Finite Group Databasebeta

← #13272038

Subgroups — #13272038

Order 1792.

482 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11741348C211yesmaximal, characteristic
2C2×C7×#359C211yesmaximal, characteristic, complemented
3C2×#89362C211yesmaximal, characteristic, complemented
4C2×#89305C211yesmaximal, characteristic, complemented
5C2×#89297C211yesmaximal, characteristic, complemented
6#11728447C211yesmaximal, characteristic, complemented
7C2×#89292C211yesmaximal, characteristic, complemented
8C2×C7×#135C2211yescharacteristic
9#90523—21no—
10C2×#6513—21no—
11C2×#6467C2211yescharacteristic
12C22×C7×C16C2211yescharacteristic
13C2×C7×#108C2211yescharacteristic
14#89963C411yescharacteristic
15#89953C411yescharacteristic
16#89947—21no—
17#89940—21no—
18#89927C411yescharacteristic
19#89923C411yescharacteristic
20C2×#6396—21no—
21#89890—21no—
22C2×#6393C2211yescharacteristic
23C2×C8×Dic7C2211yescharacteristic
24C22×C7⋊C16C2211yescharacteristic
25C7×#359—22no—
26#89362—22no—
27#89305—22no—
28#89297—21no—
29#89297—21no—
30#89292—22no—
31#13209—71nomaximal, Sylow
32C2×C7×#41—21no—
33C2×#1157—21no—
34C7×#135—21no—
35C7×#135—21no—
36C7×#135—21no—
37C7×#135—21no—
38C2×C7×Q16C2×C411yescharacteristic
39C2×C7×SD16—21no—
40C2×C7×D8C2×C411yescharacteristic
41C2×C7×M16—21no—
42C22×C7×C8C2311yescharacteristic
43#6513—42no—
44#6513—42no—
45#6510—21no—
46#6507—21no—
47C2×#1144—21no—
48C2×#1143—21no—
49#6503—21no—
50#6502—42no—
51#6499—21no—
52C2×#1142—21no—
53C2×#1141—21no—
54C4×C22⋊D7—42no—
55C2×C4×Dic7D411yescharacteristic
56C2×#1136—21no—
57C22×C7⋊C8D411yescharacteristic
58C2×Dic28C2×C411yescharacteristic
59#6467—21no—
60#6467—21no—
61#6467—21no—
62#6467—21no—
63C2×D56C2×C411yescharacteristic
64C2×#1132—21no—
65C2×C7×C16—21no—
66C2×C7×C16—21no—
67C2×C7×C16D412yescomplemented
68C7×#108—21no—
69C7×#108—21no—
70#6396—42no—
71#6393—21no—
72#6393—21no—
73Dic7⋊C8—42no—
74C8×Dic7C2×C411yescharacteristic
75C8×Dic7C2×C411yescharacteristic
76C8×Dic7D411yescharacteristic
77C8×Dic7D411yescharacteristic
78C2×C7⋊C16—21no—
79C2×C7⋊C16—21no—
80C2×C7⋊C16D412yescomplemented
81#3147—71no—
82C2×#359—71no—
83C2×#359—71no—
84C2×#359—71no—
85C2×#359D711yescharacteristic, complemented
86C2×#346—71no—
87#1848—71no—
88C7×#41—41no—
89C7×#41—41no—
90C7×#41—41no—
91C7×#41—41no—
92C2×C7×Q8—21no—
93C2×C7×D4—21no—
94C2×C7×D4—41no—
95C22×C4×C7—41no—
96C22×C4×C7C2×D411yescharacteristic
97C2×C22⋊D7—41no—
98C2×C22⋊D7—42no—
99C22×Dic7SD1612yes—
100#1157—41no—
101#1157—41no—
102#1157—41no—
103#1157—41no—
104C2×D28—21no—
105C2×C4×D7—41no—
106C2×Dic14—21no—
107C7×Q16—21no—
108C7×Q16—21no—
109C7×SD16—41no—
110C7×SD16—41no—
111C7×D8—21no—
112C7×D8—21no—
113C7×M16—41no—
114C7×M16—41no—
115C2×C7×C8—41no—
116C2×C7×C8C22×C411yescharacteristic
117C2×C7×C8C2×D411yescharacteristic
118C2×C7×C8C2×D411yescharacteristic
119C2×C7×C8C2×D411yescharacteristic
120C2×C7×C8#4111yescharacteristic
121C2×C7×C8#4111yescharacteristic
122C22⋊Dic7—42no—
123#1144—42no—
124#1143—42no—
125#1142—42no—
126#1141—42no—
127(C2×D7)⋊C4—42no—
