Finite Group Databasebeta

← #13249473

Subgroups — #13249473

Order 1792.

568 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740714C211yesmaximal, characteristic
2C2×#89607C211yesmaximal, characteristic
3C2×C7×#333C211yesmaximal, characteristic, complemented
4C2×#89341C211yesmaximal, characteristic, complemented
5#11728229C211yesmaximal, characteristic
6#11725508C211yesmaximal, characteristic, complemented
7#11725508C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×#6509C412yes—
10C2×C42×D7C2211yescharacteristic
11C2×C7×C4⋊C8C2211yescharacteristic
12C2×C7×C4⋊C8C2211yescharacteristic
13#90002C412yes—
14C2×(C2×D7)⋊C8—21no—
15C2×(C2×D7)⋊C8—21no—
16C2×#6389—21no—
17#89759—21no—
18#89759—21no—
19#89745—21no—
20#89745—21no—
21#89707C2211yescharacteristic
22C2×C4⋊(C7⋊C8)C2211yescharacteristic
23C2×C4⋊(C7⋊C8)C2211yescharacteristic
24#89607—22no—
25#89607—22no—
26C7×#333—22no—
27#89345—21no—
28#89341—22no—
29#9136—71nomaximal, Sylow
30C22×C7×Q8C2×C412yes—
31C22×C4×D7C2×C411yescharacteristic
32C22×C4×D7D411yescharacteristic
33C22×C4×D7D411yescharacteristic
34C22×C7×C8—21no—
35C22×C7×C8—21no—
36C7×C4⋊Q8—21no—
37C7×C4⋊Q8—21no—
38C7×C4⋊Q8—21no—
39C7×C4⋊Q8—21no—
40C2×C7×C4⋊C4—21no—
41C2×C7×C4⋊C4—21no—
42C2×C42×C7C2311yescharacteristic
43#6509—44no—
44C2×(C2×D7)⋊C4—22no—
45C2×C4⋊Dic7—21no—
46C2×C4⋊Dic7—21no—
47C2×C4⋊Dic7C2×C412yes—
48C2×Dic7⋊C4—22no—
49C2×C4×Dic7C2×C411yescharacteristic
50C2×C4×Dic7D411yescharacteristic
51C2×C4×Dic7D411yescharacteristic
52C22×C7⋊C8—21no—
53C22×C7⋊C8—21no—
54C42×D7—21no—
55C42×D7—21no—
56C42×D7—21no—
57C42×D7—21no—
58C7×C4⋊C8—21no—
59C7×C4⋊C8—21no—
60C7×C4⋊C8—21no—
61C7×C4⋊C8D412yes—
62C7⋊#95—22no—
63C7⋊#95—22no—
64(C2×D7)⋊C8—24no—
65(C2×D7)⋊C8—42no—
66#6389—24no—
67C4⋊(C7⋊C8)—21no—
68C4⋊(C7⋊C8)—21no—
69C4⋊(C7⋊C8)—21no—
70C4⋊(C7⋊C8)D412yes—
71C2×#432—71no—
72#2857—71no—
73#1797—71no—
74C2×#333—71no—
75C2×#333D711yescharacteristic, complemented
76#1296—71no—
77#1296—71no—
78C23×D7C22⋊C411yescharacteristic
79C2×C7×Q8—22no—
80C2×C7×Q8—22no—
81C2×C7×Q8—42no—
82C2×C7×Q8—42no—
83C22×C4×C7—22no—
84C22×C4×C7C22×C411yescharacteristic
85C22×C4×C7C2×D411yescharacteristic
86C22×C4×C7C2×D411yescharacteristic
87C22×Dic7—22no—
88C22×Dic7C22⋊C411yescharacteristic
89C22×Dic7C22⋊C411yescharacteristic
90C22×Dic7C22⋊C411yescharacteristic
91C2×C4×D7—22no—
92C2×C4×D7—21no—
93C2×C4×D7—21no—
94C2×C4×D7—21no—
95C2×C4×D7—21no—
96C2×C4×D7—21no—
97C2×C4×D7—21no—
98C2×C4×D7—21no—
99C2×C4×D7—21no—
100C2×C4×D7—21no—
101C2×C4×D7—21no—
102C2×C4×D7—21no—
103C2×C4×D7—21no—
104C2×C4×D7—21no—
105C2×C4×D7—21no—
106C2×C4×D7—41no—
107C2×C7×C8—22no—
108C2×C7×C8—41no—
109C2×C7×C8—41no—
110C2×C7×C8—41no—
111C2×C7×C8—41no—
112C2×C7×C8—41no—
113C7×C4⋊C4—41no—
114C7×C4⋊C4—41no—
115C7×C4⋊C4—41no—
116C7×C4⋊C4—41no—
117C42×C7C2×D411yescharacteristic
118C42×C7C2×D411yescharacteristic
119C42×C7#4111yescharacteristic
120C42×C7#4111yescharacteristic
121(C2×D7)⋊C4—44no—
122C4⋊Dic7—41no—
123C4⋊Dic7—41no—
124C4⋊Dic7—41no—
125C4⋊Dic7—41no—
126C4⋊Dic7—42no—
127Dic7⋊C4—44no—
128C4×Dic7—21no—
129C4×Dic7—21no—
130C4×Dic7—21no—
131C4×Dic7—21no—
132C4×Dic7—21no—
133C4×Dic7—21no—
134C2×C7⋊C8—22no—
135C2×C7⋊C8—41no—
136C2×C7⋊C8—41no—
137C2×C7⋊C8—41no—
138C2×C7⋊C8—41no—
139C2×C7⋊C8—41no—
140C2×C4⋊Q8C2×D711yescharacteristic
141C2×C22⋊Q8—72no—
142C22×C42—71no—
143#432—142no—
144#432—142no—
145C2×C4⋊C8—71no—
146C2×C4⋊C8—71no—
