Finite Group Databasebeta

← #32976979

Subgroups — #32976979

Order 18688.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618621C211yesmaximal, characteristic
2#22609709C211yesmaximal, characteristic, complemented
3C22⋊C4×#10596831C211yesmaximal, characteristic, complemented
4#22608420C211yesmaximal, characteristic
5#22608420C211yesmaximal, characteristic
6#22607818C211yesmaximal, characteristic, complemented
7C73×#1297C211yesmaximal, characteristic, complemented
8C2×#14556599C411yescharacteristic, complemented
9C23×#10596831C2211yescharacteristic
10#17989098C2211yescharacteristic
11#17988655—21no—
12#17988655—21no—
13#17988650—21no—
14#17988650—21no—
15#17988615C411yescharacteristic, complemented
16#17988555C411yescharacteristic, complemented
17C2×C22⋊#10596831C2211yescharacteristic
18C2×C22⋊#10596831C2211yescharacteristic
19#17988545C411yescharacteristic, complemented
20C2×#14556502—21no—
21C2×C4×#10596831—21no—
22#17988342—21no—
23#17988342—21no—
24#17988323C412yescomplemented
25#17988323C412yescomplemented
26#17988320C412yescomplemented
27#17988320C412yescomplemented
28#407×C73C2211yescharacteristic
29C4×C22⋊C4×C73C2211yescharacteristic
30C4×C22⋊C4×C73C2211yescharacteristic
31C2×#11924028C2×C411yescharacteristic
32#14556599—42no—
33C2×#11924011—21no—
34C22×#10596831—21no—
35C22×#10596831—21no—
36C22×#10596831—42no—
37C22×#10596831C2×C411yescharacteristic
38C22×#10596831C2×C411yescharacteristic
39C22×#10596831D411yescharacteristic
40C22×#10596831D411yescharacteristic
41C22×#10596831D411yescharacteristic
42C22×#10596831D411yescharacteristic
43C2×C8×D73—21no—
44#14556574—21no—
45#14556570C2×C411yescharacteristic
46#14556570C2×C411yescharacteristic
47#14556565C2×C411yescharacteristic
48#14556565C2×C411yescharacteristic
49#14556560—21no—
50C4×C22⋊D73—21no—
51C4×C22⋊D73—21no—
52#14556550C2×C411yescharacteristic
53#14556520—21no—
54#14556520—21no—
55C22⋊#10596831—21no—
56C22⋊#10596831—21no—
57C22⋊#10596831C2×C412yes—
58C22⋊#10596831C2×C412yes—
59#14556503—21no—
60#14556503—21no—
61#14556502—42no—
62#14556501—21no—
63C4×#10596831—42no—
64C8×Dic73—21no—
65C23×C4×C73C2311yescharacteristic
66C2×M16×C73C2×C411yescharacteristic
67C2×M16×C73C2×C411yescharacteristic
68C2×C22⋊C4×C73—21no—
69C2×C22⋊C4×C73—21no—
70C2×C42×C73—21no—
71C2×C42×C73—21no—
72C22⋊C8×C73—21no—
73C22⋊C8×C73—21no—
74#95×C73C2×C412yes—
75#95×C73C2×C412yes—
76#11924028—41no—
77#11924028—41no—
78C2×Dic146C4211yescharacteristic
79C2×D292C4211yescharacteristic
80C2×C22⋊D73—21no—
81C2×C22⋊D73—21no—
82C2×C22⋊D73—21no—
83C2×C4×D73—21no—
84#11924011—42no—
85C2×#10596831—22no—
86C2×#10596831—22no—
87C2×#10596831—22no—
88C2×#10596831—22no—
89C2×#10596831—22no—
90C2×#10596831—41no—
91C2×#10596831—41no—
92C2×#10596831—41no—
93C2×#10596831—41no—
94C2×#10596831—41no—
95C2×#10596831—41no—
96C2×#10596831—41no—
97C2×#10596831C22⋊C411yescharacteristic
98C2×#10596831C22⋊C411yescharacteristic
99C2×#10596831C22⋊C411yescharacteristic
100C2×#10596831C22⋊C411yescharacteristic
101C8×D73—42no—
102C4⋊Dic73C4211yescharacteristic
103C4⋊Dic73C4211yescharacteristic
104#11924007—21no—
105#11924007—21no—
106C22⋊Dic73—21no—
107C22⋊Dic73—21no—
108C22⋊Dic73—21no—
109#11924005—21no—
110#11924005—21no—
111C4×Dic73—21no—