128Dic7⋊C4—42no—
129C4×Dic7C22⋊C411yescharacteristic
130C4×Dic7C22⋊C411yescharacteristic
131C4×Dic7D812yes—
132#1136—41no—
133#1136—41no—
134C2×C7⋊C8—41no—
135C2×C7⋊C8C22⋊C411yescharacteristic
136C2×C7⋊C8C22⋊C411yescharacteristic
137C2×C7⋊C8D812yes—
138C2×C7⋊C8SD1612yes—
139Dic28—21no—
140Dic28—21no—
141D56—21no—
142D56—21no—
143#1132—41no—
144#1132—41no—
145C7×C16—22no—
146C7⋊C16—22no—
147C2×#135—71no—
148C2×#135—141no—
149C2×#135C2×D711yescharacteristic
150#532—141no—
151C22×C16—71no—
152C22×C16C2×D711yescharacteristic
153#495—71no—
154#495—71no—
155#495—141no—
156#494—71no—
157#493—71no—
158#492—141no—
159C2×#108—71no—
160C2×#108—141no—
161C2×#108C2×D711yescharacteristic
162#423—141no—
163C2×C4×C8—71no—
164#359—22no—
165#359—142no—
166#359—142no—
167#359—142no—
168#346—141no—
169#346—141no—
170C23×C7—41no—
171C23×C7C2×SD1611yescharacteristic
172C22×D7—41no—
173C7×Q8—41no—
174C7×Q8—41no—
175C7×D4—41no—
176C7×D4—41no—
177C7×D4—81no—
178C7×D4—81no—
179C2×C4×C7—41no—
180C2×C4×C7—81no—
181C2×C4×C7—81no—
182C2×C4×C7C2×C22⋊C411yescharacteristic
183C2×C4×C7#12411yescharacteristic
184C2×C4×C7#12711yescharacteristic
185C2×C4×C7C2×D811yescharacteristic
186C2×C4×C7C2×D811yescharacteristic
187C2×C4×C7C2×SD1611yescharacteristic
188C22⋊D7—84no—
189C22⋊D7—81no—
190C22⋊D7—81no—
191C2×Dic7—42no—
192C2×Dic7—41no—
193C2×Dic7#10212yes—
194C2×Dic7#10212yes—
195D28—41no—
196D28—41no—
197C4×D7—81no—
198C4×D7—81no—
199Dic14—41no—
200Dic14—41no—
201C7×C8—81no—
202C7×C8C4×D411yescharacteristic
203C7×C8C4×D411yescharacteristic
204C7×C8#12111yescharacteristic
205C7×C8#12111yescharacteristic
206C7⋊C8—81no—
207C7⋊C8#10212yes—
208C7⋊C8#10212yes—
209C2×#41—21no—
210C2×#41—141no—
211#135—21no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—141no—
216#135—141no—
217#135—141no—
218#135—141no—
219#135—282no—
220#135—282no—
221C2×Q16—71no—
222C2×Q16—141no—
223C2×Q16C4×D711yescharacteristic
224C2×SD16—21no—
225C2×SD16—141no—
226C2×SD16—141no—
227C2×SD16—141no—
228C2×D8—71no—
229C2×D8—141no—
230C2×D8C4×D711yescharacteristic
231C2×M16—21no—
232C2×M16—141no—
233C22×C8—71no—
234C22×C8C22×D711yescharacteristic
235C4⋊Q8—141no—
236#127—141no—
237#124—141no—
238#124—141no—
239#121—282no—
240C4×D4—282no—
241C2×C42—71no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—72no—
245C2×C16—141no—
246C2×C16—141no—
247C2×C16C22⋊D712yescomplemented
248#108—21no—
249#108—21no—
250#108—141no—
251#108—141no—
252#108—282no—
253C4⋊C8—282no—
254C4×C8—71no—
255C4×C8—71no—
256C4×C8—71no—
257C4×C8—71no—
258C22×C7—22no—
259C22×C7—82no—
260C22×C7—81no—
261C22×C7C2×#10211yescharacteristic
262C22×C7#48611yescharacteristic
263C22×C7#49211yescharacteristic
264C2×D7—82no—
265C2×D7—81no—
266C4×C7—81no—
267C4×C7#39011yescharacteristic
268C4×C7C2×#10211yescharacteristic
269C4×C7#48611yescharacteristic
270C4×C7#49311yescharacteristic
271Dic7—22no—
272Dic7—22no—
273Dic7—81no—
274#41—41no—
275#41—41no—
276#41—41no—
277#41—41no—
278#41—281no—
279#41—281no—
280#41—281no—
281#41—281no—
282C2×Q8—21no—
