Finite Group Databasebeta

← #13249145

Subgroups — #13249145

Order 1792.

606 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
1C4×#6487C211yesmaximal, characteristic
2C2×#89697C211yesmaximal, characteristic
3C7×#1797C211yesmaximal, characteristic
4C2×#89279C212yesmaximal, complemented
5#11725510C212yesmaximal, complemented
6C22×C42×C7C2211yescharacteristic
7C2×#6487C411yescharacteristic
8C2×C4×Dic14C2211yescharacteristic
9C2×C7×C4⋊C8C2212yes—
10C2×C7×C22⋊C8—21no—
11#89984C411yescharacteristic
12#89982—21no—
13C4×C22⋊Dic7—21no—
14C2×C22⋊(C7⋊C8)—21no—
15C4×C4⋊Dic7C2211yescharacteristic
16#89705—21no—
17C4×Dic7⋊C4—21no—
18#89701C411yescharacteristic
19#89700C411yescharacteristic
20#89697—24no—
21C2×C4⋊(C7⋊C8)—21no—
22C2×C4×C7⋊C8C2212yes—
23C7×#336—21no—
24#89279—24no—
25#9075—71nomaximal, Sylow
26C23×C4×C7C2×C411yescharacteristic
27C23×C4×C7D411yescharacteristic
28C23×C4×C7D411yescharacteristic
29C22×Dic14C2×C411yescharacteristic
30C22×C7×C8—22no—
31C2×C42×C7—22no—
32C2×C42×C7—22no—
33C2×C42×C7C2×C411yescharacteristic
34C2×C42×C7D411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C42×C7C2311yescharacteristic
37C2×C22⋊Dic7—21no—
38C2×C22⋊Dic7—21no—
39C2×C4⋊Dic7C2×C411yescharacteristic
40C2×C4⋊Dic7C2×C411yescharacteristic
41C2×C4⋊Dic7C2×C411yescharacteristic
42#6487—22no—
43#6487—22no—
44C2×Dic7⋊C4—21no—
45C2×Dic7⋊C4—21no—
46C2×Dic7⋊C4—21no—
47C2×C4×Dic7—21no—
48C2×C4×Dic7—21no—
49C22×C7⋊C8—22no—
50C4×Dic14—22no—
51C4×Dic14—22no—
52C7×C4⋊C8—22no—
53C7×C4⋊C8—22no—
54C7×C22⋊C8—42no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59C7⋊#95—21no—
60C22⋊(C7⋊C8)—24no—
61C4⋊(C7⋊C8)—24no—
62C4×C7⋊C8—22no—
63C4×C7⋊C8D414yes—
64C2×#431—71no—
65C4×C22⋊Q8—71no—
66#1797D711yescharacteristic
67C2×Q8⋊C8—72no—
68#1279—72no—
69C24×C7C22⋊C411yescharacteristic
70C22×C4×C7—22no—
71C22×C4×C7—22no—
72C22×C4×C7—22no—
73C22×C4×C7—21no—
74C22×C4×C7—21no—
75C22×C4×C7—21no—
76C22×C4×C7—21no—
77C22×C4×C7—22no—
78C22×C4×C7—41no—
79C22×C4×C7—41no—
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C22⋊C411yescharacteristic
82C22×C4×C7C22⋊C411yescharacteristic
83C22×C4×C7SD1612yes—
84C22×C4×C7Q1612yes—
85C22×C4×C7C22×C411yescharacteristic
86C22×C4×C7C2×D411yescharacteristic
87C22×C4×C7C2×D411yescharacteristic
88C22×Dic7—21no—
89C22×Dic7—21no—
90C22×Dic7—21no—
91C22×Dic7—21no—
92C2×Dic14—22no—
93C2×Dic14—22no—
94C2×Dic14—21no—
95C2×Dic14M1612yes—
96C2×C7×C8—42no—
97C2×C7×C8—42no—
98C2×C7×C8—42no—
99C42×C7—22no—
100C42×C7—21no—
101C42×C7—22no—
102C42×C7—21no—
103C42×C7C2×D412yes—
104C42×C7#4112yes—
105C22⋊Dic7—24no—
106C22⋊Dic7—42no—
107C4⋊Dic7—21no—
108C4⋊Dic7—22no—
109C4⋊Dic7—22no—
110C4⋊Dic7M1612yes—
111Dic7⋊C4—24no—
112Dic7⋊C4—42no—
113Dic7⋊C4—41no—
114Dic7⋊C4—41no—
115C4×Dic7—42no—
116C4×Dic7—42no—
117C2×C7⋊C8—24no—
118C2×C7⋊C8—42no—
119C2×C7⋊C8—42no—
120C2×C22⋊Q8—71no—
121C2×C4×Q8—71no—
122C22×C42C2×D711yescharacteristic
