Finite Group Databasebeta

← #32982039

Subgroups — #32982039

Order 18688.

516 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 105 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#22615746C211yesmaximal, characteristic
2#22612533C211yesmaximal, characteristic
3#22608503C211yesmaximal, characteristic
4C2×#17988312C211yesmaximal, characteristic
5#22607799C211yesmaximal, characteristic
6#22607798C211yesmaximal, characteristic
7C73×#1520C211yesmaximal, characteristic
8C22×#11924007C2211yescharacteristic
9C2×C22⋊#10596831C2211yescharacteristic
10#17988525C412yescomplemented
11#17988520—22no—
12#17988506C412yescomplemented
13#17988474—22no—
14#17988468—22no—
15#17988459—21no—
16#17988448—21no—
17#17988448—21no—
18#17988447C2211yescharacteristic
19#17988447C2211yescharacteristic
20C22⋊C4×Dic73—21no—
21#17988324—22no—
22#17988312—22no—
23C2×C22⋊Q8×C73C2211yescharacteristic
24C2×C22⋊C8×C73C2211yescharacteristic
25#380×C73C2211yescharacteristic
26#328×C73—22no—
27C23×Dic73D411yescharacteristic
28C23×Dic73D411yescharacteristic
29C22×#10596831—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×#11924007—22no—
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×#11924007C2×C412yes—
38C2×#11924007D412yes—
39C2×C22⋊Dic73—21no—
40C2×C22⋊Dic73—21no—
41C2×C4×Dic73—22no—
42C22⋊#10596831—21no—
43C22⋊#10596831—21no—
44#14556498—22no—
45#14556498—24no—
46#14556498—22no—
47#14556498—22no—
48#14556498—22no—
49#14556498C2×C412yes—
50#14556498D412yes—
51C22×Q8×C73C2×C411yescharacteristic
52C23×C4×C73C2311yescharacteristic
53C22×C8×C73—21no—
54C22⋊Q8×C73—21no—
55C22⋊Q8×C73—21no—
56C22⋊Q8×C73—21no—
57C22⋊Q8×C73—21no—
58C2×C4⋊C4×C73—21no—
59C2×C4⋊C4×C73—21no—
60C2×C4⋊C4×C73C2×C411yescharacteristic
61C2×C22⋊C4×C73—21no—
62C2×C22⋊C4×C73—21no—
63C22⋊C8×C73—21no—
64C22⋊C8×C73—21no—
65#95×C73D412yes—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C22×Dic73—21no—
73C22×Dic73—21no—
74C22×Dic73—22no—
75C22×Dic73—22no—
76C22×Dic73—81no—
77C22×Dic73C22⋊C412yes—
78C22×Dic73C22⋊C412yes—
79C2×#10596831—41no—
80C2×#10596831—81no—
81C4⋊Dic73—81no—
82C4⋊Dic73—81no—
83#11924007—22no—
84#11924007—22no—
85#11924007—22no—
86#11924007—22no—
87#11924007—82no—
88C22⋊Dic73—41no—
89C22⋊Dic73—41no—
90C22⋊Dic73—41no—
91C22⋊Dic73—41no—
92C4×Dic73—82no—
93C24×C73C2×D411yescharacteristic
94C2×Q8×C73—21no—
95C2×Q8×C73—21no—
96C2×Q8×C73—81no—
97C22×C4×C73—21no—
98C22×C4×C73—21no—
99C22×C4×C73—22no—
100C22×C4×C73—81no—
101C22×C4×C73C22×C411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73C2×D411yescharacteristic
105C22×C4×C73#4111yescharacteristic
106C22×C4×C73#4111yescharacteristic
107C2×C8×C73—41no—
108C2×C8×C73—81no—
109C4⋊C4×C73—21no—
110C4⋊C4×C73—21no—
111C4⋊C4×C73—41no—
112C4⋊C4×C73—41no—
113C4⋊C4×C73—81no—
114C22⋊C4×C73—41no—
115C22⋊C4×C73—41no—
116C22⋊C4×C73—41no—
117C22⋊C4×C73—41no—
118C23×C73—41no—
119C23×C73—41no—
120C23×C73C2×C22⋊C411yescharacteristic
121C23×C73#12011yescharacteristic
122C23×C73#12311yescharacteristic
123C23×C73#13511yescharacteristic
124C23×C73#13511yescharacteristic
125C23×C73#13711yescharacteristic
126C23×C73#13711yescharacteristic
127Q8×C73—81no—
128Q8×C73—81no—
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—42no—
136C2×C4×C73—42no—
137C2×C4×C73—42no—
138C2×C4×C73—42no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73—42no—
142C2×C4×C73C4×D411yescharacteristic
143C2×C4×C73C4×D411yescharacteristic
144C2×C4×C73#12111yescharacteristic
145C2×C4×C73#12111yescharacteristic
146C2×Dic73—22no—
147C2×Dic73—22no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73—42no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73—42no—
156C2×Dic73—42no—
157C2×Dic73—42no—
158C2×Dic73—42no—
159C2×Dic73—42no—
160C2×Dic73—42no—
161C2×Dic73—42no—
162C2×Dic73—81no—
163C8×C73—81no—
164#10596831—81no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73#38611yescharacteristic
176C22×C73#41611yescharacteristic
177C22×C73#41911yescharacteristic
178C22×C73#45211yescharacteristic
179C22×C73#45211yescharacteristic
180C22×C73#48511yescharacteristic
181C22×C73#48511yescharacteristic
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—82no—
187C4×C73—81no—
188C4×C73—81no—
189Dic73—42no—
190Dic73—42no—
191Dic73—82no—
192Dic73—82no—
193#9202—731nomaximal, Sylow
194C2×C73—21no—
