Finite Group Databasebeta

← #13248609

Subgroups — #13248609

Order 1792.

592 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89859C211yesmaximal, characteristic
2#11731083C211yesmaximal, characteristic
3C7×#1981C211yesmaximal, characteristic, complemented
4#11729541C211yesmaximal, characteristic, complemented
5C2×#89278C211yesmaximal, characteristic
6#11725508C211yesmaximal, characteristic, complemented
7#11725425C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×#6455—21no—
10C2×C4×D28C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×C7×#103—21no—
13C2×C7×#103—21no—
14C4×C7×C4⋊C4C2211yescharacteristic
15#89859—22no—
16#89859C414yescomplemented
17#89759—21no—
18C2×#6383—21no—
19C2×#6381—21no—
20#89711—21no—
21#89707C2211yescharacteristic
22C4×C4⋊Dic7—21no—
23C2×C4⋊(C7⋊C8)C2211yescharacteristic
24C2×C4×C7⋊C8C2211yescharacteristic
25#89442—22no—
26#89324—22no—
27#89278—22no—
28#8984—71nomaximal, Sylow
29C22×C7×Q8—21no—
30C22×D28D411yescharacteristic
31C22×C4×D7—21no—
32C22×C7×C8—21no—
33C7×C4⋊Q8—21no—
34C7×C4⋊Q8—21no—
35C7×C4⋊Q8—21no—
36C7×C4⋊Q8C2×C412yes—
37C2×C7×C4⋊C4—21no—
38C2×C7×C4⋊C4—21no—
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C7×C4⋊C4D411yescharacteristic
41C2×C42×C7—21no—
42C2×C42×C7C2311yescharacteristic
43C2×(C2×D7)⋊C4—21no—
44C2×(C2×D7)⋊C4—22no—
45C2×(C2×D7)⋊C4—22no—
46C2×C4⋊Dic7—21no—
47C2×C4⋊Dic7—21no—
48C2×C4⋊Dic7D411yescharacteristic
49C2×C4⋊Dic7D412yes—
50C2×C4×Dic7—22no—
51C22×C7⋊C8—21no—
52C22×C7⋊C8—21no—
53#6455—42no—
54#6455—42no—
55C4×D28—21no—
56C4×D28—21no—
57C4×D28C2×C412yes—
58C4×D28D412yes—
59C7×C4⋊C8—21no—
60C7×C4⋊C8—21no—
61C7×#103—42no—
62C7×#103—42no—
63C7×#95—21no—
64C7⋊#95—22no—
65#6383—24no—
66#6381—24no—
67C4⋊(C7⋊C8)—21no—
68C4⋊(C7⋊C8)C2×C412yes—
69C4×C7⋊C8—21no—
70C4×C7⋊C8—21no—
71C2×#474—71no—
72#2354—71no—
73#1990—71no—
74#1981D711yescharacteristic, complemented
75C2×D4⋊C8—71no—
76#1296—71no—
77#1279—71no—
78C23×D7—21no—
79C2×C7×Q8—22no—
80C2×C7×Q8—41no—
81C2×C7×Q8—41no—
82C2×C7×Q8—41no—
83C2×C7×Q8—41no—
84C2×C7×Q8—41no—
85C22×C4×C7—21no—
86C22×C4×C7—21no—
87C22×C4×C7—41no—
88C22×C4×C7C2×D411yescharacteristic
89C22×C4×C7C2×D411yescharacteristic
90C22×C4×C7C2×D411yescharacteristic
91C22×Dic7—21no—
92C22×Dic7—22no—
93C2×D28—21no—
94C2×D28—21no—
95C2×D28—21no—
96C2×D28—21no—
97C2×D28—21no—
98C2×D28C22⋊C412yes—
99C2×C4×D7—22no—
100C2×C4×D7—22no—
101C2×C4×D7—41no—
102C2×C4×D7—41no—
103C2×C4×D7—41no—
104C2×C4×D7—41no—
105C2×C7×C8—41no—
106C2×C7×C8—41no—
107C2×C7×C8—41no—
108C7×C4⋊C4—21no—
109C7×C4⋊C4—22no—
110C7×C4⋊C4—22no—
111C7×C4⋊C4—21no—
112C7×C4⋊C4—21no—
113C7×C4⋊C4—41no—
114C7×C4⋊C4—41no—
115C7×C4⋊C4D812yes—
116C42×C7—41no—
117C42×C7—41no—
118C42×C7C22×C411yescharacteristic
119C42×C7C2×D411yescharacteristic
120C42×C7#4111yescharacteristic
121C42×C7#4111yescharacteristic
122(C2×D7)⋊C4—22no—
123(C2×D7)⋊C4—22no—
124(C2×D7)⋊C4—44no—
125(C2×D7)⋊C4—82no—
126C4⋊Dic7—21no—
127C4⋊Dic7—41no—
128C4⋊Dic7—41no—
129C4⋊Dic7—41no—
130C4⋊Dic7—41no—
131C4⋊Dic7—42no—
132C4⋊Dic7C22⋊C412yes—
133C4×Dic7—44no—
134C2×C7⋊C8—22no—
135C2×C7⋊C8—22no—
136C2×C7⋊C8—41no—
137C2×C7⋊C8—41no—
138C2×C7⋊C8—41no—
139C2×C7⋊C8—41no—
140C2×C4⋊Q8C2×D711yescharacteristic
141C2×C4×D4—71no—
142C2×#117—141no—
143#474—74no—
144#474—142no—
145C2×#107—141no—
146C2×C4⋊C8—71no—
147C2×C4⋊C8C2×D711yescharacteristic
