Finite Group Databasebeta

← #33240785

Subgroups — #33240785

Order 18688.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619512C211yesmaximal, characteristic
2C2×#17988625C211yesmaximal, characteristic, complemented
3#22612140C212yesmaximal, complemented
4#22612134C211yesmaximal, characteristic, complemented
5#22612129C211yesmaximal, characteristic, complemented
6#22612123C212yesmaximal, complemented
7#22612117C211yesmaximal, characteristic, complemented
8#22612112C211yesmaximal, characteristic, complemented
9#22611715C212yesmaximal, complemented
10#22611639C212yesmaximal, complemented
11C2×C22⋊C16×C73C211yesmaximal, characteristic, complemented
12C2×#14556613C2211yescharacteristic
13#17989098—21no—
14C2×#14556550—21no—
15#17988828C2211yescharacteristic
16#17988828C2211yescharacteristic
17#17988823C2211yescharacteristic
18#17988823C2211yescharacteristic
19#17988816—21no—
20#17988816—21no—
21#17988625—21no—
22#17988625—21no—
23#17988625C2211yescharacteristic
24#17988625C2212yes—
25#17988625C2212yes—
26C2×#14556525C2211yescharacteristic
27C2×#14556525C2211yescharacteristic
28C2×#14556523—21no—
29#17988584—21no—
30#17988415C2212yescomplemented
31#17988415C2212yescomplemented
32#17988413C2212yescomplemented
33#17988413C2212yescomplemented
34#17988392C2212yescomplemented
35#17988392C2212yescomplemented
36#17988389C2212yescomplemented
37#17988389C2212yescomplemented
38C23×C8×C73C2211yescharacteristic
39C22×C16×C73C2212yes—
40C22⋊C16×C73C2211yescharacteristic
41C22⋊C16×C73C2211yescharacteristic
42C22⋊C16×C73C2212yes—
43C2×#11924028—21no—
44#14556613—24no—
45C2×Dic292C2311yescharacteristic
46C2×#11924017—21no—
47C2×D584C2311yescharacteristic
48#14556574—41no—
49#14556570—21no—
50#14556570—21no—
51#14556565—21no—
52#14556565—21no—
53#14556560—41no—
54C4×C22⋊D73—41no—
55C4×C22⋊D73—41no—
56#14556550—22no—
57#14556550—22no—
58#14556550—21no—
59#14556550—41no—
60#14556550—41no—
61C2×C4⋊Dic73—21no—
62C2×C4⋊Dic73—21no—
63C2×C22⋊Dic73—41no—
64C2×C4×Dic73—41no—
65#14556525—21no—
66#14556525—21no—
67#14556525C2312yes—
68#14556525C2312yes—
69#14556525C2311yescharacteristic
70#14556525C2311yescharacteristic
71#14556523—22no—
72#14556523—22no—
73#14556523—21no—
74#14556516—21no—
75#14556516—21no—
76#14556513—21no—
77#14556513—21no—
78C23×C4×C73D411yescharacteristic
79C22×C8×C73—24no—
80C22×C8×C73D411yescharacteristic
81C22×C8×C73D411yescharacteristic
82C22×C8×C73D411yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86C2×C16×C73—24no—
87C2×C16×C73C2312yes—
88C2×C16×C73C2312yes—
89#11924028—42no—
90#11924028—42no—
91C2×Dic146—21no—
92C2×D292—21no—
93C2×C22⋊D73—41no—
94C2×C22⋊D73—41no—
95C2×C22⋊D73—41no—
96C22×Dic73—41no—
97C22×Dic73—41no—
98C2×C4×D73—41no—
99Dic292—22no—
100#11924017—42no—
101D584—22no—
102C4⋊Dic73—21no—
103C4⋊Dic73—21no—
104C4⋊Dic73—22no—
105C4⋊Dic73—22no—
106C4⋊Dic73—41no—
107C4⋊Dic73—41no—
108#11924007—41no—
109#11924007—41no—
110C22⋊Dic73—42no—
111C22⋊Dic73—42no—
112C22⋊Dic73—41no—
113C22⋊Dic73—41no—
114C22⋊Dic73—41no—
115#11924005—41no—
116#11924005—41no—
117C4×Dic73—42no—
118C4×Dic73—42no—
119C4×Dic73—41no—
120C24×C73D811yescharacteristic
121C22×C4×C73—22no—
122C22×C4×C73—22no—
123C22×C4×C73D811yescharacteristic
124C22×C4×C73D811yescharacteristic
125C22×C4×C73D811yescharacteristic
126C22×C4×C73C2×D411yescharacteristic
127C22×C4×C73C2×D411yescharacteristic
128C22×C4×C73C2×D411yescharacteristic
