Finite Group Databasebeta

← #32974412

Subgroups — #32974412

Order 18688.

488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618272C211yesmaximal, characteristic
2#22609692C211yesmaximal, characteristic
3#22609688C211yesmaximal, characteristic
4#22607757C211yesmaximal, characteristic, complemented
5#22607755C211yesmaximal, characteristic, complemented
6#22607753C211yesmaximal, characteristic, complemented
7C73×#1272C211yesmaximal, characteristic, complemented
8C2×#14556567C411yescharacteristic
9C2×C42×D73C2211yescharacteristic
10C2×#14556503—21no—
11C2×#14556503—21no—
12C2×#14556501—21no—
13C2×C8×Dic73—21no—
14#17988494C411yescharacteristic
15#17988486C411yescharacteristic
16#17988485C2211yescharacteristic
17#17988470—21no—
18#17988469—21no—
19#17988461—21no—
20#17988449—21no—
21#17988444C411yescharacteristic
22#17988342C2211yescharacteristic
23#17988342C2211yescharacteristic
24#391×C73C2211yescharacteristic
25#336×C73C2211yescharacteristic
26#336×C73C2211yescharacteristic
27C22×C4×D73C2×C411yescharacteristic
28C22×C4×D73D411yescharacteristic
29C22×C4×D73D411yescharacteristic
30C22×#10596831—21no—
31C22×#10596831—21no—
32#14556567—42no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924007—21no—
37C2×#11924007—21no—
38C2×#11924005—21no—
39C2×#11924005—21no—
40C2×C4×Dic73C2×C411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42C2×C4×Dic73D411yescharacteristic
43C42×D73—42no—
44#14556503—24no—
45#14556503—24no—
46#14556501—42no—
47C8×Dic73—42no—
48#14556498—21no—
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53C22×Q8×C73C2×C411yescharacteristic
54C22×C8×C73—21no—
55C22×C8×C73—21no—
56C2×C4⋊C4×C73C2×C411yescharacteristic
57C2×C42×C73C2311yescharacteristic
58#95×C73—21no—
59#95×C73—21no—
60C23×D73C22⋊C411yescharacteristic
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73C22⋊C411yescharacteristic
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C22⋊C411yescharacteristic
66C2×C4×D73—22no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—22no—
74C2×C4×D73—22no—
75C2×C4×D73—41no—
76C2×C4×D73—41no—
77C2×C4×D73—41no—
78C2×#10596831—22no—
79C2×#10596831—22no—
80C2×#10596831—41no—
81C2×#10596831—41no—
82C2×#10596831—41no—
83C2×#10596831—41no—
84C4⋊Dic73—21no—
85C4⋊Dic73—21no—
86C4⋊Dic73—42no—
87C4⋊Dic73—41no—
88#11924007—41no—
89#11924007—41no—
90#11924007—42no—
91#11924005—42no—
92#11924005—42no—
93C4×Dic73—22no—
94C4×Dic73—22no—
95C4×Dic73—41no—
96C2×Q8×C73—21no—
97C2×Q8×C73—21no—
98C2×Q8×C73—41no—
99C2×Q8×C73—41no—
100C22×C4×C73—21no—
101C22×C4×C73—21no—
102C22×C4×C73C22×C411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73C2×D411yescharacteristic
105C2×C8×C73—22no—
106C2×C8×C73—22no—
107C2×C8×C73—41no—
108C2×C8×C73—41no—
109C2×C8×C73—41no—
110C2×C8×C73—41no—
111C4⋊C4×C73—41no—
112C42×C73—41no—
113C23×C73C2×C22⋊C411yescharacteristic
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73#10412yes—
121Q8×C73—81no—
122Q8×C73—81no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73#13111yescharacteristic
136C2×C4×C73#13111yescharacteristic
137C2×C4×C73#13511yescharacteristic
138C2×C4×C73#13511yescharacteristic
139C2×C4×C73#13711yescharacteristic
140C2×C4×C73#13711yescharacteristic
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73#9912yes—
155C2×Dic73#10412yes—
156C4×D73—42no—
157C4×D73—42no—
158C4×D73—42no—
159C4×D73—42no—
160C4×D73—42no—
161C4×D73—42no—
162C8×C73—42no—
163C8×C73—42no—
164#10596831—42no—
165#10596831—42no—
166C22×C73#40811yescharacteristic
167C22×C73C2×#9911yescharacteristic
168C22×C73#41311yescharacteristic
169C22×C73#41611yescharacteristic
170C22×C73#41911yescharacteristic
171C22×C73C2×#10411yescharacteristic
172C22×C73C2×#10411yescharacteristic
173C2×D73—22no—
174C2×D73—22no—
175C2×D73—22no—
176C2×D73—41no—
177C2×D73—41no—
178C2×D73—41no—
179C2×D73—41no—
180C4×C73—21no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—81no—
187C4×C73—81no—
188Dic73—22no—
189Dic73—22no—
190Dic73—41no—
191Dic73—81no—
192Dic73—81no—
193#7675—731nomaximal, Sylow
194C2×C73#146811yescharacteristic
195C2×C73#148511yescharacteristic
196C2×C73#149411yescharacteristic
197C2×C73#150111yescharacteristic
198C2×C73#150811yescharacteristic