112C24×C73#4111yescharacteristic
113C22×C4×C73—22no—
114C22×C4×C73—22no—
115C22×C4×C73—41no—
116C22×C4×C73—41no—
117C22×C4×C73C22×C411yescharacteristic
118C22×C4×C73C22×C411yescharacteristic
119C22×C4×C73C22×C411yescharacteristic
120C22×C4×C73C2×D411yescharacteristic
121C22×C4×C73C2×D411yescharacteristic
122C22×C4×C73#4111yescharacteristic
123M16×C73—41no—
124M16×C73—41no—
125C2×C8×C73—21no—
126C2×C8×C73—21no—
127C22⋊C4×C73—24no—
128C22⋊C4×C73—42no—
129C42×C73—41no—
130C42×C73—41no—
131C42×C73—41no—
132C42×C73—41no—
133C23×C73—22no—
134C23×C73—22no—
135C23×C73—41no—
136C23×C73#11711yescharacteristic
137C23×C73C4×D411yescharacteristic
138C23×C73C4×D411yescharacteristic
139C22×D73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—24no—
147C2×C4×C73—41no—
148C2×C4×C73—41no—
149C2×C4×C73—41no—
150C2×C4×C73—42no—
151C2×C4×C73—42no—
152C2×C4×C73—42no—
153C2×C4×C73—42no—
154C2×C4×C73—42no—
155C2×C4×C73C2×C4211yescharacteristic
156C2×C4×C73C2×C22⋊C411yescharacteristic
157C2×C4×C73C4×D411yescharacteristic
158C2×C4×C73C4×D411yescharacteristic
159C22⋊D73—42no—
160C22⋊D73—42no—
161C22⋊D73—42no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73—21no—
165D292—41no—
166C4×D73—41no—
167C4×D73—41no—
168Dic146—41no—
169C8×C73—41no—
170C8×C73—41no—
171#10596831—21no—
172#10596831—21no—
173#10596831—21no—
174#10596831—42no—
175#10596831—42no—
176#10596831#9912yes—
177C22×C73—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—21no—
183C22×C73—21no—
184C22×C73—44no—
185C22×C73C4×C22⋊C411yescharacteristic
186C22×C73#44312yes—
187C22×C73#44412yes—
188C2×D73—41no—
189C2×D73—41no—
190C2×D73—41no—
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—44no—
195C4×C73—82no—
196C4×C73C2×#9911yescharacteristic
197C4×C73#41011yescharacteristic
198Dic73—41no—
199Dic73—41no—
200Dic73—41no—
201#8240—731nomaximal, Sylow
202C2×C73—22no—
203C2×C73—22no—
204C2×C73—41no—
205C2×C73C4×#9911yescharacteristic
206C2×C73#176411yescharacteristic
207C2×C73#176511yescharacteristic
208D73—81no—
209#2929—731no—
210#1752—731no—
211C8×C22⋊C4—731no—
212#1501—731no—
213#1501—731no—
214#1298—731no—
215#1297D7311yescharacteristic, complemented
216C73#824011yescharacteristic, complemented, Sylow
217C2×#131—731no—
218C23×C8—731no—
219#525—731no—
220#435—1461no—
221#435—1461no—
222C8×D4—1461no—
223C8×D4—1461no—
224#424—731no—
225#408—731no—
226#407C2×D7311yescharacteristic
227C2×C22⋊C8—731no—
228C2×C22⋊C8—731no—
229#405—731no—
230C2×#97—1461no—
231C2×C4×C8—1461no—
232C4×C22⋊C4C2×D7311yescharacteristic
233C4×C22⋊C4C2×D7311yescharacteristic
234#336—1461no—
235#336—1461no—
236#328—732no—
237#328—732no—
238#327—732no—
239#327—732no—
240C2×#41—731no—
241C23×C4C22×D7311yescharacteristic
242#131—2922no—
243C2×M16—1461no—
244C2×M16C4×D7311yescharacteristic
245C2×M16C4×D7311yescharacteristic
246C22×C8—2922no—
247C22×C8—731no—
248C22×C8—731no—
249C22×C8—731no—
250C22×C8—731no—
251C22×C8—731no—
252C22×C8—731no—
253C22×C8—1461no—
254C22×C8—1461no—
255C22×C8—1461no—
256#123—1461no—
257C22⋊Q8—731no—
258C22⋊Q8—731no—
259#121—731no—
260#121—731no—
261#120—1461no—
262C4×D4—1461no—
263C4×D4—1461no—
264#117—731no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C42—21no—
268C2×C42—21no—
269C4⋊C8—1461no—
