Finite Group Databasebeta

← #32985115

Subgroups — #32985115

Order 18688.

742 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618232C211yesmaximal, characteristic
2#22609911C211yesmaximal, characteristic, complemented
3C2×#17988323C212yesmaximal, complemented
4C2×#17988320C212yesmaximal
5C4×#95×C73C211yesmaximal, characteristic, complemented
6C2×#14556579C411yescharacteristic, complemented
7C2×#14556570C2211yescharacteristic
8C2×#14556565C2211yescharacteristic
9C2×C4⋊#10596831—21no—
10C2×C22⋊#10596831C2212yes—
11#17988493C411yescharacteristic, complemented
12#17988489C411yescharacteristic, complemented
13#17988478—21no—
14#17988478—21no—
15#17988466—21no—
16#17988466—21no—
17#17988453C411yescharacteristic, complemented
18#17988342—21no—
19#17988323—24no—
20#17988320—24no—
21C22×C42×C73—21no—
22C22×C42×C73C2211yescharacteristic
23C2×#95×C73—21no—
24C2×#95×C73C2212yes—
25C22×Dic146C2×C411yescharacteristic
26C22×D292C2×C411yescharacteristic
27C22×C22⋊D73—21no—
28C22×#10596831—22no—
29#14556579—42no—
30#14556570—22no—
31#14556570—22no—
32#14556565—22no—
33#14556565—22no—
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924007—21no—
37C2×C22⋊Dic73—21no—
38C2×#11924005—21no—
39C2×#11924005—21no—
40C2×#11924005—21no—
41C2×#11924005—21no—
42C2×#11924005—21no—
43C4⋊#10596831—42no—
44C22⋊#10596831—22no—
45C22⋊#10596831—22no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50C23×C4×C73—22no—
51C23×C4×C73D411yescharacteristic
52C23×C4×C73D411yescharacteristic
53C23×C4×C73C2311yescharacteristic
54C2×C42×C73—24no—
55C2×C42×C73—42no—
56C2×C42×C73—42no—
57C2×C42×C73—42no—
58C2×C42×C73C2×C411yescharacteristic
59C2×C42×C73C2×C411yescharacteristic
60C2×C42×C73D411yescharacteristic
61C2×C42×C73D411yescharacteristic
62#95×C73—24no—
63#95×C73—22no—
64#95×C73D414yes—
65C23×D73—21no—
66C2×Dic146—22no—
67C2×Dic146—41no—
68C2×Dic146—41no—
69C2×D292—22no—
70C2×D292—41no—
71C2×D292—41no—
72C2×C22⋊D73—42no—
73C2×C22⋊D73—42no—
74C2×C22⋊D73—41no—
75C2×C22⋊D73—41no—
76C22×Dic73—21no—
77C22×Dic73—21no—
78C22×Dic73—21no—
79C2×#10596831—42no—
80C2×#10596831—42no—
81C2×#10596831—42no—
82C4⋊Dic73—22no—
83C4⋊Dic73—22no—
84#11924007—41no—
85#11924007—41no—
86C22⋊Dic73—42no—
87#11924005—42no—
88#11924005—42no—
89#11924005—42no—
90#11924005—42no—
91#11924005—41no—
92#11924005—41no—
93C24×C73C2×D411yescharacteristic
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73—22no—
97C22×C4×C73—22no—
98C22×C4×C73—24no—
99C22×C4×C73—24no—
100C22×C4×C73—24no—
101C22×C4×C73—22no—
102C22×C4×C73—22no—
103C22×C4×C73—41no—
104C22×C4×C73—41no—
105C22×C4×C73—41no—
106C22×C4×C73—42no—
107C22×C4×C73—42no—
108C22×C4×C73—42no—
109C22×C4×C73—42no—
110C22×C4×C73C22⋊C411yescharacteristic
111C22×C4×C73C22⋊C411yescharacteristic
112C22×C4×C73C22⋊C411yescharacteristic
113C22×C4×C73C22⋊C411yescharacteristic
114C22×C4×C73C22×C411yescharacteristic
115C22×C4×C73C2×D411yescharacteristic
116C22×C4×C73C2×D412yes—
117C22×C4×C73#4112yes—
118C42×C73—22no—
119C42×C73—22no—
120C42×C73—41no—
121C42×C73—41no—
122C42×C73—48no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73C2×C22⋊C411yescharacteristic
128C23×C73#12112yes—
129C23×C73#13512yes—
130C23×C73AGL(1,ℤ/8)11yescharacteristic