283C2×Q8—141no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—141no—
287C2×D4—282no—
288C2×D4—281no—
289C22×C4—41no—
290C22×C4—72no—
291C22×C4—281no—
292C22×C4D4×D711yescharacteristic
293Q16—21no—
294Q16—21no—
295Q16—141no—
296Q16—141no—
297Q16—282no—
298SD16—41no—
299SD16—41no—
300SD16—282no—
301SD16—282no—
302SD16—281no—
303SD16—281no—
304D8—21no—
305D8—21no—
306D8—141no—
307D8—141no—
308D8—282no—
309M16—41no—
310M16—41no—
311M16—281no—
312M16—281no—
313C2×C8—41no—
314C2×C8—71no—
315C2×C8—71no—
316C2×C8—72no—
317C2×C8—72no—
318C2×C8—281no—
319C2×C8C2×C4×D711yescharacteristic
320C2×C8#115711yescharacteristic
321C2×C8D4×D711yescharacteristic
322C2×C8D4×D711yescharacteristic
323C2×C8#115911yescharacteristic
324C2×C8C2×C22⋊D711yescharacteristic
325C4⋊C4—282no—
326C22⋊C4—282no—
327C22⋊C4—282no—
328C42—71no—
329C42—71no—
330C42—72no—
331C16—22no—
332C16—142no—
333C2×C7—21no—
334C2×C7—21no—
335C2×C7—161no—
336C2×C7#195711yescharacteristic
337C2×C7#214312yes—
338D7—161no—
339C23—41no—
340C23—281no—
341C23D7×SD1611yescharacteristic
342Q8—41no—
343Q8—41no—
344Q8—281no—
345Q8—281no—
346D4—41no—
347D4—41no—
348D4—81no—
349D4—81no—
350D4—281no—
351D4—281no—
352D4—564no—
353D4—561no—
354D4—561no—
355C2×C4—41no—
356C2×C4—72no—
357C2×C4—72no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—282no—
361C2×C4—281no—
362C2×C4—561no—
363C2×C4—561no—
364C2×C4D7×C22⋊C411yescharacteristic
365C2×C4#644811yescharacteristic
366C2×C4D7×D811yescharacteristic
367C2×C4D7×D811yescharacteristic
368C2×C4D7×SD1611yescharacteristic
369C2×C4#650311yescharacteristic
370C8—72no—
371C8—72no—
372C8—81no—
373C8—561no—
374C8(C22⋊D7)⋊C411yescharacteristic
375C8#644711yescharacteristic
376C8C4×C22⋊D711yescharacteristic
377C8#650211yescharacteristic
378C7#1320911yescharacteristic, complemented, Sylow
379C22—22no—
380C22—81no—
381C22—82no—
382C22—561no—
383C22—562no—
384C22#8953211yescharacteristic
385C22D7×#10211yescharacteristic
386C22#8994711yescharacteristic
387C4—81no—
388C4—142no—
389C4—142no—
390C4—561no—
391C4#8953211yescharacteristic
392C4D7×#10211yescharacteristic
393C4#8972911yescharacteristic
394C4#8992311yescharacteristic
395C2—21no—
396C2—21no—
397C2—161no—
398C2—1121no—
399C2#1172699512yes—
400C2#1172791111yescharacteristic
subgroupG/H
centerC2×C4D7×D8
commutatorC2×C7×C8C22×C4
FrattiniC22×C8C22×D7
FittingC2×C7×#359C2
socleC22×C7C2×#102
prime radical#11741348C2
cosocleC22×C7×C8C23
hypercenterC2×#359D7
hypocenterC7#13209
LCSG ▷ C2×C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#359

Complements

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

NH ≅ G/Ntype
2. C2×C7×#359C2semidirect
3. C2×#89362C2semidirect
4. C2×#89305C2semidirect
5. C2×#89297C2semidirect
6. #11728447C2semidirect
7. C2×#89292C2semidirect
67. C2×C7×C16D4semidirect
80. C2×C7⋊C16D4semidirect
85. C2×#359D7semidirect
247. C2×C16C22⋊D7semidirect
378. C7#13209semidirect

Maximal subgroups

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

subgroupindex
#117413482
C2×C7×#3592
C2×#893622
C2×#893052
C2×#892972
#117284472
C2×#892922
#132097