Finite Group Databasebeta

← #13249078

Subgroups — #13249078

Order 1792.

618 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2365C211yesmaximal, characteristic, complemented
2C2×#89860C211yesmaximal, characteristic
3C2×#89342C211yesmaximal, characteristic, complemented
4#11727241C211yesmaximal, characteristic
5#11727241C211yesmaximal, characteristic
6#11725425C211yesmaximal, characteristic, complemented
7#11725425C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×C4×C7×Q8—21no—
10C2×#6437C2211yescharacteristic
11C7×#391—21no—
12C7×#389—21no—
13C7×#387—22no—
14C4×C7×C4⋊C4—21no—
15C4×C7×C4⋊C4C2211yescharacteristic
16C4×C7×C4⋊C4C2211yescharacteristic
17#89860—22no—
18#89860C414yescomplemented
19C2×#6383—22no—
20C2×#6383—21no—
21C2×#6383—21no—
22C2×#6383—21no—
23C2×#6383—21no—
24C2×C4⋊(C7⋊C8)C2211yescharacteristic
25C2×C4⋊(C7⋊C8)C2211yescharacteristic
26C2×C4×C7⋊C8C2211yescharacteristic
27#89342—22no—
28#9062—71nomaximal, Sylow
29C22×C7×Q8—21no—
30C22×D28—21no—
31C22×D28—21no—
32C22×D28—21no—
33C7×C4⋊Q8—21no—
34C7×C4⋊Q8—21no—
35C7×C4⋊Q8C2×C412yes—
36C7×C4⋊Q8D412yes—
37C4×C7×Q8—42no—
38C4×C7×Q8—42no—
39C2×C7×C4⋊C4—21no—
40C2×C7×C4⋊C4—22no—
41C2×C7×C4⋊C4D411yescharacteristic
42C2×C7×C4⋊C4D411yescharacteristic
43C2×C7×C4⋊C4D412yes—
44C2×C7×C4⋊C4D411yescharacteristic
45C2×C7×C4⋊C4D411yescharacteristic
46C2×C42×C7—22no—
47C2×C42×C7—21no—
48C2×C42×C7—21no—
49C2×C42×C7C2311yescharacteristic
50C22×C7⋊C8—21no—
51C22×C7⋊C8—21no—
52C22×C7⋊C8—21no—
53#6437—21no—
54#6437—21no—
55#6437—21no—
56#6437C2×C412yes—
57C7×#95—22no—
58C7×#95—22no—
59C7×#95—21no—
60C7×#95—21no—
61#6383—28no—
62#6383—42no—
63#6383—42no—
64#6383—42no—
65#6383—42no—
66C4⋊(C7⋊C8)—21no—
67C4⋊(C7⋊C8)—21no—
68C4⋊(C7⋊C8)—21no—
69C4⋊(C7⋊C8)—21no—
70C4×C7⋊C8—21no—
71C4×C7⋊C8C2×C412yes—
72C2×#486—71no—
73#2365D711yescharacteristic, complemented
74#1982—71no—
75#1982—71no—
76C2×#332—71no—
77#1279—71no—
78#1279—71no—
79C23×D7—41no—
80C2×C7×Q8—22no—
81C2×C7×Q8—22no—
82C2×C7×Q8—41no—
83C2×C7×Q8—41no—
84C2×C7×Q8—41no—
85C2×C7×Q8—41no—
86C22×C4×C7—21no—
87C22×C4×C7—22no—
88C22×C4×C7—21no—
89C22×C4×C7—21no—
90C22×C4×C7—21no—
91C22×C4×C7C2×D411yescharacteristic
92C22×C4×C7C2×D411yescharacteristic
93C22×C4×C7C2×D411yescharacteristic
94C2×D28—22no—
95C2×D28—22no—
96C2×D28—22no—
97C2×D28—42no—
98C2×D28—42no—
99C2×D28—41no—
100C2×D28—41no—
101C2×D28—41no—
102C2×D28—41no—
103C2×D28—41no—
104C2×D28—41no—
105C2×D28—41no—
106C2×D28—41no—
107C2×D28—41no—
108C2×D28—41no—
109C2×D28—41no—
110C7×C4⋊C4—22no—
111C7×C4⋊C4—22no—
112C7×C4⋊C4—22no—
113C7×C4⋊C4—21no—
114C7×C4⋊C4—21no—
115C7×C4⋊C4—21no—
116C7×C4⋊C4—21no—
117C7×C4⋊C4—21no—
118C7×C4⋊C4—21no—
119C7×C4⋊C4—44no—
120C7×C4⋊C4C22⋊C414yes—
121C7×C4⋊C4D812yes—
122C7×C4⋊C4SD1612yes—
123C42×C7—44no—
124C42×C7—41no—
125C42×C7—41no—
126C42×C7—41no—
127C42×C7—41no—
128C42×C7C22×C411yescharacteristic
129C42×C7C2×D411yescharacteristic
130C42×C7#4111yescharacteristic
131C42×C7#4111yescharacteristic
132C2×C7⋊C8—22no—
133C2×C7⋊C8—41no—
134C2×C7⋊C8—41no—
135C2×C7⋊C8—41no—
136C2×C7⋊C8—41no—
137C2×C7⋊C8—41no—
138C2×C7⋊C8—41no—
139C2×C7⋊C8—41no—
140C2×C7⋊C8—41no—
141C2×C4⋊Q8C2×D711yescharacteristic
142C2×#127—71no—
143C2×C4×Q8—21no—
144#486—74no—
145#486—142no—
146C2×C4⋊C8—71no—
147C2×C4⋊C8—71no—