270C4⋊C8—1461no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—732no—
274C22⋊C8—732no—
275C22⋊C8—1461no—
276C22⋊C8—1461no—
277C22⋊C8—1461no—
278C22⋊C8—1461no—
279#97—2922no—
280#97—1461no—
281C4×C8—2922no—
282C4×C8—1461no—
283#95C4×D7312yes—
284#95C4×D7312yes—
285C24#1192402711yescharacteristic
286#41—2921no—
287#41—2921no—
288C2×Q8—731no—
289C2×D4—731no—
290C2×D4—1461no—
291C2×D4—1461no—
292C2×D4—1461no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—1461no—
298C22×C4C2×C4×D7311yescharacteristic
299C22×C4C2×C4×D7311yescharacteristic
300C22×C4C2×C4×D7311yescharacteristic
301C22×C4D4×D7311yescharacteristic
302C22×C4D4×D7311yescharacteristic
303C22×C4#1192402911yescharacteristic
304M16—41no—
305M16—41no—
306M16—2922no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—2922no—
310C2×C8—2921no—
311C2×C8—2921no—
312C2×C8—2921no—
313C2×C8—2921no—
314C2×C8—2921no—
315C2×C8—2921no—
316C2×C8—2921no—
317C2×C8—731no—
318C2×C8—731no—
319C2×C8—731no—
320C2×C8—731no—
321C2×C8—1462no—
322C2×C8—1462no—
323C2×C8—1462no—
324C2×C8—1462no—
325C2×C8—1462no—
326C4⋊C4—731no—
327C4⋊C4—731no—
328C4⋊C4—1461no—
329C4⋊C4—1461no—
330C22⋊C4—24no—
331C22⋊C4—42no—
332C22⋊C4—1461no—
333C22⋊C4—1461no—
334C22⋊C4—1461no—
335C22⋊C4—1461no—
336C22⋊C4—1461no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—41no—
341C42—1461no—
342C23—22no—
343C23—22no—
344C23—41no—
345C23—1461no—
346C23#1455654911yescharacteristic
347C23#1455655111yescharacteristic
348C23#1455655111yescharacteristic
349Q8—2921no—
350D4—2921no—
351D4—2922no—
352D4—2922no—
353D4—2922no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—2921no—
370C2×C4—2921no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4—1461no—
374C2×C4C42×D7311yescharacteristic
375C2×C4C22⋊C4×D7311yescharacteristic
376C2×C4#1455655311yescharacteristic
377C2×C4#1455655311yescharacteristic
378C8—41no—
379C8—41no—
380C8—2922no—
381C8—2922no—
382C8—732no—
383C8—1461no—
384C8—1461no—
385C8—1461no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—2921no—
395C22—2921no—
396C22—2921no—
397C22#1798843411yescharacteristic
398C22#1798870112yes—
399C22#1798870612yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—82no—
405C4—2921no—
406C4—2921no—
407C4—2921no—
408C4#99×D7311yescharacteristic
409C4#1798855911yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—5841no—
414C2#2260971811yescharacteristic
415C2#2260976511yescharacteristic
416C2#2260977211yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D73
commutatorC2×C4×C73C2×C42
FrattiniC23×C4C22×D73
FittingC73×#1297C2
socleC22×C73C4×C22⋊C4
prime radical#17989098C22
cosocleC23×C4×C73C23
hypercenter#1297D73
hypocenterC73#8240
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #22609709C2semidirect
3. C22⋊C4×#10596831C2semidirect
6. #22607818C2semidirect
7. C73×#1297C2semidirect
8. C2×#14556599C4semidirect
15. #17988615C4semidirect
16. #17988555C4semidirect
19. #17988545C4semidirect
24. #17988323C4semidirect
25. #17988323C4semidirect
26. #17988320C4semidirect
27. #17988320C4semidirect
215. #1297D73semidirect
216. C73#8240semidirect

Maximal subgroups

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

subgroupindex
#226186212
#226097092
C22⋊C4×#105968312
#226084202
#226078182
C73×#12972
#824073