Finite Group Databasebeta

← #13249012

Subgroups — #13249012

Order 1792.

488 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3105C211yesmaximal, characteristic
2#11740575C211yesmaximal, characteristic, complemented
3#11729500C211yesmaximal, characteristic, complemented
4#11729369C211yesmaximal, characteristic, complemented
5#11729353C211yesmaximal, characteristic, complemented
6#11725550C211yesmaximal, characteristic, complemented
7#11725548C211yesmaximal, characteristic, complemented
8C7×#529C2211yescharacteristic
9C2×C4×C7×D4C2211yescharacteristic
10C7×#484C411yescharacteristic
11C7×#481C411yescharacteristic
12C7×#478—21no—
13C7×#463—21no—
14C7×#450C411yescharacteristic
15C7×#447C411yescharacteristic
16C4×C7×SD16—21no—
17C4×C7×D8—21no—
18C7×#431C2211yescharacteristic
19C2×C22⋊(C7⋊C8)—21no—
20C2×C22⋊(C7⋊C8)—21no—
21#89796—21no—
22#89783—21no—
23#89783—21no—
24D4×C7⋊C8—21no—
25#89772—21no—
26#89771—21no—
27#89698C2211yescharacteristic
28C2×C4⋊(C7⋊C8)C2211yescharacteristic
29C4×#1136C2211yescharacteristic
30C2×#6377C2211yescharacteristic
31#89338—21no—
32#89335—21no—
33D4⋊(C7⋊C8)—21no—
34D4⋊(C7⋊C8)—21no—
35#9052—71nomaximal, Sylow
36C22×C7×D4C2×C411yescharacteristic
37C23×C4×C7—21no—
38C2×C7×SD16—21no—
39C2×C7×D8—21no—
40C7×#126—21no—
41C7×#125D411yescharacteristic
42C7×#124D411yescharacteristic
43C7×#123—21no—
44C7×C22⋊Q8C2×C411yescharacteristic
45C7×#121C2×C411yescharacteristic
46C4×C7×Q8D411yescharacteristic
47C4×C7×D4—21no—
48C4×C7×D4—21no—
49C4×C7×D4—21no—
50C4×C7×D4—21no—
51C4×C7×D4—21no—
52C4×C7×D4D411yescharacteristic
53C7×#117—21no—
54C2×C7×C4⋊C4C2×C411yescharacteristic
55C2×C7×C22⋊C4—21no—
56C2×C42×C7C2311yescharacteristic
57C2×#1136—21no—
58C2×#1136—21no—
59C22×C7⋊C8—21no—
60C22×C7⋊C8—21no—
61C22×C7⋊C8D411yescharacteristic
62C22×C7⋊C8D411yescharacteristic
63C7×#107—21no—
64C7×#106—21no—
65C7×C4⋊C8—21no—
66C7×#103—21no—
67C7×#102—21no—
68C7×#102—21no—
69C7×#102—21no—
70C7×C22⋊C8C2×C411yescharacteristic
71C7×C22⋊C8C2×C411yescharacteristic
72C4×C7×C8—21no—
73C22⋊(C7⋊C8)—21no—
74C22⋊(C7⋊C8)—21no—
75C22⋊(C7⋊C8)—21no—
76C22⋊(C7⋊C8)—42no—
77C22⋊(C7⋊C8)—42no—
78C4⋊(C7⋊C8)—21no—
79C4⋊(C7⋊C8)—21no—
80C4⋊(C7⋊C8)—21no—
81C4⋊(C7⋊C8)—21no—
82C4⋊(C7⋊C8)D411yescharacteristic
83C4⋊(C7⋊C8)D411yescharacteristic
84#6377—21no—
85#6377—21no—
86#6377—21no—
87#6377—21no—
88#6377—21no—
89C4×C7⋊C8—21no—
90C4×C7⋊C8—21no—
91#3105D711yescharacteristic
92#2992—71no—
93#1955—71no—
94#1524—71no—
95#1490—71no—
96#1302—71no—
97#1283—71no—
98C24×C7—21no—
99C2×C7×Q8C22⋊C411yescharacteristic
100C2×C7×D4—21no—
101C2×C7×D4—21no—
102C2×C7×D4—21no—
103C2×C7×D4—42no—
104C2×C7×D4C22⋊C411yescharacteristic
105C22×C4×C7—21no—
106C22×C4×C7—21no—
107C22×C4×C7—41no—
108C22×C4×C7—41no—
109C22×C4×C7—41no—
110C22×C4×C7—41no—
111C22×C4×C7—41no—
112C22×C4×C7—41no—
113C22×C4×C7C22×C411yescharacteristic
114C22×C4×C7C2×D411yescharacteristic
115C22×C4×C7#4111yescharacteristic
116C7×SD16—42no—
117C7×D8—42no—
118C2×C7×C8—21no—
119C2×C7×C8—21no—
120C7×C4⋊C4—21no—
121C7×C4⋊C4—21no—
122C7×C4⋊C4—21no—
123C7×C4⋊C4—21no—
124C7×C4⋊C4—21no—
125C7×C4⋊C4—21no—
126C7×C4⋊C4C22⋊C411yescharacteristic
