Finite Group Databasebeta

← #33001143

Subgroups — #33001143

Order 18688.

456 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618632C211yesmaximal, characteristic
2#22611573C211yesmaximal, characteristic
3#22611570C211yesmaximal, characteristic
4#22609731C211yesmaximal, characteristic, complemented
5#22608053C211yesmaximal, characteristic, complemented
6#22608051C211yesmaximal, characteristic, complemented
7C73×#1757C211yesmaximal, characteristic, complemented
8C22×#11924011C411yescharacteristic, complemented
9#17989094C2211yescharacteristic
10#17988663—21no—
11#17988663—21no—
12#17988658—21no—
13#17988658—21no—
14#17988615C411yescharacteristic, complemented
15#17988571C2211yescharacteristic
16#17988561C2211yescharacteristic
17#17988554C2211yescharacteristic
18#17988550C411yescharacteristic, complemented
19#17988542—21no—
20#17988542C411yescharacteristic, complemented
21#17988378C412yescomplemented
22#17988376C412yescomplemented
23#17988375C412yescomplemented
24#17988373C412yescomplemented
25#17988358—21no—
26C2×#131×C73C2211yescharacteristic
27#413×C73C2211yescharacteristic
28#410×C73C2211yescharacteristic
29#405×C73—21no—
30#344×C73—21no—
31C22×C4×D73C2×C411yescharacteristic
32C2×#11924012—21no—
33C2×#11924012C2×C411yescharacteristic
34C2×#11924011—21no—
35C2×#11924011—21no—
36C2×#11924011—41no—
37C2×#11924011—41no—
38C22×#10596831C2×C411yescharacteristic
39#14556572C2×C411yescharacteristic
40#14556572C2×C411yescharacteristic
41#14556567—21no—
42#14556562—21no—
43#14556559C2×C411yescharacteristic
44#14556559C2×C411yescharacteristic
45C4×C22⋊D73—21no—
46C4×C22⋊D73—21no—
47#14556550—21no—
48#14556550C2×C411yescharacteristic
49#14556520—21no—
50#14556520—21no—
51#14556510—21no—
52#14556508C2×C412yes—
53#14556506—21no—
54#14556506C2×C412yes—
55C22⋊#10596831—21no—
56C22⋊#10596831—21no—
57#14556503—21no—
58#14556503—21no—
59#14556501—21no—
60#14556501—41no—
61C8×Dic73—21no—
62C8×Dic73—41no—
63C2×#41×C73C2311yescharacteristic
64#131×C73—41no—
65#131×C73—41no—
66C2×M16×C73—21no—
67C2×M16×C73C2×C411yescharacteristic
68C2×M16×C73D411yescharacteristic
69C2×M16×C73D411yescharacteristic
70C22×C8×C73C2×C411yescharacteristic
71C22×C8×C73D411yescharacteristic
72C22×C8×C73D411yescharacteristic
73#117×C73—21no—
74#101×C73—21no—
75#100×C73C2×C412yes—
76#99×C73—21no—
77#99×C73C2×C412yes—
78#97×C73—41no—
79C4×C8×C73—41no—
80C23×D73C4211yescharacteristic
81C2×C22⋊D73—21no—
82C2×C22⋊D73—21no—
83C22×Dic73C4211yescharacteristic
84C2×C4×D73—21no—
85C2×C4×D73—21no—
86C2×C4×D73—41no—
87C2×C4×D73—41no—
88#11924012—22no—
89#11924012—41no—
90#11924012—41no—
91#11924011—42no—
92#11924011—41no—
93#11924011—41no—
94C2×#10596831—21no—
95C2×#10596831—21no—
96C2×#10596831—41no—
97C2×#10596831—41no—
98C4⋊Dic73—21no—
99C4⋊Dic73—41no—
100#11924007—21no—
101#11924007—21no—
102C22⋊Dic73—21no—
103C22⋊Dic73—21no—
104C22⋊Dic73—22no—
105C22⋊Dic73C4211yescharacteristic
106C22⋊Dic73C4211yescharacteristic
107#11924005—21no—
108#11924005—21no—
109C4×Dic73—21no—
110C4×Dic73—41no—
111#41×C73—41no—
112#41×C73—41no—
113C2×Q8×C73#4111yescharacteristic
114C2×D4×C73C22×C411yescharacteristic
115C2×D4×C73C22×C411yescharacteristic
116C2×D4×C73#4111yescharacteristic
117C22×C4×C73C22×C411yescharacteristic