147C2×C4⋊C8C2×D711yescharacteristic
148C2×C4⋊C8C2×D711yescharacteristic
149C2×C22⋊C8—141no—
150C2×C22⋊C8—141no—
151C2×#97—141no—
152#391—72no—
153#389—141no—
154#389—141no—
155#384—71no—
156#380—141no—
157#380—141no—
158#336—141no—
159#333—22no—
160#333—142no—
161C23×C7C2×C22⋊C411yescharacteristic
162C22×D7—21no—
163C22×D7—21no—
164C22×D7—21no—
165C22×D7—21no—
166C22×D7—21no—
167C22×D7—21no—
168C22×D7#10012yes—
169C7×Q8—82no—
170C7×Q8—82no—
171C2×C4×C7—21no—
172C2×C4×C7—21no—
173C2×C4×C7—42no—
174C2×C4×C7—42no—
175C2×C4×C7—42no—
176C2×C4×C7C4×D411yescharacteristic
177C2×C4×C7C4×D411yescharacteristic
178C2×C4×C7#12011yescharacteristic
179C2×C4×C7#12111yescharacteristic
180C2×C4×C7#12111yescharacteristic
181C2×C4×C7#12311yescharacteristic
182C2×C4×C7#13511yescharacteristic
183C2×C4×C7#13511yescharacteristic
184C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C7#13711yescharacteristic
186C2×C4×C7#13711yescharacteristic
187C2×C4×C7#13711yescharacteristic
188C2×C4×C7#13711yescharacteristic
189C2×C4×C7#13711yescharacteristic
190C2×Dic7—21no—
191C2×Dic7—21no—
192C2×Dic7—21no—
193C2×Dic7—21no—
194C2×Dic7—21no—
195C2×Dic7—21no—
196C2×Dic7—21no—
197C2×Dic7—21no—
198C2×Dic7—21no—
199C2×Dic7—42no—
200C2×Dic7—42no—
201C2×Dic7—42no—
202C4×D7—42no—
203C4×D7—42no—
204C4×D7—41no—
205C4×D7—41no—
206C4×D7—41no—
207C4×D7—41no—
208C4×D7—41no—
209C4×D7—41no—
210C4×D7—41no—
211C4×D7—41no—
212C7×C8—42no—
213C7×C8—81no—
214C7⋊C8—42no—
215C7⋊C8—81no—
216C22×Q8C4×D712yes—
217C23×C4—71no—
218C23×C4—71no—
219C23×C4—71no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—141no—
223C22×C8—141no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C22⋊Q8—284no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—72no—
232C2×C4⋊C4—142no—
233C2×C4⋊C4—141no—
234C2×C4⋊C4—141no—
235C2×C22⋊C4—142no—
236C2×C42—71no—
237C2×C42—71no—
238C2×C42—71no—
239C2×C42—141no—
240C2×C42—141no—
241C2×C42—141no—
242C2×C42—141no—
243C2×C42C22×D711yescharacteristic
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—72no—
248C4⋊C8—141no—
249C4⋊C8—141no—
250C4⋊C8—141no—
251C4⋊C8C22⋊D712yes—
252C22⋊C8—144no—
253C22⋊C8—282no—
254#97—144no—
255#95—142no—
256#95—142no—
257C22×C7#38611yescharacteristic
258C22×C7C2×#10011yescharacteristic
259C22×C7#41311yescharacteristic
260C22×C7#41611yescharacteristic
261C22×C7#41711yescharacteristic
262C22×C7#41911yescharacteristic
263C22×C7#41911yescharacteristic
264C2×D7—22no—
265C2×D7—22no—
266C2×D7—22no—
267C2×D7—41no—
268C2×D7—41no—
269C2×D7—41no—
270C2×D7—41no—
271C4×C7—21no—
272C4×C7—21no—
273C4×C7—82no—
274C4×C7#45211yescharacteristic
275C4×C7#45211yescharacteristic
276C4×C7#46811yescharacteristic
277C4×C7#46811yescharacteristic
278C4×C7#47011yescharacteristic
279C4×C7#47011yescharacteristic
280C4×C7#48511yescharacteristic
281C4×C7#48511yescharacteristic
282Dic7—41no—
283Dic7—41no—
284Dic7—41no—
285Dic7—82no—
286C24—71no—
287C2×Q8—22no—
288C2×Q8—22no—
289C2×Q8—42no—
290C2×Q8—42no—
291C22×C4—22no—
292C22×C4—71no—
293C22×C4—71no—
294C22×C4—71no—
295C22×C4—142no—
296C22×C4—141no—
297C22×C4—141no—
298C22×C4—141no—
299C22×C4—141no—
300C22×C4—141no—
301C22×C4—141no—
302C22×C4—141no—
303C22×C4—141no—
304C22×C4—141no—
305C22×C4—141no—
306C22×C4—141no—
307C22×C4—141no—
308C22×C4—141no—
309C22×C4—141no—
310C22×C4—142no—
311C22×C4—281no—
312C22×C4C2×C4×D711yescharacteristic
313C22×C4D4×D711yescharacteristic
