
60C2×C8×D7—21no—
61#6460—24no—
62#6460—42no—
63C2×C7×C16—21no—
64C2×C7×C16—21no—
65C2×C7×C16—21no—
66C7×#107—21no—
67C7×#107D412yescomplemented
68#6406—24no—
69#6401—28no—
70#6392—21no—
71#6392D412yes—
72C2×C7⋊C16—21no—
73C2×C7⋊C16—21no—
74C2×C7⋊C16D412yescomplemented
75#6384—24no—
76C22×SD32—71no—
77C2×#467—71no—
78C2×#466—71no—
79C2×#358—71no—
80C2×#357D711yescharacteristic, complemented
81C2×C22⋊C16—71no—
82#1380—71no—
83C24×C7—41no—
84C23×D7D811yescharacteristic
85C2×C7×D4—22no—
86C2×C7×D4—41no—
87C2×C7×D4—41no—
88C2×C7×D4—41no—
89C2×C7×D4—41no—
90C2×C7×D4—41no—
91C22×C4×C7—41no—
92C22×C4×C7C2×D411yescharacteristic
93C2×C22⋊D7—44no—
94C2×C22⋊D7—82no—
95C2×C22⋊D7—82no—
96C22×Dic7—41no—
97C22×Dic7—41no—
98C22×Dic7D811yescharacteristic
99C2×C4×D7—21no—
100C2×C4×D7—21no—
101C2×C4×D7—21no—
102C2×C4×D7—21no—
103C2×C4×D7—21no—
104C2×C4×D7—21no—
105C2×Dic14—22no—
106C2×Dic14—41no—
107C2×Dic14—41no—
108C2×Dic14—41no—
109C2×Dic14—41no—
110C2×Dic14—41no—
111C7×D8—22no—
112C7×D8—22no—
113C7×D8—41no—
114C7×D8—41no—
115C2×C7×C8C2×D411yescharacteristic
116C2×C7×C8C2×D411yescharacteristic
117C2×C7×C8C2×D411yescharacteristic
118C2×C7×C8C2×D411yescharacteristic
119C2×C7×C8C2×D411yescharacteristic
120C2×C7×C8#4111yescharacteristic
121C7×C4⋊C4—22no—
122C7×C4⋊C4—41no—
123C22⋊Dic7—44no—
124(C2×D7)⋊C4—44no—
125C4⋊Dic7—22no—
126C4⋊Dic7—44no—
127C4⋊Dic7—41no—
128C2×C7⋊C8—21no—
129C2×C7⋊C8—21no—
130C2×C7⋊C8—21no—
131Dic28—22no—
132Dic28—22no—
133Dic28—41no—
134Dic28—41no—
135C8×D7—41no—
136C8×D7—41no—
137C8×D7—41no—
138C8×D7—41no—
139C7×C16—41no—
140C7⋊C16—22no—
141C22×Q16—71no—
142C22×D8C2×D711yescharacteristic
143C23×C8—71no—
144C2×C22⋊Q8—141no—
145C2×#121—141no—
146C2×SD32—142no—
147C2×SD32—142no—
148C2×SD32—142no—
149C22×C16—71no—
150C22×C16C2×D711yescharacteristic
151#467—142no—
152#467—142no—
153#466—142no—
154#466—142no—
155C2×#107—71no—
156C2×#107C2×D711yescharacteristic
157C2×#103—141no—
158C2×#102—141no—
159#358—142no—
160#357—22no—
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×D4—42no—
178C7×D4—42no—
179C7×D4—81no—
180C7×D4—81no—
181C2×C4×C7—42no—
182C2×C4×C7—81no—
183C2×C4×C7—81no—
184C2×C4×C7#12011yescharacteristic
185C2×C4×C7#12011yescharacteristic
186C2×C4×C7#12111yescharacteristic
187C2×C4×C7#13511yescharacteristic
188C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
190C22⋊D7—88no—
191C2×Dic7—21no—
192C2×Dic7—21no—
193C2×Dic7—21no—
194C2×Dic7—42no—
195C2×Dic7—42no—
196C2×Dic7—81no—
197C2×Dic7—81no—
198C2×Dic7—81no—
199C2×Dic7—81no—
200C4×D7—41no—
201C4×D7—41no—
202C4×D7—41no—
203C4×D7—41no—
204Dic14—42no—
205Dic14—42no—
206Dic14—81no—
207Dic14—81no—
208C7×C8#12011yescharacteristic
209C7×C8#12111yescharacteristic
210C7×C8#12111yescharacteristic
211C7×C8#12711yescharacteristic
212C7⋊C8—41no—
213C22×Q8—141no—
214C22×D4—21no—
215C22×D4—281no—
216C23×C4—71no—
217C2×Q16—72no—
218C2×Q16—141no—
219C2×Q16—141no—
220C2×Q16—141no—
221C2×Q16—141no—
222C2×Q16—141no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8D2812yes—
