Finite Group Databasebeta

← #13245449

Subgroups — #13245449

Order 1792.

814 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#553C211yesmaximal, characteristic
2#11729489C212yesmaximal, complemented
3C4×#6407C211yesmaximal, characteristic, complemented
4#11729357C211yesmaximal, characteristic, complemented
5#11729353C212yesmaximal, complemented
6C7×#553—24no—
7C7×#553—24no—
8C2×C7×#126—21no—
9C2×C7×#125C2211yescharacteristic
10C2×C7×#123—21no—
11C2×C7×#121—21no—
12C2×C7×#121C411yescharacteristic
13C2×C7×#121C411yescharacteristic
14C2×C4×C7×D4—21no—
15C2×C4×C7×D4C2211yescharacteristic
16C2×C4×C7×D4C2211yescharacteristic
17C2×C7×#117C411yescharacteristic
18C22×C7×C4⋊C4C411yescharacteristic
19C2×#6407—21no—
20#89698C2212yes—
21C4×#1136C2212yes—
22#89338—24no—
23D4⋊(C7⋊C8)—24no—
24#89325—21no—
25#89320—21no—
26#89320—21no—
27#8373—71nomaximal, Sylow
28C22×C7×D4—21no—
29C22×C7×D4—21no—
30C22×C7×D4C2×C411yescharacteristic
31C22×C7×D4D411yescharacteristic
32C23×C4×C7—21no—
33C23×C4×C7—21no—
34C23×C4×C7C2×C411yescharacteristic
35C23×C4×C7C2×C411yescharacteristic
36C7×#126—28no—
37C7×#125—22no—
38C7×#125D414yes—
39C7×#123—28no—
40C7×#121—28no—
41C7×#121—22no—
42C7×#121—22no—
43C7×#121—22no—
44C7×#121—22no—
45C4×C7×D4—28no—
46C4×C7×D4—22no—
47C4×C7×D4—22no—
48C4×C7×D4—22no—
49C4×C7×D4D414yes—
50C7×#117—22no—
51C7×#117—22no—
52C2×C7×C4⋊C4—21no—
53C2×C7×C4⋊C4—21no—
54C2×C7×C4⋊C4—21no—
55C2×C7×C4⋊C4—22no—
56C2×C7×C4⋊C4—22no—
57C2×C7×C4⋊C4C2×C411yescharacteristic
58C2×C7×C4⋊C4C2×C411yescharacteristic
59C2×C7×C4⋊C4C2×C411yescharacteristic
60C2×C7×C4⋊C4D411yescharacteristic
61C2×C7×C22⋊C4—21no—
62C2×C7×C22⋊C4—21no—
63C2×C7×C22⋊C4—21no—
64C2×C7×C22⋊C4—21no—
65C2×C7×C22⋊C4D411yescharacteristic
66C2×C7×C22⋊C4D411yescharacteristic
67C2×C42×C7—21no—
68C2×C42×C7C2311yescharacteristic
69C2×#1136—22no—
70#6407—24no—
71C22⋊(C7⋊C8)—22no—
72C4⋊(C7⋊C8)—22no—
73#6377—22no—
74#6377—22no—
75C4×C7⋊C8—22no—
76C2×#553D711yescharacteristic
77C4×#100—71no—
78#1528—72no—
79#1490—72no—
80#1466—71no—
81C24×C7—21no—
82C24×C7C22⋊C411yescharacteristic
83C24×C7C22⋊C411yescharacteristic
84C2×C7×D4—24no—
85C2×C7×D4—22no—
86C2×C7×D4—24no—
87C2×C7×D4—21no—
88C2×C7×D4—22no—
89C2×C7×D4—42no—
90C2×C7×D4—41no—
91C2×C7×D4—42no—
92C2×C7×D4—42no—
93C2×C7×D4—82no—
94C2×C7×D4C22⋊C412yes—
95C22×C4×C7—21no—
96C22×C4×C7—21no—
97C22×C4×C7—21no—
98C22×C4×C7—24no—
99C22×C4×C7—21no—
100C22×C4×C7—21no—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—24no—
104C22×C4×C7—42no—
105C22×C4×C7—42no—
106C22×C4×C7—82no—
107C22×C4×C7—82no—
108C22×C4×C7C22⋊C411yescharacteristic
109C22×C4×C7C22⋊C411yescharacteristic
110C22×C4×C7C22×C411yescharacteristic
111C22×C4×C7C2×D411yescharacteristic
112C22×C4×C7C2×D411yescharacteristic
113C7×C4⋊C4—24no—
114C7×C4⋊C4—21no—
115C7×C4⋊C4—21no—
116C7×C4⋊C4—21no—
117C7×C4⋊C4—24no—
118C7×C4⋊C4—24no—
119C7×C4⋊C4—22no—
120C7×C4⋊C4C22⋊C412yes—
121C7×C4⋊C4C22⋊C412yes—