129C2×C8×C73—22no—
130C2×C8×C73—22no—
131C2×C8×C73—22no—
132C2×C8×C73—22no—
133C2×C8×C73—22no—
134C2×C8×C73C2×D411yescharacteristic
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73#4114yes—
138C2×C8×C73C2411yescharacteristic
139C16×C73—22no—
140C16×C73—22no—
141C23×C73—22no—
142C23×C73—22no—
143C23×C73—41no—
144C23×C73C2×D811yescharacteristic
145C23×C73C2×D811yescharacteristic
146C23×C73C2×D811yescharacteristic
147C22×D73—41no—
148C2×C4×C73—22no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—22no—
154C2×C4×C73—22no—
155C2×C4×C73#12312yes—
156C2×C4×C73C2×D811yescharacteristic
157C2×C4×C73C2×D811yescharacteristic
158C2×C4×C73C2×D811yescharacteristic
159C2×C4×C73#13712yes—
160C2×C4×C73C22×D411yescharacteristic
161C22⋊D73—82no—
162C22⋊D73—82no—
163C22⋊D73—82no—
164C2×Dic73—42no—
165C2×Dic73—42no—
166C2×Dic73—41no—
167C2×Dic73—41no—
168C2×Dic73—41no—
169C2×Dic73—82no—
170C2×Dic73—82no—
171D292—41no—
172D292—41no—
173C4×D73—82no—
174Dic146—41no—
175Dic146—41no—
176C8×C73—21no—
177C8×C73—21no—
178C8×C73#12312yes—
179C8×C73C2×#4112yes—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—21no—
183C22×C73—21no—
184C22×C73—21no—
185C22×C73—21no—
186C22×C73—21no—
187C22×C73—44no—
188C22×C73#48012yes—
189C22×C73#50812yes—
190C22×C73C22×D811yescharacteristic
191C2×D73—81no—
192C2×D73—81no—
193C2×D73—81no—
194C4×C73—21no—
195C4×C73—21no—
196C4×C73#48012yes—
197C4×C73C2×#12311yescharacteristic
198C4×C73C2×#13711yescharacteristic
199Dic73—81no—
200Dic73—82no—
201Dic73—81no—
202Dic73—82no—
203Dic73—81no—
204#33645—731nomaximal, Sylow
205C2×C73—22no—
206C2×C73—22no—
207C2×C73—41no—
208C2×C73C2×#48011yescharacteristic
209C2×C73C2×#50811yescharacteristic
210C2×C73#341411yescharacteristic
211D73—161no—
212#3050—731no—
213C2×#427—731no—
214#2237—732no—
215#2236—731no—
216#2235—731no—
217#2234—732no—
218#2233—731no—
219#2232—731no—
220#2158—732no—
221#2138—732no—
222C2×C22⋊C16D7311yescharacteristic, complemented
223C73#3364511yescharacteristic, complemented, Sylow
224C2×#135—731no—
225C23×C8C2×D7311yescharacteristic
226#525—1461no—
227C2×#117—1461no—
228C22×C16C2×D7312yes—
229#467—731no—
230#467—731no—
231#466—731no—
232#466—731no—
233#465—1461no—
234#465—1461no—
235#427—732no—
236#427—732no—
237#427—731no—
238#427—1461no—
239#427—1461no—
240C2×#107—731no—
241C2×#107—731no—
242C2×#106—1461no—
243#416—1461no—
244#367—732no—
245#367—732no—
246#366—732no—
247#366—732no—
248#358—732no—
249#358—732no—
250#357—732no—
251#357—732no—
252C22⋊C16C2×D7311yescharacteristic
253C22⋊C16C2×D7311yescharacteristic
254C22⋊C16C2×D7312yes—
255C2×#41—1461no—
256C23×C4D29211yescharacteristic
257#135—1464no—
258C2×Q16—731no—
259C2×SD16—1461no—
260C2×D8—731no—
261C22×C8—24no—
262C22×C8D29211yescharacteristic
263C22×C8D29211yescharacteristic
264C22×C8D29211yescharacteristic
265C22×C8C22×D7311yescharacteristic
266C22×C8C22×D7311yescharacteristic
267C22×C8C22×D7311yescharacteristic
268#123—2921no—
269C22⋊Q8—1461no—
270C22⋊Q8—1461no—
271#121—1461no—
272#121—1461no—
273#120—2921no—
274C4×D4—2921no—
275C4×D4—2921no—
276#117—2921no—
277#117—2921no—
278#117—1462no—
279#117—1462no—
280#117—1461no—
281C2×C4⋊C4—1461no—
282C2×C4⋊C4—1461no—
283C2×C22⋊C4—2921no—
284C2×C42—2921no—
285C2×C16—24no—
286C2×C16C22×D7312yes—
287C2×C16C22×D7312yes—
288#107—732no—
289#107—732no—
290#107—731no—
291#107—731no—
292#107—1461no—