123#431—144no—
124C2×C4⋊C8—141no—
125C2×C4⋊C8C2×D712yes—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—141no—
128C2×C4×C8—72no—
129#391—71no—
130#389—71no—
131#387—141no—
132#385—141no—
133#380—71no—
134C4×C4⋊C4—71no—
135C4×C4⋊C4—141no—
136C4×C22⋊C4—141no—
137#336—21no—
138Q8⋊C8—144no—
139C23×C7—21no—
140C23×C7—21no—
141C23×C7—21no—
142C23×C7—21no—
143C23×C7—21no—
144C23×C7—21no—
145C23×C7#10312yes—
146C23×C7C2×C22⋊C411yescharacteristic
147C2×C4×C7—21no—
148C2×C4×C7—21no—
149C2×C4×C7—21no—
150C2×C4×C7—21no—
151C2×C4×C7—24no—
152C2×C4×C7—24no—
153C2×C4×C7—21no—
154C2×C4×C7—21no—
155C2×C4×C7—21no—
156C2×C4×C7—21no—
157C2×C4×C7—21no—
158C2×C4×C7—21no—
159C2×C4×C7—42no—
160C2×C4×C7—42no—
161C2×C4×C7—42no—
162C2×C4×C7—42no—
163C2×C4×C7#10312yes—
164C2×C4×C7C4×D412yes—
165C2×C4×C7#12011yescharacteristic
166C2×C4×C7#12112yes—
167C2×C4×C7#12311yescharacteristic
168C2×C4×C7C2×M1611yescharacteristic
169C2×C4×C7C2×M1611yescharacteristic
170C2×C4×C7#13112yes—
171C2×C4×C7C2×SD1611yescharacteristic
172C2×C4×C7C2×Q1611yescharacteristic
173C2×C4×C7#13512yes—
174C2×Dic7—22no—
175C2×Dic7—22no—
176C2×Dic7—41no—
177C2×Dic7—41no—
178C2×Dic7—41no—
179C2×Dic7—41no—
180C2×Dic7—41no—
181C2×Dic7—41no—
182C2×Dic7—41no—
183C2×Dic7—41no—
184C2×Dic7—41no—
185C2×Dic7—41no—
186Dic14—24no—
187Dic14—42no—
188C7×C8—82no—
189C7⋊C8—44no—
190C22×Q8—71no—
191C23×C4C4×D711yescharacteristic
192C23×C4D2811yescharacteristic
193C23×C4C22⋊D711yescharacteristic
194C22×C8—22no—
195C22×C8—142no—
196C22⋊Q8—142no—
197C22⋊Q8—142no—
198C4×Q8—142no—
199C4×Q8—142no—
200C2×C4⋊C4—71no—
201C2×C4⋊C4—71no—
202C2×C4⋊C4—71no—
203C2×C4⋊C4—141no—
204C2×C4⋊C4—141no—
205C2×C4⋊C4—141no—
206C2×C22⋊C4—141no—
207C2×C22⋊C4—141no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—141no—
211C2×C42—141no—
212C2×C42C4×D711yescharacteristic
213C2×C42D2811yescharacteristic
214C2×C42C22⋊D711yescharacteristic
215C2×C42C22×D711yescharacteristic
216C4⋊C8—22no—
217C4⋊C8—22no—
218C4⋊C8—144no—
219C22⋊C8—42no—
220C22⋊C8—144no—
221C4×C8—74no—
222C4×C8—142no—
223#95—141no—
224#95—141no—
225#95—141no—
226#95—141no—
227#95—141no—
228C22×C7—22no—
229C22×C7—22no—
230C22×C7—22no—
231C22×C7—41no—
232C22×C7—41no—
233C22×C7—41no—
234C22×C7—41no—
235C22×C7#38611yescharacteristic
236C22×C7#40711yescharacteristic
237C22×C7#40811yescharacteristic
238C22×C7C2×#10311yescharacteristic
239C22×C7#41611yescharacteristic
240C22×C7#42111yescharacteristic
241C22×C7#42111yescharacteristic
242C4×C7—22no—
243C4×C7—21no—
244C4×C7—21no—
245C4×C7—41no—
246C4×C7—41no—
247C4×C7#43512yes—
248C4×C7#43612yes—
249C4×C7#46512yes—
250C4×C7#46712yes—
251Dic7—42no—
252Dic7—42no—
253Dic7—81no—
254Dic7—81no—
255C24(C2×D7)⋊C411yescharacteristic
256C2×Q8—72no—
257C2×Q8—141no—
258C2×Q8—142no—
259C2×Q8—142no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—141no—
271C22×C4—141no—
272C22×C4—141no—