148C2×#103—21no—
149C2×#103—21no—
150C2×#102—141no—
151C2×C4×C8—71no—
152#390—141no—
153#388—142no—
154#384—71no—
155#380—141no—
156C4×C4⋊C4—141no—
157C4×C4⋊C4C2×D711yescharacteristic
158#340—142no—
159D4⋊C8—142no—
160C23×C7#12011yescharacteristic
161C22×D7—22no—
162C22×D7—41no—
163C22×D7—41no—
164C22×D7—41no—
165C22×D7—41no—
166C22×D7—41no—
167C22×D7—41no—
168C7×Q8—42no—
169C7×Q8—42no—
170C7×Q8—81no—
171C7×Q8—81no—
172C2×C4×C7—21no—
173C2×C4×C7—21no—
174C2×C4×C7—22no—
175C2×C4×C7—41no—
176C2×C4×C7—41no—
177C2×C4×C7—42no—
178C2×C4×C7—41no—
179C2×C4×C7—41no—
180C2×C4×C7—41no—
181C2×C4×C7—81no—
182C2×C4×C7—81no—
183C2×C4×C7C2×C22⋊C411yescharacteristic
184C2×C4×C7C4×D411yescharacteristic
185C2×C4×C7C4×D411yescharacteristic
186C2×C4×C7#12111yescharacteristic
187C2×C4×C7#12111yescharacteristic
188C2×C4×C7#12311yescharacteristic
189C2×C4×C7C2×D811yescharacteristic
190C2×C4×C7#13511yescharacteristic
191C2×C4×C7#13511yescharacteristic
192C2×C4×C7#13511yescharacteristic
193C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C7#13711yescharacteristic
196C2×C4×C7#13711yescharacteristic
197C2×Dic7—22no—
198C2×Dic7—41no—
199C2×Dic7—41no—
200C2×Dic7—42no—
201C2×Dic7—42no—
202C2×Dic7—42no—
203D28—22no—
204D28—22no—
205D28—41no—
206D28—41no—
207C4×D7—42no—
208C4×D7—42no—
209C4×D7—42no—
210C4×D7—42no—
211C7×C8—81no—
212C7⋊C8—42no—
213C7⋊C8—42no—
214C22×Q8—21no—
215C22×D4—71no—
216C23×C4—141no—
217C22×C8—21no—
218C22×C8—141no—
219C22×C8—141no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8C4×D712yes—
224C4×D4—72no—
225C4×D4—72no—
226C4×D4—141no—
227C4×D4—141no—
228#117—282no—
229#117—282no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—71no—
233C2×C4⋊C4—72no—
234C2×C4⋊C4—141no—
235C2×C4⋊C4—141no—
236C2×C4⋊C4C22⋊D711yescharacteristic
237C2×C4⋊C4C22⋊D711yescharacteristic
238C2×C22⋊C4—141no—
239C2×C22⋊C4—142no—
240C2×C22⋊C4—142no—
241C2×C42—21no—
242C2×C42—142no—
243C2×C42C22×D711yescharacteristic
244#107—144no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—72no—
248C4⋊C8—141no—
249#103—42no—
250#103—42no—
251#102—144no—
252C4×C8—141no—
253C4×C8—141no—
254#95—21no—
255#95—142no—
256C22×C7#38611yescharacteristic
257C22×C7#44711yescharacteristic
258C22×C7#44911yescharacteristic
259C22×C7#45211yescharacteristic
260C22×C7#45211yescharacteristic
261C22×C7#45511yescharacteristic
262C22×C7#45611yescharacteristic
263C2×D7—42no—
264C2×D7—42no—
265C2×D7—42no—
266C2×D7—81no—
267C2×D7—81no—
268C2×D7—81no—
269C2×D7—81no—
270C4×C7—21no—
271C4×C7—21no—
272C4×C7—42no—
273C4×C7—82no—
274C4×C7—81no—
275C4×C7#41611yescharacteristic
276C4×C7#41911yescharacteristic
277C4×C7C4×D811yescharacteristic
278C4×C7#44211yescharacteristic
279C4×C7#45911yescharacteristic
280C4×C7#46311yescharacteristic
281C4×C7#48511yescharacteristic
282C4×C7#48511yescharacteristic
283Dic7—42no—
284Dic7—82no—
285C24—141no—
286C2×Q8—22no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×D4—72no—
293C2×D4—141no—
294C2×D4—141no—
295C2×D4—141no—
296C2×D4—141no—
297C2×D4—141no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—141no—
302C22×C4—142no—
303C22×C4—142no—
304C22×C4—142no—
305C22×C4—281no—
306C22×C4—281no—
307C22×C4—281no—
308C22×C4—281no—
309C22×C4D4×D711yescharacteristic
310C22×C4D4×D711yescharacteristic
311C22×C4C2×C22⋊D711yescharacteristic