199C2×C73#152411yescharacteristic
200C2×C73#155411yescharacteristic
201D73—42no—
202#2855—731no—
203#1749—731no—
204C4×C22⋊C8—731no—
205#1272—731no—
206#1272D7311yescharacteristic, complemented
207#1271—731no—
208#1271—731no—
209C73#767511yescharacteristic, complemented, Sylow
210C2×C22⋊Q8—731no—
211C22×C42—731no—
212C2×C22⋊C8—1461no—
213C2×C22⋊C8—1461no—
214C2×#97—1461no—
215C2×C4×C8—1461no—
216#391—731no—
217#391C2×D7311yescharacteristic
218#389—731no—
219#389—731no—
220#387—1461no—
221#387—1461no—
222#385—1461no—
223#381—1461no—
224#380—731no—
225#336—731no—
226#336—731no—
227#336C2×D7311yescharacteristic
228#336C2×D7311yescharacteristic
229C22×Q8C4×D7311yescharacteristic
230C23×C4—731no—
231C23×C4—731no—
232C23×C4—731no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—1461no—
236C22×C8—1461no—
237C22⋊Q8—2922no—
238C2×C4⋊C4—731no—
239C2×C4⋊C4—731no—
240C2×C4⋊C4—1461no—
241C2×C4⋊C4—1461no—
242C2×C4⋊C4—1461no—
243C2×C4⋊C4C4×D7311yescharacteristic
244C2×C22⋊C4—1461no—
245C2×C22⋊C4—1461no—
246C2×C42—2922no—
247C2×C42—731no—
248C2×C42—731no—
249C2×C42—731no—
250C2×C42C22×D7311yescharacteristic
251C22⋊C8—1464no—
252C22⋊C8—1464no—
253#97—2922no—
254C4×C8—2922no—
255#95—21no—
256#95—21no—
257#95—1461no—
258#95—1461no—
259#95—1461no—
260#95—1461no—
261#95—1461no—
262C24—731no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—41no—
266C2×Q8—41no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—2921no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—1462no—
276C22×C4—1462no—
277C22×C4—1462no—
278C22×C4—1461no—
279C22×C4—1461no—
280C22×C4—1461no—
281C22×C4—1461no—
282C22×C4—1461no—
283C22×C4—1461no—
284C22×C4—1461no—
285C22×C4—1461no—
286C22×C4C2×C4×D7311yescharacteristic
287C22×C4D4×D7311yescharacteristic
288C22×C4D4×D7311yescharacteristic
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—2921no—
296C2×C8—2921no—
297C2×C8—2921no—
298C2×C8—2921no—
299C2×C8—1462no—
300C2×C8—1462no—
301C4⋊C4—41no—
302C4⋊C4—2921no—
303C4⋊C4—2922no—
304C4⋊C4—2922no—
305C4⋊C4—2921no—
306C4⋊C4—2921no—
307C4⋊C4—1461no—
308C4⋊C4—1461no—
309C22⋊C4—2922no—
310C22⋊C4—2922no—
311C42—41no—
312C42—2921no—
313C42—1462no—
314C42—1462no—
315C23—732no—
316C23—1461no—
317C23—1461no—
318C23—1461no—
319C23—1461no—
320C23—1461no—
321C23—1461no—
322C23C22⋊C4×D7311yescharacteristic
323Q8—81no—
324Q8—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—2922no—
338C2×C4—2922no—
339C2×C4—2922no—
340C2×C4—2922no—
341C2×C4—2922no—
342C2×C4—2922no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—2921no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2921no—
349C2×C4—732no—
350C2×C4—732no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4#1455659711yescharacteristic
359C2×C4#1455659911yescharacteristic
360C2×C4#1455661211yescharacteristic
361C2×C4#1455661411yescharacteristic
362C2×C4#1455662011yescharacteristic
363C2×C4#1455662311yescharacteristic
364C8—42no—
365C8—42no—
366C8—2922no—
367C8—2922no—
368C22—2921no—
369C22—2921no—
370C22—2921no—
371C22—2921no—
372C22—1462no—
373C22—1462no—
374C22—1462no—
375C22#1798855211yescharacteristic
376C22#99×D7311yescharacteristic
377C22#1798856811yescharacteristic
378C22#1798858211yescharacteristic
379C22#1798859411yescharacteristic
380C22#104×D7311yescharacteristic
381C22#104×D7311yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—81no—
390C4—2921no—
391C4—5841no—
392C4—5841no—
393C4—1462no—
394C4—1462no—
395C2—2922no—
396C2#2260827611yescharacteristic
397C2#2260835011yescharacteristic
398C2#2260839011yescharacteristic
399C2#2260842111yescharacteristic
400C2#2260844911yescharacteristic
401C2#2260851611yescharacteristic
402C2#2260864011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1272C2
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1272D73
hypocenterC73#7675
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #22607757C2semidirect
5. #22607755C2semidirect
6. #22607753C2semidirect
7. C73×#1272C2semidirect
206. #1272D73semidirect
209. C73#7675semidirect

Maximal subgroups

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

subgroupindex
#226182722
#226096922
#226096882
#226077572
#226077552
#226077532
C73×#12722
#767573