148C2×#102—142no—
149C2×#102—141no—
150C2×#102—141no—
151C2×#102—141no—
152C2×#102—141no—
153C2×C4×C8—71no—
154#391—21no—
155#389—21no—
156#387—22no—
157C4×C4⋊C4—21no—
158C4×C4⋊C4C2×D711yescharacteristic
159C4×C4⋊C4C2×D711yescharacteristic
160#332—142no—
161C23×C7#12011yescharacteristic
162C22×D7—42no—
163C22×D7—81no—
164C22×D7—81no—
165C22×D7—81no—
166C22×D7—81no—
167C22×D7—81no—
168C22×D7—81no—
169C7×Q8—42no—
170C7×Q8—42no—
171C7×Q8—42no—
172C7×Q8—42no—
173C2×C4×C7—21no—
174C2×C4×C7—21no—
175C2×C4×C7—24no—
176C2×C4×C7—22no—
177C2×C4×C7—22no—
178C2×C4×C7—41no—
179C2×C4×C7—42no—
180C2×C4×C7—41no—
181C2×C4×C7—42no—
182C2×C4×C7—41no—
183C2×C4×C7—41no—
184C2×C4×C7—41no—
185C2×C4×C7—41no—
186C2×C4×C7—41no—
187C2×C4×C7—41no—
188C2×C4×C7—41no—
189C2×C4×C7—41no—
190C2×C4×C7C2×C22⋊C411yescharacteristic
191C2×C4×C7C4×D411yescharacteristic
192C2×C4×C7C4×D411yescharacteristic
193C2×C4×C7#12111yescharacteristic
194C2×C4×C7#12111yescharacteristic
195C2×C4×C7#12311yescharacteristic
196C2×C4×C7C2×D811yescharacteristic
197C2×C4×C7C2×SD1611yescharacteristic
198C2×C4×C7#13511yescharacteristic
199C2×C4×C7#13511yescharacteristic
200C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C7#13711yescharacteristic
204D28—44no—
205D28—42no—
206D28—42no—
207D28—42no—
208D28—42no—
209D28—82no—
210D28—81no—
211D28—81no—
212D28—81no—
213D28—81no—
214C7⋊C8—42no—
215C7⋊C8—81no—
216C7⋊C8—81no—
217C22×Q8—21no—
218C22×D4—141no—
219C22×D4—141no—
220C22×D4—141no—
221C22×C8—141no—
222C22×C8—141no—
223C22×C8—141no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8C4×D712yes—
227C4⋊Q8D2812yes—
228#127—72no—
229#127—141no—
230#127—141no—
231#127—141no—
232C4×Q8—42no—
233C4×Q8—42no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4C22⋊D711yescharacteristic
237C2×C4⋊C4C22⋊D711yescharacteristic
238C2×C4⋊C4C22⋊D712yes—
239C2×C4⋊C4C22⋊D711yescharacteristic
240C2×C4⋊C4C22⋊D711yescharacteristic
241C2×C42—22no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42C22×D711yescharacteristic
245C4⋊C8—141no—
246C4⋊C8—141no—
247C4⋊C8—141no—
248C4⋊C8—141no—
249#102—148no—
250#102—282no—
251#102—282no—
252#102—282no—
253#102—282no—
254C4×C8—72no—
255C4×C8—141no—
256#95—22no—
257#95—22no—
258#95—21no—
259#95—21no—
260C22×C7#38611yescharacteristic
261C22×C7#44711yescharacteristic
262C22×C7#44811yescharacteristic
263C22×C7#44911yescharacteristic
264C22×C7#44911yescharacteristic
265C22×C7#45411yescharacteristic
266C22×C7#45411yescharacteristic
267C2×D7—82no—
268C2×D7—82no—
269C2×D7—82no—
270C2×D7—161no—
271C2×D7—161no—
272C2×D7—161no—
273C2×D7—161no—
274C4×C7—21no—
275C4×C7—21no—
276C4×C7—44no—
277C4×C7—42no—
278C4×C7—42no—
279C4×C7—81no—
280C4×C7—81no—
281C4×C7C4×D811yescharacteristic
282C4×C7C4×SD1611yescharacteristic
283C4×C7#44011yescharacteristic
284C4×C7#44211yescharacteristic
285C4×C7#45911yescharacteristic
286C4×C7#46011yescharacteristic
287C4×C7#46311yescharacteristic
288C4×C7#46411yescharacteristic
289C24—281no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×D4—142no—
297C2×D4—142no—
298C2×D4—142no—
299C2×D4—282no—
300C2×D4—282no—
301C2×D4—281no—
302C2×D4—281no—
303C2×D4—281no—
304C2×D4—281no—
305C2×D4—281no—
306C2×D4—281no—
307C2×D4—281no—
308C2×D4—281no—
309C2×D4—281no—
310C2×D4—281no—
