Finite Group Databasebeta

← #13264178

Subgroups — #13264178

Order 1792.

470 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739867C211yesmaximal, characteristic
2C4×C7×#100C211yesmaximal, characteristic, complemented
3#11729354C211yesmaximal, characteristic, complemented
4#11725302C212yesmaximal, complemented
5#11725299C212yesmaximal, complemented
6C2×C4×C7×D4C2211yescharacteristic
7C2×#6493C411yescharacteristic
8C2×C7×#100—21no—
9C4×C7×M16—21no—
10#89995—21no—
11#89985—21no—
12#89983C411yescharacteristic
13C2×C22⋊(C7⋊C8)—21no—
14#89763C2211yescharacteristic
15#89758C2211yescharacteristic
16#89732C411yescharacteristic
17#89731—21no—
18#89721C411yescharacteristic
19#89712—21no—
20C7×#343C2212yes—
21#89323C2212yes—
22#89320—21no—
23#11737—71nomaximal, Sylow
24C22×C7×D4D411yescharacteristic
25C23×C4×C7C2×C411yescharacteristic
26C23×C4×C7D411yescharacteristic
27C22×C22⋊D7—21no—
28C22×C22⋊D7—21no—
29C22×D28C2×C411yescharacteristic
30C2×C7×M16—22no—
31C4×C7×D4—41no—
32C4×C7×D4—41no—
33C2×C7×C4⋊C4C2311yescharacteristic
34C2×C7×C22⋊C4C2×C411yescharacteristic
35C2×C7×C22⋊C4D411yescharacteristic
36C2×C42×C7D411yescharacteristic
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39#6493—41no—
40#6493—41no—
41C2×(C2×D7)⋊C4—21no—
42C2×(C2×D7)⋊C4—21no—
43C2×(C2×D7)⋊C4—21no—
44C2×(C2×D7)⋊C4—21no—
45C2×C4⋊Dic7C2×C411yescharacteristic
46C2×Dic7⋊C4—21no—
47C22×C7⋊C8—41no—
48C7×#100—24no—
49C7×#97—41no—
50C4×C7×C8—41no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95C2×C411yescharacteristic
55C7⋊#95C2×C411yescharacteristic
56C22⋊(C7⋊C8)—22no—
57C22⋊(C7⋊C8)—41no—
58#2635—71no—
59C4×#100D711yescharacteristic, complemented
60#1459—71no—
61#1353—72no—
62#1345—72no—
63C24×C7C22⋊C411yescharacteristic
64C24×C7C22⋊C411yescharacteristic
65C23×D7—21no—
66C2×C7×D4—22no—
67C2×C7×D4—22no—
68C2×C7×D4—41no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—81no—
74C22×C4×C7—81no—
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22⋊C411yescharacteristic
77C22×C4×C7C22×C411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C22×C4×C7C2×D411yescharacteristic
80C2×C22⋊D7—42no—
81C2×C22⋊D7—42no—
82C2×C22⋊D7—81no—
83C2×C22⋊D7—81no—
84C2×C22⋊D7—81no—
85C2×C22⋊D7—81no—
86C22×Dic7—21no—
87C22×Dic7—21no—
88C22×Dic7—21no—
89C2×D28—41no—
90C2×D28—81no—
91C7×M16—24no—
92C7×M16—42no—
93C2×C7×C8—42no—
94C7×C4⋊C4—41no—
95C7×C22⋊C4—41no—
96C7×C22⋊C4—41no—
97C42×C7—21no—
98C42×C7—21no—
99C22⋊Dic7—81no—
100C22⋊Dic7—81no—
101(C2×D7)⋊C4—41no—
102(C2×D7)⋊C4—41no—
103(C2×D7)⋊C4—42no—
104(C2×D7)⋊C4—81no—
105(C2×D7)⋊C4—81no—
106C4⋊Dic7—41no—
107Dic7⋊C4—81no—
108C2×C7⋊C8—42no—
109C2×C7⋊C8—82no—
110C2×#121—71no—
111C2×C4×D4C2×D711yescharacteristic
112C2×#100—21no—
113C2×C22⋊C8—141no—
114C4×M16—21no—
115#400—71no—
116#399—71no—
117#394—71no—
118#394—141no—
119#392—71no—
120#392—141no—
121#388—141no—
122#386—141no—
123#381—71no—
124#343C2×D712yes—
125#324—72no—
126#323—141no—
127C23×C7—21no—
128C23×C7—21no—
129C23×C7—21no—
130C23×C7—21no—
131C23×C7—21no—
132C23×C7—41no—
133C23×C7—41no—
134C23×C7—41no—
135C23×C7—41no—
136C23×C7#10412yes—
137C23×C7C2×C22⋊C411yescharacteristic
138C22×D7—41no—
139C22×D7—41no—
140C22×D7—41no—
141C22×D7—41no—
142C22×D7—41no—
143C22×D7—41no—
144C22×D7—41no—
145C7×D4—44no—
146C2×C4×C7—21no—
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—41no—
152C2×C4×C7—42no—
153C2×C4×C7—41no—
154C2×C4×C7—41no—
155C2×C4×C7—41no—
156C2×C4×C7—81no—
157C2×C4×C7—81no—
158C2×C4×C7—81no—
159C2×C4×C7#9911yescharacteristic
160C2×C4×C7#9911yescharacteristic
161C2×C4×C7#13512yes—
162C22⋊D7—84no—
163C22⋊D7—84no—
164C2×Dic7—41no—
165C2×Dic7—41no—
166C2×Dic7—41no—
167C2×Dic7—41no—
168C2×Dic7—41no—
169C2×Dic7—41no—
170C2×Dic7—41no—
171C2×Dic7—41no—
172C2×Dic7—41no—
173D28—82no—
174C7×C8—44no—
175C7⋊C8—82no—
176C22×D4—71no—
177C22×D4—141no—
178C22×D4—141no—