127C7×C4⋊C4C22⋊C411yescharacteristic
128C7×C22⋊C4—21no—
129C7×C22⋊C4—21no—
130C7×C22⋊C4—21no—
131C7×C22⋊C4—21no—
132C7×C22⋊C4—21no—
133C7×C22⋊C4—41no—
134C7×C22⋊C4—41no—
135C42×C7—21no—
136C42×C7C2×D411yescharacteristic
137C42×C7C2×D411yescharacteristic
138C42×C7C2×D411yescharacteristic
139C42×C7#4111yescharacteristic
140#1136—22no—
141#1136—41no—
142#1136—81no—
143C2×C7⋊C8—22no—
144C2×C7⋊C8—21no—
145C2×C7⋊C8—21no—
146C2×C7⋊C8—21no—
147C2×C7⋊C8—21no—
148C2×C7⋊C8—41no—
149C2×C7⋊C8—41no—
150C2×C7⋊C8—41no—
151C2×C7⋊C8—41no—
152C2×C7⋊C8—41no—
153C2×C7⋊C8—81no—
154#529C2×D711yescharacteristic
155C2×C4×D4C2×D711yescharacteristic
156#484Dic711yescharacteristic
157#481Dic711yescharacteristic
158#478—21no—
159#463—21no—
160#450Dic711yescharacteristic
161#447Dic711yescharacteristic
162#446—141no—
163C4×SD16—21no—
164C4×D8—21no—
165#435—141no—
166#435—141no—
167C8×D4—141no—
168#433—141no—
169#432—71no—
170#431C2×D711yescharacteristic
171#424—141no—
172C2×C4⋊C8—71no—
173C2×C22⋊C8—141no—
174C2×C22⋊C8—141no—
175C4×M16—71no—
176C2×#97—71no—
177#330—141no—
178#329—141no—
179D4⋊C8—141no—
180D4⋊C8—141no—
181C23×C7—22no—
182C23×C7—21no—
183C23×C7—41no—
184C23×C7—41no—
185C23×C7—41no—
186C23×C7—41no—
187C23×C7—41no—
188C23×C7—41no—
189C23×C7C4×D411yescharacteristic
190C7×Q8—41no—
191C7×D4—22no—
192C7×D4—22no—
193C7×D4—41no—
194C7×D4—41no—
195C7×D4—41no—
196C7×D4—41no—
197C7×D4—41no—
198C2×C4×C7—21no—
199C2×C4×C7—21no—
200C2×C4×C7—21no—
201C2×C4×C7—21no—
202C2×C4×C7—21no—
203C2×C4×C7—21no—
204C2×C4×C7—21no—
205C2×C4×C7—41no—
206C2×C4×C7—41no—
207C2×C4×C7—41no—
208C2×C4×C7—41no—
209C2×C4×C7—41no—
210C2×C4×C7—41no—
211C2×C4×C7—81no—
212C2×C4×C7—81no—
213C2×C4×C7—81no—
214C2×C4×C7—81no—
215C2×C4×C7C2×C22⋊C411yescharacteristic
216C2×C4×C7C4×D411yescharacteristic
217C2×C4×C7#12011yescharacteristic
218C2×C4×C7#12111yescharacteristic
219C2×C4×C7#12111yescharacteristic
220C2×C4×C7#12311yescharacteristic
221C7×C8—41no—
222C7×C8—41no—
223C7⋊C8—42no—
224C7⋊C8—42no—
225C7⋊C8—41no—
226C7⋊C8—41no—
227C7⋊C8—41no—
228C7⋊C8—41no—
229C22×D4C2×Dic711yescharacteristic
230C23×C4—21no—
231C2×SD16—21no—
232C2×D8—21no—
233C2×M16—141no—
234C2×M16—141no—
235C22×C8—71no—
236C22×C8—71no—
237C22×C8—141no—
238C22×C8—141no—
239#126—21no—
240#125C22⋊D711yescharacteristic
241#124C22⋊D711yescharacteristic
242#123—21no—
243C22⋊Q8C2×Dic711yescharacteristic
244#121C2×Dic711yescharacteristic
245C4×Q8C22⋊D711yescharacteristic
246C4×D4—21no—
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C22⋊D711yescharacteristic
252#117—21no—
253C2×C4⋊C4C2×Dic711yescharacteristic
254C2×C22⋊C4—21no—
255C2×C42C22×D711yescharacteristic
256#107—21no—
257#106—21no—
258C4⋊C8—21no—
259C4⋊C8—71no—
260C4⋊C8—71no—
261C4⋊C8—141no—
262C4⋊C8—141no—
263C4⋊C8—141no—
264C4⋊C8—141no—
265#103—21no—
266#102—21no—
267#102—21no—
268#102—21no—
269C22⋊C8—141no—
270C22⋊C8—141no—
271C22⋊C8—141no—
272C22⋊C8—282no—
273C22⋊C8—282no—
274C22⋊C8C2×Dic711yescharacteristic
275C22⋊C8C2×Dic711yescharacteristic
276#97—141no—
277#97—141no—
278#97—141no—
279#97—141no—
280#97—141no—
281C4×C8—21no—
282C4×C8—141no—
283C4×C8—141no—
