Finite Group Databasebeta

← #13271980

Subgroups — #13271980

Order 1792.

430 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89916C211yesmaximal, characteristic
2C2×C7×#350C211yesmaximal, characteristic, complemented
3#11729758C211yesmaximal, characteristic, complemented
4#11729186C211yesmaximal, characteristic, complemented
5C2×#89306C211yesmaximal, characteristic, complemented
6C2×#89303C211yesmaximal, characteristic, complemented
7C2×#89297C211yesmaximal, characteristic, complemented
8C2×C7×#131C2211yescharacteristic
9C2×#6513C411yescharacteristic
10C2×#6464C2211yescharacteristic
11C2×C7×M32C2211yescharacteristic
12C22×C7×C16C2211yescharacteristic
13C2×#6411C411yescharacteristic
14#89916—22no—
15#89916—22no—
16C2×#6399C411yescharacteristic
17C2×#6396C411yescharacteristic
18C2×C8×Dic7C2211yescharacteristic
19C2×#6386C2211yescharacteristic
20C22×C7⋊C16C2211yescharacteristic
21C7×#350—22no—
22C22⋊(C7⋊C16)—22no—
23#89306—22no—
24#89303—22no—
25(C2×D7)⋊C16—22no—
26#89297—22no—
27#13196—71nomaximal, Sylow
28C2×C7×#41C2×C411yescharacteristic
29C2×#1157C2×C411yescharacteristic
30C7×#131—21no—
31C7×#131—21no—
32C7×#131—21no—
33C7×#131—21no—
34C2×C7×M16—21no—
35C2×C7×M16C2×C411yescharacteristic
36C22×C7×C8—21no—
37C22×C7×C8C2311yescharacteristic
38#6513—22no—
39#6513—22no—
40C2×#1144C811yescharacteristic
41C2×#1143C811yescharacteristic
42C2×#1142C811yescharacteristic
43C2×#1141C811yescharacteristic
44C2×C4×Dic7C2×C411yescharacteristic
45C2×#1136C2×C411yescharacteristic
46C22×C7⋊C8C2×C411yescharacteristic
47#6464—21no—
48#6464—21no—
49#6464—21no—
50#6464—21no—
51C2×#1131—21no—
52C2×C8×D7—21no—
53C7×M32—21no—
54C7×M32—21no—
55C2×C7×C16—21no—
56C2×C7×C16—21no—
57C2×C7×C16—21no—
58C2×C7×C16D412yes—
59#6411—22no—
60#6399—22no—
61#6396—22no—
62C8×Dic7D412yes—
63C8×Dic7D412yes—
64#6386—21no—
65#6386—21no—
66C2×C7⋊C16—21no—
67C2×C7⋊C16—21no—
68C2×C7⋊C16—21no—
69C2×C7⋊C16D412yes—
70C2×#443—71no—
71C2×#364—71no—
72C2×#350—71no—
73C2×#350D711yescharacteristic, complemented
74#2113—71no—
75#2113—71no—
76C2×#346—71no—
77C7×#41—21no—
78C7×#41—21no—
79C7×#41—21no—
80C7×#41—21no—
81C2×C7×Q8C2×C811yescharacteristic
82C2×C7×D4—21no—
83C2×C7×D4C2×C811yescharacteristic
84C22×C4×C7—21no—
85C22×C4×C7C22×C411yescharacteristic
86C2×C22⋊D7—21no—
87C22×Dic7—21no—
88#1157—21no—
89#1157—21no—
90#1157—21no—
91#1157—21no—
92C2×D28C2×C811yescharacteristic
93C2×C4×D7—21no—
94C2×Dic14C2×C811yescharacteristic
95C7×M16—21no—
96C7×M16—21no—
97C7×M16—41no—
98C7×M16—41no—
99C2×C7×C8—21no—
100C2×C7×C8—41no—
101C2×C7×C8—41no—
102C2×C7×C8C2×D411yescharacteristic
103C2×C7×C8C2×D411yescharacteristic
104C2×C7×C8C2×D411yescharacteristic
105C2×C7×C8C2×D411yescharacteristic
106C2×C7×C8#4111yescharacteristic
107C2×C7×C8#4111yescharacteristic