273C22×C4—141no—
274C22×C4(C2×D7)⋊C411yescharacteristic
275C22×C4(C2×D7)⋊C411yescharacteristic
276C22×C4(C2×D7)⋊C411yescharacteristic
277C22×C4#114212yes—
278C22×C4#114412yes—
279C22×C4C2×C4×D711yescharacteristic
280C22×C4C2×D2811yescharacteristic
281C22×C4C2×C22⋊D711yescharacteristic
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—144no—
286C2×C8—282no—
287C2×C8—282no—
288C4⋊C4—72no—
289C4⋊C4—144no—
290C4⋊C4—141no—
291C4⋊C4—142no—
292C4⋊C4—142no—
293C4⋊C4—282no—
294C4⋊C4—281no—
295C4⋊C4—281no—
296C22⋊C4—144no—
297C22⋊C4—282no—
298C42—22no—
299C42—21no—
300C42—21no—
301C42—22no—
302C42—282no—
303C42—282no—
304C42D4×D712yes—
305C42#115912yes—
306C2×C7—42no—
307C2×C7#148111yescharacteristic
308C2×C7#148211yescharacteristic
309C2×C7#148711yescharacteristic
310C2×C7#148811yescharacteristic
311C2×C7#187011yescharacteristic
312C2×C7#189211yescharacteristic
313C2×C7#189711yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23#638412yes—
321C23C2×(C2×D7)⋊C411yescharacteristic
322Q8—144no—
323Q8—282no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—142no—
341C2×C4—142no—
342C2×C4—281no—
343C2×C4—281no—
344C2×C4—281no—
345C2×C4—281no—
346C2×C4—281no—
347C2×C4—281no—
348C2×C4—281no—
349C2×C4—281no—
350C2×C4—281no—
351C2×C4—281no—
352C2×C4#638412yes—
353C2×C4(C22⋊D7)⋊C412yes—
354C2×C4#644511yescharacteristic
355C2×C4#644911yescharacteristic
356C2×C4#646412yes—
357C2×C4D7×M1611yescharacteristic
358C2×C4D7×M1611yescharacteristic
359C2×C4C2×#114211yescharacteristic
360C2×C4#650212yes—
361C2×C4C2×#114411yescharacteristic
362C2×C4#651312yes—
363C8—82no—
364C8—284no—
365C7#907511yescharacteristic, complemented, Sylow
366C22—22no—
367C22—22no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22#8973011yescharacteristic
374C22C2×#638411yescharacteristic
375C22#8977411yescharacteristic
376C22#8988211yescharacteristic
377C22#8989811yescharacteristic
378C22#8991111yescharacteristic
379C22#8991111yescharacteristic
380C4—21no—
381C4—21no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—282no—
386C4—282no—
387C4—561no—
388C4—561no—
389C4#8950012yes—
390C4#8950112yes—
391C4#8981312yes—
392C4#8982312yes—
393C2—42no—
394C2#1172726811yescharacteristic
395C2#1172770711yescharacteristic
396C2#1172772011yescharacteristic
397C2#1172818311yescharacteristic
398C2#1172825411yescharacteristic
399C2#1172851311yescharacteristic
400C2#1172855211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D7
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#1797C2
socleC23×C7C2×C22⋊C4
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#1797D7
hypocenterC7#9075
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
4. C2×#89279C2semidirect
5. #11725510C2semidirect
365. C7#9075semidirect

Maximal subgroups

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

subgroupindex
C4×#64872
C2×#896972
C7×#17972
C2×#892792
#117255102
#90757