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—21no—
242C2×C4⋊C4—141no—
243C2×C4⋊C4—281no—
244C2×C22⋊C4—281no—
245C2×C22⋊C4—281no—
246SD32—148no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—72no—
251C2×C16—141no—
252C2×C16—141no—
253#107—21no—
254#107—72no—
255#107—141no—
256#107C22⋊D712yescomplemented
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—142no—
291C2×Q8—281no—
292C2×Q8—281no—
293C2×Q8—281no—
294C2×Q8—281no—
295C2×Q8—281no—
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—142no—
317Q16—142no—
318Q16—281no—
319Q16—281no—
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×C8C2×D2811yescharacteristic
332C2×C8#115711yescharacteristic
333C2×C8D4×D711yescharacteristic
334C2×C8D4×D711yescharacteristic
335C2×C8D4×D711yescharacteristic
336C2×C8C2×C22⋊D711yescharacteristic
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—142no—
340C4⋊C4—284no—
341C4⋊C4—281no—
342C22⋊C4—284no—
343C22⋊C4—284no—
344C16—41no—
345C16—142no—
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—282no—
371Q8—282no—
372Q8—561no—
373Q8—561no—
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#644511yescharacteristic
396C2×C4#644711yescharacteristic
397C2×C4#647411yescharacteristic
398C2×C4#647711yescharacteristic
399C2×C4#647911yescharacteristic
400C2×C4#650011yescharacteristic
401C8—281no—
402C8#644511yescharacteristic
403C8#644711yescharacteristic
404C8#649311yescharacteristic
405C8#650311yescharacteristic
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—
421C22#8954511yescharacteristic
422C22#8954711yescharacteristic
423C22#8968311yescharacteristic
424C22#8968411yescharacteristic
425C22D7×SD3211yescharacteristic
426C22#8968711yescharacteristic
427C22#8992811yescharacteristic
428C4—82no—
429C4—281no—
430C4—562no—
431C4—562no—
432C4#8955311yescharacteristic
433C4#8955411yescharacteristic
434C4#8973211yescharacteristic
435C4#8994411yescharacteristic
436C2—162no—
437C2—282no—
438C2#1172694711yescharacteristic
439C2#1172694811yescharacteristic
440C2#1172695011yescharacteristic
441C2#1172695211yescharacteristic
442C2#1172795811yescharacteristic
443C2#1172922211yescharacteristic
444C2#1172923711yescharacteristic
subgroupG/H
centerC23D7×D8
commutator, cosocleC22×C7×C8C23
FrattiniC22×C8C22×D7
FittingC2×C7×#357C2
socleC23×C7C2×D8
prime radicalC2×#89929C2
hypercenterC2×#357D7
hypocenterC7#13305
LCSG ▷ C22×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C22×#6401C2semidirect
3. C2×#89659C2semidirect
4. C2×C7×#357C2semidirect
5. C2×#89298C2semidirect
6. C2×(C2×D7)⋊C16C2semidirect
7. #11725528C2semidirect
54. C2×Dic28D4semidirect
67. C7×#107D4semidirect
74. C2×C7⋊C16D4semidirect
80. C2×#357D7semidirect
176. C22×D7SD32semidirect
256. #107C22⋊D7semidirect
406. C7#13305semidirect

Maximal subgroups

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

subgroupindex
C2×#899292
C22×#64012
C2×#896592
C2×C7×#3572
C2×#892982
C2×(C2×D7)⋊C162
#117255282
#133057