108#1144—22no—
109#1143—22no—
110#1142—22no—
111#1141—22no—
112C4×Dic7—21no—
113C4×Dic7C22⋊C412yes—
114#1136—21no—
115#1136—21no—
116C2×C7⋊C8—21no—
117C2×C7⋊C8C22⋊C412yes—
118C2×C7⋊C8C2×C811yescharacteristic
119C2×C7⋊C8C2×C811yescharacteristic
120C2×C7⋊C8M1612yes—
121#1131—41no—
122#1131—41no—
123C8×D7—41no—
124C8×D7—41no—
125C7×C16—22no—
126C7×C16—41no—
127C7⋊C16—22no—
128C7⋊C16—41no—
129C2×#135—71no—
130C2×#131—71no—
131C2×#131C2×D711yescharacteristic
132C2×M32—71no—
133C2×M32C2×D711yescharacteristic
134C22×C16—71no—
135C22×C16C2×D711yescharacteristic
136#443—142no—
137#443—142no—
138C2×#108—71no—
139C2×#104—71no—
140C2×#104—71no—
141C2×C4×C8—71no—
142#364—142no—
143#350—22no—
144#350—142no—
145C22⋊C16—142no—
146C22⋊C16—142no—
147#346—142no—
148C23×C7—21no—
149C23×C7#13111yescharacteristic
150C22×D7—21no—
151C7×Q8—21no—
152C7×Q8—21no—
153C7×D4—21no—
154C7×D4—21no—
155C7×D4—41no—
156C7×D4—41no—
157C2×C4×C7—21no—
158C2×C4×C7—41no—
159C2×C4×C7—41no—
160C2×C4×C7C2×C22⋊C411yescharacteristic
161C2×C4×C7C4×D411yescharacteristic
162C2×C4×C7C4×D411yescharacteristic
163C2×C4×C7C22×C811yescharacteristic
164C2×C4×C7C2×M1611yescharacteristic
165C2×C4×C7#13111yescharacteristic
166C22⋊D7—41no—
167C22⋊D7—41no—
168C2×Dic7—22no—
169C2×Dic7—21no—
170C2×Dic7—42no—
171D28—21no—
172D28—21no—
173C4×D7—41no—
174C4×D7—41no—
175Dic14—21no—
176Dic14—21no—
177C7×C8—41no—
178C7×C8#12111yescharacteristic
179C7×C8#12111yescharacteristic
180C7×C8#12411yescharacteristic
181C7×C8#12711yescharacteristic
182C7⋊C8—41no—
183C7⋊C8C22⋊C812yes—
184C7⋊C8C22⋊C812yes—
185C2×#41—71no—
186C2×#41C4×D711yescharacteristic
187#135—142no—
188#135—142no—
189C2×Q16—71no—
190C2×SD16—71no—
191C2×SD16—71no—
192C2×D8—71no—
193#131—21no—
194#131—21no—
195#131—21no—
196#131—21no—
197#131—141no—
198#131—141no—
199#131—141no—
200#131—141no—
201C2×M16—21no—
202C2×M16—71no—
203C2×M16—141no—
204C2×M16C4×D711yescharacteristic
205C22×C8—21no—
206C22×C8—71no—
207C22×C8—141no—
208C22×C8C22×D711yescharacteristic
209C2×C42—71no—
210M32—21no—
211M32—21no—
212M32—141no—
213M32—141no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—72no—
218C2×C16—141no—
219C2×C16—141no—
220C2×C16—141no—
221C2×C16C22⋊D712yes—
222#108—142no—
223#104—142no—
224#104—142no—
225C4×C8—72no—
226C4×C8—72no—
227C22×C7—22no—
228C22×C7—42no—
229C22×C7—41no—
230C22×C7#40811yescharacteristic
231C22×C7C8×D411yescharacteristic
232C22×C7#43611yescharacteristic
233C2×D7—42no—
234C2×D7—41no—
235C4×C7—41no—
236C4×C7#39011yescharacteristic
237C4×C7C2×C22⋊C811yescharacteristic
238C4×C7C8×D411yescharacteristic
239C4×C7#43611yescharacteristic
240Dic7—42no—
241Dic7—41no—
242#41—21no—
243#41—21no—
244#41—21no—
245#41—21no—
246#41—141no—
247#41—141no—
248#41—141no—
249#41—141no—
250C2×Q8—71no—