131C23×C73#13711yescharacteristic
132C22×D73—41no—
133C22×D73—41no—
134C22×D73—41no—
135C22×D73—41no—
136C22×D73—41no—
137C22×D73—41no—
138C22×D73—41no—
139C2×C4×C73—24no—
140C2×C4×C73—24no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—28no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—42no—
156C2×C4×C73—42no—
157C2×C4×C73—44no—
158C2×C4×C73—44no—
159C2×C4×C73—44no—
160C2×C4×C73—44no—
161C2×C4×C73—44no—
162C2×C4×C73—44no—
163C2×C4×C73—44no—
164C2×C4×C73#9912yes—
165C2×C4×C73#10412yes—
166C2×C4×C73#10412yes—
167C2×C4×C73C4×D412yes—
168C2×C4×C73#12411yescharacteristic
169C2×C4×C73#12711yescharacteristic
170C22⋊D73—82no—
171C22⋊D73—82no—
172C2×Dic73—41no—
173C2×Dic73—41no—
174C2×Dic73—41no—
175C2×Dic73—41no—
176C2×Dic73—41no—
177C2×Dic73—41no—
178C2×Dic73—41no—
179C2×Dic73—41no—
180C2×Dic73—41no—
181D292—82no—
182Dic146—82no—
183#10596831—82no—
184C22×C73—22no—
185C22×C73—22no—
186C22×C73—22no—
187C22×C73—22no—
188C22×C73—21no—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—21no—
192C22×C73#39011yescharacteristic
193C22×C73C2×#9911yescharacteristic
194C22×C73#41011yescharacteristic
195C22×C73#41611yescharacteristic
196C22×C73#41711yescharacteristic
197C22×C73C2×#10411yescharacteristic
198C22×C73C2×#10411yescharacteristic
199C22×C73#46312yes—
200C22×C73#46412yes—
201C2×D73—81no—
202C2×D73—81no—
203C2×D73—81no—
204C2×D73—81no—
205C2×D73—81no—
206C2×D73—81no—
207C2×D73—81no—
208C4×C73—21no—
209C4×C73—22no—
210C4×C73—21no—
211C4×C73—22no—
212C4×C73—22no—
213C4×C73—22no—
214C4×C73—48no—
215C4×C73—41no—
216Dic73—81no—
217Dic73—81no—
218Dic73—81no—
219#9713—731nomaximal, Sylow
220C2×C73—22no—
221C2×C73—22no—
222C2×C73#150011yescharacteristic
223C2×C73#150111yescharacteristic
224C2×C73#150411yescharacteristic
225C2×C73#150911yescharacteristic
226C2×C73#196211yescharacteristic
227C2×C73#196411yescharacteristic
228C2×C73#198311yescharacteristic
229D73—161no—
230#2850—731no—
231#1797—731no—
232C2×#328—732no—
233C2×#327—732no—
234C4×#95D7311yescharacteristic, complemented
235C73#971311yescharacteristic, complemented, Sylow
236C2×#124—731no—
237C2×C22⋊Q8—731no—
238C2×#121—731no—
239C22×C42—21no—
240C22×C42C2×D7311yescharacteristic
241C2×C4⋊C8—1461no—
242C2×C22⋊C8—732no—
243#391—731no—
244#390—731no—
245#388—1461no—
246#388—1461no—
247#386—1461no—
248#386—1461no—
249#382—731no—
250C2×#95—21no—
251C2×#95C2×D7312yes—
252#336—1461no—
253#328—1464no—
254#327—1464no—
255C22×Q8—731no—
256C22×D4—731no—
257C22×D4—1461no—
258C23×C4—22no—
259C23×C4C22⋊D7311yescharacteristic
260C23×C4C22⋊D7311yescharacteristic
261C23×C4C22×D7311yescharacteristic
262C22×C8—1462no—
263#124—2922no—
264C22⋊Q8—1462no—
265C22⋊Q8—1462no—
266#121—1462no—
267#121—1462no—
268C2×C4⋊C4—731no—
269C2×C4⋊C4—731no—
270C2×C4⋊C4—1461no—
271C2×C22⋊C4—1461no—
272C2×C22⋊C4—1461no—
273C2×C22⋊C4—1461no—
274C2×C22⋊C4—1461no—
275C2×C22⋊C4—1461no—
276C2×C22⋊C4—1461no—
277C2×C42—24no—
278C2×C42—42no—
279C2×C42—42no—
280C2×C42—42no—
281C2×C42C4×D7311yescharacteristic
282C2×C42C4×D7311yescharacteristic
283C2×C42D29211yescharacteristic
284C2×C42D29211yescharacteristic
285C4⋊C8—2922no—
286C22⋊C8—1462no—
287C22⋊C8—1462no—
288#95—24no—
289#95—22no—
290#95—1461no—
291#95—1461no—
292#95—1461no—