122C7×C4⋊C4C22⋊C412yes—
123C7×C22⋊C4—24no—
124C7×C22⋊C4—24no—
125C7×C22⋊C4—24no—
126C7×C22⋊C4—24no—
127C7×C22⋊C4—22no—
128C7×C22⋊C4—22no—
129C42×C7—24no—
130C42×C7C2×D412yes—
131C42×C7C2×D412yes—
132#1136—24no—
133#1136—42no—
134C2×C7⋊C8—42no—
135C2×C7⋊C8—42no—
136#553—24no—
137#553—24no—
138C2×#126—21no—
139C2×#125C2×D711yescharacteristic
140C2×#123—21no—
141C2×#121—21no—
142C2×#121Dic711yescharacteristic
143C2×#121Dic711yescharacteristic
144C2×C4×D4—21no—
145C2×C4×D4C2×D711yescharacteristic
146C2×C4×D4C2×D711yescharacteristic
147C2×#117Dic711yescharacteristic
148C22×C4⋊C4Dic711yescharacteristic
149#432—72no—
150C2×#100—141no—
151C4×M16—72no—
152#343—141no—
153#330—144no—
154D4⋊C8—144no—
155#323—141no—
156#323—141no—
157C23×C7—21no—
158C23×C7—21no—
159C23×C7—21no—
160C23×C7—22no—
161C23×C7—21no—
162C23×C7—21no—
163C23×C7—41no—
164C23×C7—41no—
165C23×C7—42no—
166C23×C7—42no—
167C23×C7—41no—
168C23×C7—41no—
169C23×C7—41no—
170C23×C7—41no—
171C23×C7#10412yes—
172C23×C7C2×C22⋊C411yescharacteristic
173C7×D4—24no—
174C7×D4—44no—
175C7×D4—42no—
176C7×D4—48no—
177C7×D4—84no—
178C2×C4×C7—21no—
179C2×C4×C7—21no—
180C2×C4×C7—22no—
181C2×C4×C7—21no—
182C2×C4×C7—22no—
183C2×C4×C7—22no—
184C2×C4×C7—21no—
185C2×C4×C7—22no—
186C2×C4×C7—41no—
187C2×C4×C7—42no—
188C2×C4×C7—42no—
189C2×C4×C7—42no—
190C2×C4×C7—42no—
191C2×C4×C7—41no—
192C2×C4×C7—41no—
193C2×C4×C7—42no—
194C2×C4×C7—42no—
195C2×C4×C7—41no—
196C2×C4×C7—41no—
197C2×C4×C7—84no—
198C2×C4×C7—84no—
199C2×C4×C7C2×C22⋊C411yescharacteristic
200C2×C4×C7C2×C22⋊C411yescharacteristic
201C2×C4×C7#12012yes—
202C2×C4×C7#12012yes—
203C7⋊C8—44no—
204C7⋊C8—82no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4C2×Dic711yescharacteristic
208C22×D4C22⋊D711yescharacteristic
209C23×C4—21no—
210C23×C4—21no—
211C23×C4C2×Dic711yescharacteristic
212C23×C4C2×Dic711yescharacteristic
213C2×M16—142no—
214#126—28no—
215#125—22no—
216#125C22⋊D714yes—
217#123—28no—
218#121—28no—
219#121—22no—
220#121—22no—
221#121—22no—
222#121—22no—
223C4×D4—28no—
224C4×D4—22no—
225C4×D4—22no—
226C4×D4—22no—
227C4×D4C22⋊D714yes—
228#117—22no—
229#117—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4C2×Dic711yescharacteristic
236C2×C4⋊C4C2×Dic711yescharacteristic
237C2×C4⋊C4C2×Dic711yescharacteristic
238C2×C4⋊C4C22⋊D711yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4C22⋊D711yescharacteristic
244C2×C22⋊C4C22⋊D711yescharacteristic
245C2×C42—21no—
246C2×C42C22×D711yescharacteristic
247C4⋊C8—142no—
248#100—144no—
249C22⋊C8—142no—
250#97—142no—
251#97—142no—
252C4×C8—142no—
253C22×C7—21no—
254C22×C7—21no—
255C22×C7—22no—
256C22×C7—42no—
257C22×C7—42no—
258C22×C7—41no—
259C22×C7—41no—
260C22×C7—42no—
261C22×C7—41no—
262C22×C7—41no—
263C22×C7—42no—
264C22×C7—41no—
265C22×C7—42no—
266C22×C7—81no—
267C22×C7—81no—
268C22×C7—82no—
269C22×C7—82no—
270C22×C7#37911yescharacteristic
271C22×C7C2×#10411yescharacteristic
272C22×C7#42111yescharacteristic
273C4×C7—22no—