251C2×Q8C8×D711yescharacteristic
252C2×D4—21no—
253C2×D4—71no—
254C2×D4—141no—
255C2×D4C8×D711yescharacteristic
256C22×C4—21no—
257C22×C4—141no—
258C22×C4—141no—
259C22×C4C2×C4×D711yescharacteristic
260Q16—142no—
261SD16—142no—
262SD16—142no—
263D8—142no—
264M16—21no—
265M16—21no—
266M16—41no—
267M16—41no—
268M16—141no—
269M16—141no—
270M16—281no—
271M16—281no—
272C2×C8—21no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—72no—
276C2×C8—71no—
277C2×C8—71no—
278C2×C8—72no—
279C2×C8—141no—
280C2×C8—281no—
281C2×C8—281no—
282C2×C8#115711yescharacteristic
283C2×C8D4×D711yescharacteristic
284C2×C8D4×D711yescharacteristic
285C2×C8D4×D711yescharacteristic
286C2×C8#115911yescharacteristic
287C2×C8C2×C22⋊D711yescharacteristic
288C42—72no—
289C42—141no—
290C16—22no—
291C16—41no—
292C16—142no—
293C16—281no—
294C2×C7—21no—
295C2×C7—21no—
296C2×C7—81no—
297C2×C7#195411yescharacteristic
298C2×C7#217112yes—
299D7—81no—
300C23—21no—
301C23—141no—
302C23#647011yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—141no—
306Q8—141no—
307D4—21no—
308D4—21no—
309D4—41no—
310D4—41no—
311D4—141no—
312D4—141no—
313D4—281no—
314D4—281no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—141no—
319C2×C4—142no—
320C2×C4—282no—
321C2×C4—281no—
322C2×C4—281no—
323C2×C4D7×C22⋊C411yescharacteristic
324C2×C4(C22⋊D7)⋊C411yescharacteristic
325C2×C4C2×C8×D711yescharacteristic
326C2×C4#646411yescharacteristic
327C2×C4D7×M1611yescharacteristic
328C2×C4C4×C22⋊D711yescharacteristic
329C8—41no—
330C8—72no—
331C8—72no—
332C8—281no—
333C8#644711yescharacteristic
334C8#644811yescharacteristic
335C8#650211yescharacteristic
336C8#650311yescharacteristic
337C7#1319611yescharacteristic, complemented, Sylow
338C22—22no—
339C22—42no—
340C22—41no—
341C22—282no—
342C22—281no—
343C22(C22⋊D7)⋊C811yescharacteristic
344C22#8949911yescharacteristic
345C22#8990011yescharacteristic
346C4—41no—
347C4—282no—
348C4—281no—
349C4D7×C22⋊C811yescharacteristic
350C4#8950111yescharacteristic
351C4#8972911yescharacteristic
352C4C8×C22⋊D711yescharacteristic
353C2—21no—
354C2—21no—
355C2—81no—
356C2—561no—
357C2#1172687712yes—
358C2#1172767011yescharacteristic
subgroupG/H
centerC2×C8D4×D7
commutatorC2×C4×C7C22×C8
FrattiniC22×C8C22×D7
FittingC2×C7×#350C2
socleC22×C7C8×D4
prime radicalC2×#6513C4
cosocleC22×C7×C8C23
hypercenterC2×#350D7
hypocenterC7#13196
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C2×C7×#350C2semidirect
3. #11729758C2semidirect
4. #11729186C2semidirect
5. C2×#89306C2semidirect
6. C2×#89303C2semidirect
7. C2×#89297C2semidirect
73. C2×#350D7semidirect
337. C7#13196semidirect

Maximal subgroups

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

subgroupindex
C2×#899162
C2×C7×#3502
#117297582
#117291862
C2×#893062
C2×#893032
C2×#892972
#131967