293#95—1461no—
294#95D29214yes—
295C24—1461no—
296C24C2×C22⋊D7311yescharacteristic
297C2×Q8—2921no—
298C2×Q8—2921no—
299C2×Q8—1462no—
300C2×D4—2921no—
301C2×D4—2921no—
302C2×D4—2922no—
303C2×D4—2922no—
304C2×D4—2921no—
305C2×D4—2921no—
306C2×D4—1462no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—1461no—
324C22×C4—1461no—
325C22×C4—1461no—
326C22×C4#1192400511yescharacteristic
327C22×C4#1192400511yescharacteristic
328C22×C4#1192400511yescharacteristic
329C22×C4#1192400511yescharacteristic
330C22×C4C2×C4×D7311yescharacteristic
331C22×C4C2×D29211yescharacteristic
332C22×C4C2×D29212yes—
333C22×C4#1192402812yes—
334C2×C8—2922no—
335C2×C8—2922no—
336C2×C8—2922no—
337C4⋊C4—2921no—
338C4⋊C4—2921no—
339C4⋊C4—1462no—
340C4⋊C4—1462no—
341C22⋊C4—2922no—
342C22⋊C4—2922no—
343C22⋊C4—2922no—
344C22⋊C4—2922no—
345C22⋊C4—2922no—
346C22⋊C4—2921no—
347C22⋊C4—2921no—
348C42—22no—
349C42—22no—
350C42—41no—
351C42—41no—
352C42—48no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—2921no—
358C23—2921no—
359C23—2921no—
360C23—2921no—
361C23—2921no—
362C23—2921no—
363C23—2921no—
364C23C2×#1192400511yescharacteristic
365C23#1455656512yes—
366C23#1455661112yes—
367C23#1455661711yescharacteristic
368C23#1455662211yescharacteristic
369Q8—5842no—
370D4—5842no—
371D4—5842no—
372D4—5842no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—28no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—2921no—
399C2×C4—2921no—
400C2×C4—2921no—
401C2×C4—2921no—
402C2×C4—2921no—
403C2×C4—2921no—
404C2×C4—2921no—
405C2×C4—2921no—
406C2×C4—2921no—
407C2×C4#1455650512yes—
408C2×C4#1455651912yes—
409C2×C4#1455651912yes—
410C2×C4C4×D29212yes—
411C2×C4#1455657911yescharacteristic
412C2×C4#1455658811yescharacteristic
413C8—5842no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—5841no—
423C22—5841no—
424C22—5841no—
425C22—5841no—
426C22—5841no—
427C22—5841no—
428C22—5841no—
429C22#1798848911yescharacteristic
430C22C2×#1455650511yescharacteristic
431C22#1798856011yescharacteristic
432C22#1798858111yescharacteristic
433C22#1798858611yescharacteristic
434C22C2×#1455651911yescharacteristic
435C22C2×#1455651911yescharacteristic
436C22#1798880212yes—
437C22#1798880912yes—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—48no—
445C4—41no—
446C4—5841no—
447C4—5841no—
448C4—5841no—
449C2—22no—
450C2—22no—
451C2—11681no—
452C2#2260841511yescharacteristic
453C2#2260842011yescharacteristic
454C2#2260843311yescharacteristic
455C2#2260845411yescharacteristic
456C2#2261075911yescharacteristic
457C2#2261076711yescharacteristic
458C2#2261086311yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC4×#95×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556565C22
cosocleC23×C4×C73C23
hypercenterC4×#95D73
hypocenterC73#9713
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. #22609911C2semidirect
3. C2×#17988323C2semidirect
5. C4×#95×C73C2semidirect
6. C2×#14556579C4semidirect
11. #17988493C4semidirect
12. #17988489C4semidirect
17. #17988453C4semidirect
234. C4×#95D73semidirect
235. C73#9713semidirect

Maximal subgroups

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

subgroupindex
#226182322
#226099112
C2×#179883232
C2×#179883202
C4×#95×C732
#971373