118C22×C4×C73C2×D411yescharacteristic
119C22×C4×C73C2×D411yescharacteristic
120M16×C73—22no—
121M16×C73—41no—
122M16×C73—41no—
123M16×C73—41no—
124M16×C73—41no—
125C2×C8×C73—21no—
126C2×C8×C73—21no—
127C2×C8×C73—21no—
128C2×C8×C73—21no—
129C2×C8×C73—21no—
130C2×C8×C73—21no—
131C2×C8×C73—41no—
132C2×C8×C73C22⋊C411yescharacteristic
133C2×C8×C73C22⋊C411yescharacteristic
134C2×C8×C73C22⋊C411yescharacteristic
135C2×C8×C73C22⋊C411yescharacteristic
136C4⋊C4×C73—41no—
137C22⋊C4×C73—22no—
138C42×C73—41no—
139C23×C73C2×C4211yescharacteristic
140C23×C73C4×D411yescharacteristic
141C23×C73C4×D411yescharacteristic
142C22×D73—21no—
143C22×D73—41no—
144C22×D73—81no—
145Q8×C73—41no—
146D4×C73—41no—
147D4×C73—41no—
148D4×C73—41no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—42no—
156C2×C4×C73C2×C22⋊C411yescharacteristic
157C2×C4×C73#11711yescharacteristic
158C2×C4×C73C4×D411yescharacteristic
159C2×C4×C73C4×D411yescharacteristic
160C22⋊D73—81no—
161C22⋊D73—81no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73—21no—
165C2×Dic73—41no—
166C2×Dic73—42no—
167C4×D73—42no—
168C4×D73—41no—
169C4×D73—41no—
170C8×C73—21no—
171C8×C73—21no—
172C8×C73—21no—
173C8×C73—42no—
174C8×C73#9911yescharacteristic
175C8×C73#9911yescharacteristic
176#10596831—42no—
177#10596831—41no—
178#10596831—41no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73C4×C22⋊C411yescharacteristic
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—41no—
189C2×D73—82no—
190C4×C73—21no—
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—82no—
194C4×C73C2×#9911yescharacteristic
195C4×C73#41011yescharacteristic
196Dic73—41no—
197Dic73—41no—
198Dic73—41no—
199Dic73—82no—
200#12624—731nomaximal, Sylow
201C2×C73—21no—
202C2×C73—41no—
203C2×C73—41no—
204C2×C73—41no—
205C2×C73C4×#9911yescharacteristic
206D73—81no—
207#2930—731no—
208#2120—731no—
209#2120—731no—
210#1757—731no—
211#1757D7311yescharacteristic, complemented
212#1392—731no—
213#1391—731no—
214C73#1262411yescharacteristic, complemented, Sylow
215C2×#131C2×D7311yescharacteristic
216C22×M16—731no—
217#525—731no—
218#436—1461no—
219#436—1461no—
220#435—1461no—
221#435—1461no—
222#424—731no—
223#413—731no—
224#413C2×D7311yescharacteristic
225#410—731no—
226#410C2×D7311yescharacteristic
227#408—731no—
228#407—731no—
229#405—21no—
230#405—731no—
231#405—1461no—
232#352—732no—
233#352—732no—
234AΣL(1,𝔽16)—732no—
235AΣL(1,𝔽16)—732no—
236#344—21no—
237#344—1461no—
238C2×#41C22×D7311yescharacteristic
239C23×C4—731no—
240#131—41no—
241#131—41no—
242C2×M16—21no—
243C2×M16—2921no—
244C2×M16—2921no—
245C2×M16—731no—
246C2×M16—1461no—
247C2×M16—1461no—
248C2×M16—1461no—
249C2×M16C4×D7311yescharacteristic
250C2×M16D29211yescharacteristic
251C2×M16C22⋊D7311yescharacteristic
252C22×C8—731no—
253C22×C8C4×D7311yescharacteristic
254C22×C8D29211yescharacteristic
255C22×C8C22⋊D7311yescharacteristic
256#123—731no—
257#123—731no—
258C22⋊Q8—1461no—
259#121—1461no—
260#120—731no—
261#120—731no—
262C4×D4—1461no—
263C4×D4—1461no—
264#117—21no—
265#117—731no—
266#117—1461no—
267C4⋊C8—1461no—
268C4⋊C8—1461no—
269#101—21no—
270#101—1461no—
271#100—732no—
272#100C4×D7312yes—
273#99—21no—
274#99—732no—
275#99—1461no—
276#99C4×D7312yes—
277C22⋊C8—1461no—