314C22×C4D4×D711yescharacteristic
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—142no—
322C2×C8—281no—
323C2×C8—281no—
324C2×C8—281no—
325C2×C8—281no—
326C2×C8—281no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—282no—
332C4⋊C4—284no—
333C4⋊C4—281no—
334C4⋊C4—281no—
335C4⋊C4—281no—
336C4⋊C4—281no—
337C22⋊C4—284no—
338C42—141no—
339C42—141no—
340C42—141no—
341C42—141no—
342C42—141no—
343C42—141no—
344C42#115711yescharacteristic
345C42D4×D711yescharacteristic
346C42#115911yescharacteristic
347C42C2×C22⋊D711yescharacteristic
348C2×C7#155111yescharacteristic
349C2×C7#155411yescharacteristic
350C2×C7#155811yescharacteristic
351C2×C7#155911yescharacteristic
352C2×C7#187311yescharacteristic
353C2×C7#189411yescharacteristic
354C2×C7#190011yescharacteristic
355D7—42no—
356C23—72no—
357C23—141no—
358C23—141no—
359C23—141no—
360C23—141no—
361C23—141no—
362C23—141no—
363C23D7×C22⋊C411yescharacteristic
364Q8—82no—
365Q8—82no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—141no—
372C2×C4—141no—
373C2×C4—141no—
374C2×C4—141no—
375C2×C4—141no—
376C2×C4—141no—
377C2×C4—141no—
378C2×C4—141no—
379C2×C4—141no—
380C2×C4—282no—
381C2×C4—282no—
382C2×C4—281no—
383C2×C4—281no—
384C2×C4—281no—
385C2×C4—281no—
386C2×C4—281no—
387C2×C4—281no—
388C2×C4—281no—
389C2×C4—281no—
390C2×C4—282no—
391C2×C4—282no—
392C2×C4—282no—
393C2×C4(C22⋊D7)⋊C411yescharacteristic
394C2×C4#644611yescharacteristic
395C2×C4#644711yescharacteristic
396C2×C4#647711yescharacteristic
397C2×C4#647811yescharacteristic
398C2×C4#647811yescharacteristic
399C2×C4#647911yescharacteristic
400C2×C4#648111yescharacteristic
401C2×C4#648111yescharacteristic
402C2×C4#648111yescharacteristic
403C2×C4#648211yescharacteristic
404C2×C4C4×C22⋊D711yescharacteristic
405C2×C4#650011yescharacteristic
406C2×C4#650111yescharacteristic
407C8—42no—
408C8—81no—
409C8—282no—
410C8—561no—
411C7#913611yescharacteristic, complemented, Sylow
412C22—142no—
413C22—142no—
414C22—142no—
415C22—281no—
416C22—281no—
417C22—281no—
418C22—281no—
419C22D7×#10011yescharacteristic
420C22#8951711yescharacteristic
421C22#8957411yescharacteristic
422C22#8957411yescharacteristic
423C22#8957511yescharacteristic
424C22#8957611yescharacteristic
425C22#8972811yescharacteristic
426C4—21no—
427C4—21no—
428C4—82no—
429C4—281no—
430C4—281no—
431C4—281no—
432C4—562no—
433C4#8958411yescharacteristic
434C4#8958611yescharacteristic
435C4#8958711yescharacteristic
436C4#8958811yescharacteristic
437C4#8994511yescharacteristic
438C4#8994611yescharacteristic
439C4#8995911yescharacteristic
440C4#8996111yescharacteristic
441C2—282no—
442C2#1172623911yescharacteristic
443C2#1172624011yescharacteristic
444C2#1172624111yescharacteristic
445C2#1172624211yescharacteristic
446C2#1172783511yescharacteristic
447C2#1172802311yescharacteristic
448C2#1172802511yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#333C2
socleC23×C7C2×C22⋊C4
prime radicalC23×D7C22⋊C4
cosocleC2×C42×C7C23
hypercenterC2×#333D7
hypocenterC7#9136
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. C2×C7×#333C2semidirect
4. C2×#89341C2semidirect
6. #11725508C2semidirect
7. #11725508C2semidirect
75. C2×#333D7semidirect
411. C7#9136semidirect

Maximal subgroups

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

subgroupindex
#117407142
C2×#896072
C2×C7×#3332
C2×#893412
#117282292
#117255082
#91367