311C2×D4—281no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4C2×C22⋊D711yescharacteristic
318C22×C4C2×C22⋊D711yescharacteristic
319C22×C4C2×C22⋊D711yescharacteristic
320C2×C8—142no—
321C2×C8—281no—
322C2×C8—281no—
323C2×C8—281no—
324C2×C8—281no—
325C2×C8—281no—
326C2×C8—281no—
327C2×C8—281no—
328C2×C8—281no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—44no—
339C4⋊C4(C2×D7)⋊C414yes—
340C4⋊C4#114112yes—
341C4⋊C4#114312yes—
342C42—44no—
343C42—41no—
344C42—41no—
345C42—41no—
346C42—41no—
347C42C2×C4×D711yescharacteristic
348C42C2×D2811yescharacteristic
349C42#115711yescharacteristic
350C42#115711yescharacteristic
351C2×C7#162511yescharacteristic
352C2×C7#162611yescharacteristic
353C2×C7#162711yescharacteristic
354C2×C7#162811yescharacteristic
355C2×C7#187911yescharacteristic
356C2×C7#188011yescharacteristic
357C2×C7#188811yescharacteristic
358D7—162no—
359C23—282no—
360C23—561no—
361C23—561no—
362C23—561no—
363C23—561no—
364C23—561no—
365C23—561no—
366C23#651611yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—42no—
370Q8—42no—
371D4—284no—
372D4—282no—
373D4—282no—
374D4—282no—
375D4—282no—
376D4—562no—
377D4—561no—
378D4—561no—
379D4—561no—
380D4—561no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4C2×(C2×D7)⋊C411yescharacteristic
399C2×C4C4×C22⋊D711yescharacteristic
400C2×C4C4×C22⋊D711yescharacteristic
401C2×C4#649211yescharacteristic
402C2×C4#649311yescharacteristic
403C2×C4#649311yescharacteristic
404C2×C4C2×#114111yescharacteristic
405C2×C4#649511yescharacteristic
406C2×C4C2×#114311yescharacteristic
407C2×C4#650511yescharacteristic
408C2×C4#651211yescharacteristic
409C2×C4#651211yescharacteristic
410C2×C4#651311yescharacteristic
411C2×C4#651311yescharacteristic
412C8—282no—
413C8—561no—
414C8—561no—
415C7#906211yescharacteristic, complemented, Sylow
416C22—562no—
417C22—562no—
418C22—562no—
419C22—1121no—
420C22—1121no—
421C22—1121no—
422C22—1121no—
423C22#8998511yescharacteristic
424C22#8998911yescharacteristic
425C22#8999911yescharacteristic
426C22#9001011yescharacteristic
427C22#9001011yescharacteristic
428C22#9001711yescharacteristic
429C22#9001711yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—42no—
434C4—44no—
435C4—81no—
436C4—81no—
437C4C4×#114111yescharacteristic
438C4#8978611yescharacteristic
439C4#8978711yescharacteristic
440C4#8978811yescharacteristic
441C4C4×#114311yescharacteristic
442C4#8979811yescharacteristic
443C4#8979911yescharacteristic
444C4#8980011yescharacteristic
445C2—1122no—
446C2#1172936711yescharacteristic
447C2#1172938711yescharacteristic
448C2#1172941511yescharacteristic
449C2#1172966411yescharacteristic
450C2#1172966811yescharacteristic
451C2#1172968511yescharacteristic
452C2#1172968911yescharacteristic
subgroupG/H
centerC23#6516
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2365C2
socleC23×C7#120
prime radicalC2×#6437C22
cosocleC2×C42×C7C23
hypercenter#2365D7
hypocenterC7#9062
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C7×#2365C2semidirect
3. C2×#89342C2semidirect
6. #11725425C2semidirect
7. #11725425C2semidirect
18. #89860C4semidirect
73. #2365D7semidirect
415. C7#9062semidirect

Maximal subgroups

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

subgroupindex
C7×#23652
C2×#898602
C2×#893422
#117272412
#117254252
#90627