278C22⋊C8—1461no—
279C22⋊C8—1461no—
280C22⋊C8—1461no—
281#97—41no—
282#97—2921no—
283#97—1461no—
284C4×C8—41no—
285C4×C8—2921no—
286C4×C8—1461no—
287C24—731no—
288#41—41no—
289#41—41no—
290C2×Q8#1192402811yescharacteristic
291C2×D4—1461no—
292C2×D4—1461no—
293C2×D4C2×C4×D7311yescharacteristic
294C2×D4C2×C4×D7311yescharacteristic
295C2×D4#1192402811yescharacteristic
296C22×C4—2921no—
297C22×C4—2921no—
298C22×C4—731no—
299C22×C4—1461no—
300C22×C4—1461no—
301C22×C4C2×C4×D7311yescharacteristic
302C22×C4C2×C22⋊D7311yescharacteristic
303C22×C4C2×D29211yescharacteristic
304M16—22no—
305M16—41no—
306M16—41no—
307M16—41no—
308M16—41no—
309M16—2922no—
310M16—2921no—
311M16—2921no—
312M16—2921no—
313M16—2921no—
314M16—1462no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—41no—
322C2×C8—2921no—
323C2×C8—2921no—
324C2×C8—1461no—
325C2×C8—1461no—
326C2×C8#1192400511yescharacteristic
327C2×C8#1192400511yescharacteristic
328C2×C8#1192400511yescharacteristic
329C2×C8#1192400511yescharacteristic
330C4⋊C4—41no—
331C4⋊C4—2921no—
332C4⋊C4—1461no—
333C4⋊C4—1461no—
334C4⋊C4—1461no—
335C22⋊C4—22no—
336C22⋊C4—731no—
337C22⋊C4—731no—
338C22⋊C4—1462no—
339C22⋊C4—1461no—
340C22⋊C4—1461no—
341C22⋊C4—1461no—
342C22⋊C4—1461no—
343C42—41no—
344C42—2921no—
345C42—1461no—
346C23—2921no—
347C23—5841no—
348C23—1461no—
349C23C42×D7311yescharacteristic
350C23C4×C22⋊D7311yescharacteristic
351C23C4×D29211yescharacteristic
352Q8—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—5841no—
357D4—5841no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—2922no—
366C2×C4—2921no—
367C2×C4—2921no—
368C2×C4—2921no—
369C2×C4—2922no—
370C2×C4—1461no—
371C2×C4—1461no—
372C2×C4—1461no—
373C2×C4C2×#1192400511yescharacteristic
374C2×C4#1455654811yescharacteristic
375C2×C4C4×C22⋊D7311yescharacteristic
376C2×C4C4×D29211yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8—42no—
381C8—2922no—
382C8—2921no—
383C8—2921no—
384C8#1455650511yescharacteristic
385C8#1455650511yescharacteristic
386C22—21no—
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—2921no—
393C22—2921no—
394C22—2921no—
395C22—5842no—
396C22C4×#1192400511yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—82no—
401C4—2921no—
402C4—2921no—
403C4—2921no—
404C4—5842no—
405C4C2×#1455650511yescharacteristic
406C4#1798856011yescharacteristic
407C2—21no—
408C2—41no—
409C2—41no—
410C2—41no—
411C2—5841no—
412C2C4×#1455650511yescharacteristic
subgroupG/H
centerC4C2×#14556505
commutatorC23×C73C2×C42
FrattiniC2×#41C22×D73
FittingC73×#1757C2
socleC2×C73C4×#99
prime radical#17989094C22
cosocleC2×#41×C73C23
hypercenter#1757D73
hypocenterC73#12624
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
4. #22609731C2semidirect
5. #22608053C2semidirect
6. #22608051C2semidirect
7. C73×#1757C2semidirect
8. C22×#11924011C4semidirect
14. #17988615C4semidirect
18. #17988550C4semidirect
20. #17988542C4semidirect
21. #17988378C4semidirect
22. #17988376C4semidirect
23. #17988375C4semidirect
24. #17988373C4semidirect
211. #1757D73semidirect
214. C73#12624semidirect

Maximal subgroups

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

subgroupindex
#226186322
#226115732
#226115702
#226097312
#226080532
#226080512
C73×#17572
#1262473