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—142no—
316C2×C8—142no—
317C2×C8—281no—
318C2×C8—281no—
319C2×C8—281no—
320C2×C8—281no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—72no—
329C4⋊C4—141no—
330C4⋊C4—282no—
331C4⋊C4—281no—
332C4⋊C4—281no—
333C4⋊C4—281no—
334C4⋊C4—281no—
335C4⋊C4#114112yes—
336C22⋊C4—142no—
337C22⋊C4—142no—
338C22⋊C4—284no—
339C22⋊C4—562no—
340C42—41no—
341C42—41no—
342C42—284no—
343C42C2×C4×D711yescharacteristic
344C42#115711yescharacteristic
345C42D4×D711yescharacteristic
346C42#115911yescharacteristic
347C2×C7#164111yescharacteristic
348C2×C7#164611yescharacteristic
349C2×C7#164711yescharacteristic
350C2×C7#165211yescharacteristic
351C2×C7#187311yescharacteristic
352C2×C7#187911yescharacteristic
353C2×C7#188211yescharacteristic
354D7—82no—
355C23—142no—
356C23—281no—
357C23—281no—
358C23—281no—
359C23—281no—
360C23—281no—
361C23—281no—
362C23#650011yescharacteristic
363Q8—42no—
364Q8—42no—
365Q8—81no—
366Q8—81no—
367D4—142no—
368D4—142no—
369D4—281no—
370D4—281no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—142no—
383C2×C4—281no—
384C2×C4—281no—
385C2×C4—282no—
386C2×C4—282no—
387C2×C4—282no—
388C2×C4—282no—
389C2×C4—282no—
390C2×C4—282no—
391C2×C4—282no—
392C2×C4D7×C22⋊C411yescharacteristic
393C2×C4(C22⋊D7)⋊C411yescharacteristic
394C2×C4#644611yescharacteristic
395C2×C4#644711yescharacteristic
396C2×C4#647811yescharacteristic
397C2×C4#647911yescharacteristic
398C2×C4#648111yescharacteristic
399C2×C4#648211yescharacteristic
400C2×C4C4×C22⋊D711yescharacteristic
401C2×C4C2×#114111yescharacteristic
402C2×C4#649511yescharacteristic
403C2×C4#650111yescharacteristic
404C2×C4#651211yescharacteristic
405C2×C4#651311yescharacteristic
406C8—81no—
407C8—282no—
408C8—282no—
409C7#898411yescharacteristic, complemented, Sylow
410C22—282no—
411C22—282no—
412C22—282no—
413C22—561no—
414C22—561no—
415C22—561no—
416C22—561no—
417C22#8972811yescharacteristic
418C22#8980811yescharacteristic
419C22#8980911yescharacteristic
420C22#8994511yescharacteristic
421C22#8995911yescharacteristic
422C22#8997411yescharacteristic
423C22#8997711yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—82no—
428C4—81no—
429C4—282no—
430C4—562no—
431C4#8957411yescharacteristic
432C4#8957611yescharacteristic
433C4#8958611yescharacteristic
434C4#8958711yescharacteristic
435C4C4×#114111yescharacteristic
436C4#8978611yescharacteristic
437C4#8982911yescharacteristic
438C4#8984411yescharacteristic
439C2—562no—
440C2#1172741111yescharacteristic
441C2#1172802311yescharacteristic
442C2#1172810211yescharacteristic
443C2#1172880111yescharacteristic
444C2#1172880211yescharacteristic
445C2#1172881511yescharacteristic
446C2#1172882011yescharacteristic
subgroupG/H
centerC23#6500
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1981C2
socleC23×C7#120
prime radicalC22×D28D4
cosocleC2×C42×C7C23
hypercenter#1981D7
hypocenterC7#8984
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
3. C7×#1981C2semidirect
4. #11729541C2semidirect
6. #11725508C2semidirect
7. #11725425C2semidirect
16. #89859C4semidirect
74. #1981D7semidirect
409. C7#8984semidirect

Maximal subgroups

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

subgroupindex
C2×#898592
#117310832
C7×#19812
#117295412
C2×#892782
#117255082
#117254252
#89847