284C22×C7—21no—
285C22×C7—21no—
286C22×C7—42no—
287C22×C7—42no—
288C22×C7—41no—
289C22×C7—41no—
290C22×C7—42no—
291C22×C7—41no—
292C22×C7—81no—
293C22×C7—81no—
294C22×C7—81no—
295C22×C7—81no—
296C22×C7#38611yescharacteristic
297C22×C7#44311yescharacteristic
298C22×C7#44411yescharacteristic
299C4×C7—21no—
300C4×C7—21no—
301C4×C7—21no—
302C4×C7—21no—
303C4×C7—21no—
304C4×C7—41no—
305C4×C7—41no—
306C4×C7—41no—
307C4×C7—81no—
308C4×C7#45311yescharacteristic
309C4×C7#45411yescharacteristic
310C24—21no—
311C2×Q8C22⋊Dic711yescharacteristic
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—42no—
316C2×D4C22⋊Dic711yescharacteristic
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4D4×D711yescharacteristic
326C22×C4#115911yescharacteristic
327C22×C4C22×Dic711yescharacteristic
328SD16—42no—
329D8—42no—
330M16—142no—
331M16—281no—
332M16—561no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—142no—
336C2×C8—141no—
337C2×C8—141no—
338C2×C8—141no—
339C2×C8—141no—
340C2×C8—281no—
341C2×C8—281no—
342C2×C8—281no—
343C2×C8—281no—
344C2×C8—281no—
345C2×C8—561no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4C22⋊Dic711yescharacteristic
353C4⋊C4C22⋊Dic711yescharacteristic
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C42—21no—
362C42D4×D711yescharacteristic
363C42#115911yescharacteristic
364C42C2×C22⋊D711yescharacteristic
365C42C2×C22⋊D711yescharacteristic
366C2×C7—21no—
367C2×C7—21no—
368C2×C7—81no—
369C2×C7—82no—
370C2×C7#187611yescharacteristic
371C2×C7#188311yescharacteristic
372C2×C7#189111yescharacteristic
373C23—22no—
374C23—21no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23D4×Dic711yescharacteristic
382Q8—41no—
383D4—22no—
384D4—22no—
385D4—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4D4×Dic711yescharacteristic
408C2×C4#649811yescharacteristic
409C2×C4#650011yescharacteristic
410C2×C4#650211yescharacteristic
411C2×C4#650211yescharacteristic
412C2×C4C2×C22⋊Dic711yescharacteristic
413C8—41no—
414C8—41no—
415C8—282no—
416C8—282no—
417C8—281no—
418C8—281no—
419C8—281no—
420C8—281no—
421C7#905211yescharacteristic, complemented, Sylow
422C22—21no—
423C22—21no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22#8996811yescharacteristic
435C22#8996911yescharacteristic
436C22#8999211yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—81no—
446C4#8997011yescharacteristic
447C4#8997311yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2#1172946811yescharacteristic
453C2#1172984111yescharacteristic
454C2#1172984211yescharacteristic
subgroupG/H
centerC2×C4#6500
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#3105C2
socleC22×C7#386
prime radicalC7×#447C4
cosocleC2×C42×C7C23
hypercenter#3105D7
hypocenterC7#9052
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
2. #11740575C2semidirect
3. #11729500C2semidirect
4. #11729369C2semidirect
5. #11729353C2semidirect
6. #11725550C2semidirect
7. #11725548C2semidirect
421. C7#9052semidirect

Maximal subgroups

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

subgroupindex
C7×#31052
#117405752
#117295002
#117293692
#117293532
#117255502
#117255482
#90527