293#107—1461no—
294#106—1462no—
295#106—1462no—
296#106—1461no—
297#103—1461no—
298#103—1461no—
299#102—1461no—
300#102—1461no—
301C24D58411yescharacteristic
302#41—2922no—
303#41—2922no—
304C2×Q8—1461no—
305C2×D4—2921no—
306C2×D4—2921no—
307C2×D4—2921no—
308C2×D4—1461no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—2921no—
312C22×C4—2921no—
313C22×C4—2921no—
314C22×C4D58411yescharacteristic
315C22×C4D58411yescharacteristic
316C22×C4D58411yescharacteristic
317C22×C4C2×D29211yescharacteristic
318C22×C4C2×D29211yescharacteristic
319C22×C4C2×D29211yescharacteristic
320Q16—1462no—
321SD16—2922no—
322D8—1462no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8C2×D29211yescharacteristic
329C2×C8C2×D29211yescharacteristic
330C2×C8C2×D29211yescharacteristic
331C2×C8#1192402714yes—
332C2×C8C23×D7311yescharacteristic
333C4⋊C4—2921no—
334C4⋊C4—2921no—
335C4⋊C4—2921no—
336C4⋊C4—2921no—
337C4⋊C4—1461no—
338C4⋊C4—1461no—
339C4⋊C4—1462no—
340C4⋊C4—1462no—
341C22⋊C4—2922no—
342C22⋊C4—2922no—
343C22⋊C4—2921no—
344C22⋊C4—2921no—
345C22⋊C4—2921no—
346C22⋊C4—2921no—
347C22⋊C4—2921no—
348C42—2922no—
349C42—2922no—
350C42—2921no—
351C16—22no—
352C16—22no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—2921no—
357C23C2×D58411yescharacteristic
358C23C2×D58411yescharacteristic
359C23C2×D58411yescharacteristic
360Q8—2921no—
361Q8—2921no—
362D4—2921no—
363D4—2921no—
364D4—5842no—
365D4—5842no—
366D4—5842no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—2922no—
375C2×C4—2922no—
376C2×C4—2921no—
377C2×C4—2921no—
378C2×C4—2921no—
379C2×C4—5842no—
380C2×C4—5842no—
381C2×C4—5842no—
382C2×C4#1455657512yes—
383C2×C4C2×D58411yescharacteristic
384C2×C4C2×D58411yescharacteristic
385C2×C4C2×D58411yescharacteristic
386C2×C4#1455662412yes—
387C2×C4C22×D29211yescharacteristic
388C8—21no—
389C8—21no—
390C8#1455657512yes—
391C8C2×#1192402712yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—5841no—
401C22—5841no—
402C22—5841no—
403C22#1798890112yes—
404C22#1798901912yes—
405C22C22×D58411yescharacteristic
406C4—21no—
407C4—21no—
408C4—5842no—
409C4—5841no—
410C4—5842no—
411C4—5841no—
412C4—5841no—
413C4#1798890112yes—
414C4C2×#1455657511yescharacteristic
415C4C2×#1455662411yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—11681no—
420C2C2×#1798890111yescharacteristic
421C2C2×#1798901911yescharacteristic
422C2#2262306711yescharacteristic
subgroupG/H
centerC2×C4C2×D584
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×C22⋊C16×C73C2
socleC22×C73C22×D8
prime radical#22619512C2
hypercenterC2×C22⋊C16D73
hypocenterC73#33645
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#17988625C2semidirect
3. #22612140C2semidirect
4. #22612134C2semidirect
5. #22612129C2semidirect
6. #22612123C2semidirect
7. #22612117C2semidirect
8. #22612112C2semidirect
9. #22611715C2semidirect
10. #22611639C2semidirect
11. C2×C22⋊C16×C73C2semidirect
30. #17988415C22semidirect
31. #17988415C22semidirect
32. #17988413C22semidirect
33. #17988413C22semidirect
34. #17988392C22semidirect
35. #17988392C22semidirect
36. #17988389C22semidirect
37. #17988389C22semidirect
222. C2×C22⋊C16D73semidirect
223. C73#33645semidirect

Maximal subgroups

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

subgroupindex
#226195122
C2×#179886252
#226121402
#226121342
#226121292
#226121232
#226121172
#226121122
#226117152
#226116392
C2×C22⋊C16×C732
#3364573