179C22×D4C22⋊D711yescharacteristic
180C23×C4C4×D711yescharacteristic
181C23×C4D2811yescharacteristic
182C2×M16—22no—
183C22×C8—281no—
184#121—281no—
185#121—281no—
186C4×D4—41no—
187C4×D4—41no—
188C2×C4⋊C4—71no—
189C2×C4⋊C4—141no—
190C2×C4⋊C4C22×D711yescharacteristic
191C2×C22⋊C4—141no—
192C2×C22⋊C4—141no—
193C2×C22⋊C4—141no—
194C2×C22⋊C4—141no—
195C2×C22⋊C4—141no—
196C2×C22⋊C4—141no—
197C2×C22⋊C4C4×D711yescharacteristic
198C2×C22⋊C4D2811yescharacteristic
199C2×C42C22⋊D711yescharacteristic
200#100—24no—
201C22⋊C8—142no—
202C22⋊C8—281no—
203#97—41no—
204C4×C8—41no—
205#95—71no—
206#95—71no—
207#95—141no—
208#95—141no—
209#95—141no—
210C22×C7—21no—
211C22×C7—21no—
212C22×C7—22no—
213C22×C7—42no—
214C22×C7—41no—
215C22×C7—41no—
216C22×C7—41no—
217C22×C7—41no—
218C22×C7—41no—
219C22×C7—81no—
220C22×C7—81no—
221C22×C7—81no—
222C22×C7C2×#9911yescharacteristic
223C22×C7#41611yescharacteristic
224C22×C7C2×#10411yescharacteristic
225C2×D7—81no—
226C2×D7—81no—
227C2×D7—81no—
228C2×D7—81no—
229C2×D7—81no—
230C2×D7—81no—
231C2×D7—81no—
232C4×C7—21no—
233C4×C7—21no—
234C4×C7—22no—
235C4×C7—41no—
236C4×C7—41no—
237C4×C7—41no—
238Dic7—81no—
239Dic7—81no—
240Dic7—81no—
241C24—141no—
242C24(C2×D7)⋊C411yescharacteristic
243C24(C2×D7)⋊C411yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—41no—
247C2×D4—281no—
248C2×D4—282no—
249C2×D4—282no—
250C2×D4—561no—
251C2×D4—561no—
252C2×D4—561no—
253C2×D4—561no—
254C2×D4—561no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—141no—
262C22×C4—141no—
263C22×C4—141no—
264C22×C4(C2×D7)⋊C411yescharacteristic
265C22×C4(C2×D7)⋊C411yescharacteristic
266C22×C4C2×C4×D711yescharacteristic
267C22×C4C2×D2811yescharacteristic
268C22×C4C2×C22⋊D711yescharacteristic
269M16—24no—
270M16—42no—
271C2×C8—42no—
272C2×C8—282no—
273C2×C8—562no—
274C4⋊C4—41no—
275C4⋊C4—281no—
276C4⋊C4—561no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—282no—
280C22⋊C4—281no—
281C22⋊C4—281no—
282C22⋊C4—561no—
283C22⋊C4—561no—
284C22⋊C4—561no—
285C22⋊C4—561no—
286C42—21no—
287C42—21no—
288C2×C7—21no—
289C2×C7—21no—
290C2×C7—42no—
291C2×C7—81no—
292C2×C7#150111yescharacteristic
293C2×C7#212111yescharacteristic
294C2×C7#213411yescharacteristic
295D7—161no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—281no—
306C23—281no—
307C23—281no—
308C23—281no—
309C23—281no—
310C23—281no—
311C23—281no—
312C23#637912yes—
313C23C2×(C2×D7)⋊C411yescharacteristic
314D4—44no—
315D4—562no—
316D4—564no—
317D4—564no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—281no—
332C2×C4—281no—
333C2×C4—281no—
334C2×C4—281no—
335C2×C4—281no—
336C2×C4—281no—
337C2×C4—281no—
338C2×C4—281no—
339C2×C4—281no—
340C2×C4#638011yescharacteristic
341C2×C4#638011yescharacteristic
342C2×C4#651312yes—
343C8—44no—
344C8—562no—
345C7#1173711yescharacteristic, complemented, Sylow
346C22—21no—
347C22—21no—
348C22—22no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—561no—
359C22—561no—
360C22—561no—
361C22—561no—
362C22—561no—
363C22—561no—
364C22—561no—
365C22C2×#637911yescharacteristic
366C22C2×#638011yescharacteristic
367C22#8977411yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—561no—
375C4—561no—
376C4—561no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—81no—
381C2—1121no—
382C2#1172719711yescharacteristic
383C2#1172784811yescharacteristic
384C2#1172790311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC4×C7×#100C2
socleC22×C7C2×#99
prime radical#11739867C2
cosocleC2×C7×C4⋊C4C23
hypercenterC4×#100D7
hypocenterC7#11737
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. C4×C7×#100C2semidirect
3. #11729354C2semidirect
4. #11725302C2semidirect
5. #11725299C2semidirect
59. C4×#100D7semidirect
345. C7#11737semidirect

Maximal subgroups

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

subgroupindex
#117398672
C4×C7×#1002
#117293542
#117253022
#117252992
#117377