274C4×C7—21no—
275C4×C7—22no—
276C4×C7—42no—
277C4×C7—42no—
278C4×C7—41no—
279C4×C7—41no—
280C4×C7—42no—
281C4×C7#41312yes—
282C24—21no—
283C24C22⋊Dic711yescharacteristic
284C24C22⋊Dic711yescharacteristic
285C2×D4—24no—
286C2×D4—22no—
287C2×D4—24no—
288C2×D4—21no—
289C2×D4—22no—
290C2×D4—42no—
291C2×D4—41no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—82no—
295C2×D4C22⋊Dic712yes—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—24no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—24no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—82no—
308C22×C4—82no—
309C22×C4C22⋊Dic711yescharacteristic
310C22×C4C22⋊Dic711yescharacteristic
311C22×C4C22×Dic711yescharacteristic
312C22×C4C2×C22⋊D711yescharacteristic
313C22×C4C2×C22⋊D711yescharacteristic
314M16—144no—
315M16—282no—
316C2×C8—282no—
317C2×C8—282no—
318C4⋊C4—24no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—24no—
323C4⋊C4—24no—
324C4⋊C4—22no—
325C4⋊C4C22⋊Dic712yes—
326C4⋊C4C22⋊Dic712yes—
327C4⋊C4C22⋊Dic712yes—
328C22⋊C4—24no—
329C22⋊C4—24no—
330C22⋊C4—24no—
331C22⋊C4—24no—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C42—24no—
335C42C2×C22⋊D712yes—
336C42C2×C22⋊D712yes—
337C2×C7—21no—
338C2×C7—21no—
339C2×C7—42no—
340C2×C7—81no—
341C2×C7—82no—
342C2×C7#178511yescharacteristic
343C2×C7#178911yescharacteristic
344C2×C7#179511yescharacteristic
345C23—21no—
346C23—21no—
347C23—21no—
348C23—22no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23#641112yes—
360C23C2×C22⋊Dic711yescharacteristic
361D4—24no—
362D4—44no—
363D4—42no—
364D4—48no—
365D4—84no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—84no—
386C2×C4—84no—
387C2×C4C2×C22⋊Dic711yescharacteristic
388C2×C4C2×C22⋊Dic711yescharacteristic
389C2×C4#651612yes—
390C2×C4#651612yes—
391C8—284no—
392C8—562no—
393C7#837311yescharacteristic, complemented, Sylow
394C22—21no—
395C22—21no—
396C22—22no—
397C22—42no—
398C22—42no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—42no—
403C22—41no—
404C22—42no—
405C22—42no—
406C22—41no—
407C22—81no—
408C22—81no—
409C22—82no—
410C22—82no—
411C22C2×#641111yescharacteristic
412C22#9000811yescharacteristic
413C22#9001911yescharacteristic
414C4—21no—
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—42no—
420C4—42no—
421C4—42no—
422C4#9000912yes—
423C2—21no—
424C2—21no—
425C2—42no—
426C2—82no—
427C2—81no—
428C2#1172989111yescharacteristic
429C2#1172989211yescharacteristic
430C2#1172989511yescharacteristic
subgroupG/H
centerC22#90019
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
Fitting, prime radicalC2×C7×#553C2
socleC22×C7#379
cosocleC2×C42×C7C23
hypercenterC2×#553D7
hypocenterC7#8373
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
2. #11729489C2semidirect
3. C4×#6407C2semidirect
4. #11729357C2semidirect
5. #11729353C2semidirect
393. C7#8373semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5532
#117294892
C4×#64072
#117293572
#117293532
#83737