195C2×C73—21no—
196C2×C73—21no—
197C2×C73—21no—
198C2×C73—21no—
199C2×C73—21no—
200C2×C73#187311yescharacteristic
201C2×C73#191211yescharacteristic
202C2×C73#191311yescharacteristic
203#2627—731no—
204#2313—731no—
205#1520—731no—
206#1520D7311yescharacteristic
207C2×#324—731no—
208#1289—731no—
209#1289—731no—
210C73#920211yescharacteristic, complemented, Sylow
211C2×C22⋊Q8C2×D7311yescharacteristic
212C22×C4⋊C4—731no—
213C2×C22⋊C8—731no—
214C2×C22⋊C8C2×D7311yescharacteristic
215#400—732no—
216#398—1462no—
217#395—732no—
218#387—1462no—
219#387—1462no—
220#385—1461no—
221#381—1461no—
222#381—1461no—
223#380—731no—
224#380—731no—
225#380C2×D7311yescharacteristic
226C4×C22⋊C4—1461no—
227#328—22no—
228#328—1462no—
229#324—1462no—
230C22×Q8C4×D7311yescharacteristic
231C23×C4—731no—
232C23×C4—731no—
233C23×C4C22×D7311yescharacteristic
234C22×C8—21no—
235C22×C8—1461no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—732no—
243C2×C4⋊C4—732no—
244C2×C4⋊C4—1462no—
245C2×C4⋊C4—1461no—
246C2×C4⋊C4—1461no—
247C2×C4⋊C4—1461no—
248C2×C4⋊C4—1461no—
249C2×C4⋊C4—1461no—
250C2×C4⋊C4—1461no—
251C2×C4⋊C4C4×D7311yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—1461no—
255C2×C22⋊C4—1461no—
256C2×C42—1462no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—1461no—
260C22⋊C8—1461no—
261#95—732no—
262#95—732no—
263#95—1462no—
264#95—1462no—
265#95—1462no—
266#95—1462no—
267#95—1464no—
268#95C22⋊D7312yes—
269C24D4×D7311yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—81no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—81no—
277C22×C4—5841no—
278C22×C4—732no—
279C22×C4—732no—
280C22×C4—1462no—
281C22×C4—1462no—
282C22×C4—1461no—
283C22×C4—1461no—
284C22×C4—1461no—
285C22×C4—1461no—
286C22×C4—1461no—
287C22×C4—1461no—
288C22×C4—1461no—
289C22×C4—1461no—
290C22×C4C2×C4×D7311yescharacteristic
291C22×C4D4×D7311yescharacteristic
292C22×C4D4×D7311yescharacteristic
293C22×C4C2×C22⋊D7311yescharacteristic
294C22×C4#1192402711yescharacteristic
295C22×C4#1192402811yescharacteristic
296C2×C8—41no—
297C2×C8—81no—
298C2×C8—2921no—
299C2×C8—5841no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—81no—
305C4⋊C4—5842no—
306C4⋊C4—5841no—
307C4⋊C4—5841no—
308C4⋊C4—1462no—
309C4⋊C4—1462no—
310C4⋊C4—1462no—
311C4⋊C4—1462no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—2921no—
317C22⋊C4—2921no—
318C22⋊C4—2921no—
319C22⋊C4—2921no—
320C42—5842no—
321C23—41no—
322C23—41no—
323C23C22⋊C4×D7311yescharacteristic
324C23#1455655911yescharacteristic
325C23#1455657311yescharacteristic
326C23#1455661211yescharacteristic
327C23#1455661411yescharacteristic
328C23#1455662011yescharacteristic
329C23#1455662311yescharacteristic
330Q8—81no—
331Q8—81no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—2922no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2921no—
349C2×C4—2921no—
350C2×C4—2922no—
351C2×C4—2922no—
352C2×C4—2922no—
353C2×C4—2922no—
354C2×C4—2922no—
355C2×C4—2922no—
356C2×C4—2922no—
357C2×C4—5841no—
358C2×C4—1462no—
359C2×C4—1462no—
360C2×C4—1462no—
361C2×C4—1462no—
362C2×C4#1455655111yescharacteristic
363C2×C4C4×C22⋊D7311yescharacteristic
364C2×C4#1455656211yescharacteristic
365C2×C4#1455656411yescharacteristic
366C8—81no—
367C8—5841no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1798846311yescharacteristic
379C22#1798858211yescharacteristic
380C22#1798859411yescharacteristic
381C22#1798874611yescharacteristic
382C22#1798874811yescharacteristic
383C22#1798892611yescharacteristic
384C22#1798892711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—81no—
391C4—81no—
392C4—2922no—
393C4—2922no—
394C4—5842no—
395C4—5842no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#2261024011yescharacteristic
403C2#2261046511yescharacteristic
404C2#2261047011yescharacteristic
subgroupG/H
centerC22#17988463
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1520C2
socleC22×C73#386
prime radicalC24×C73C2×D4
cosocleC23×C4×C73C23
hypercenter#1520D73
hypocenterC73#9202
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
10. #17988525C4semidirect
12. #17988506C4semidirect
210. C73#9202semidirect

Maximal subgroups

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

subgroupindex
#226157462
#226125332
#226085032
C2×#179883122
#226077992
#226077982
C73×#15202
#920273