Finite Group Databasebeta

← #32982041

Subgroups — #32982041

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#22615747C211yesmaximal, characteristic
2#22612533C211yesmaximal, characteristic
3#22608504C211yesmaximal, characteristic
4#22608502C211yesmaximal, characteristic
5C2×#17988312C211yesmaximal, characteristic
6#22607798C211yesmaximal, characteristic
7C73×#1289C211yesmaximal, characteristic
8C2×#14556570C2211yescharacteristic
9C22×#11924007C2211yescharacteristic
10C2×C22⋊#10596831C2211yescharacteristic
11#17988527C412yescomplemented
12#17988517—22no—
13#17988508C412yescomplemented
14#17988474—22no—
15#17988468—22no—
16#17988462—21no—
17#17988448—21no—
18#17988448—21no—
19#17988447C2211yescharacteristic
20C22⋊C4×Dic73—21no—
21#17988325—22no—
22#17988323—22no—
23#17988312—22no—
24C2×C22⋊C8×C73C2211yescharacteristic
25#380×C73C2211yescharacteristic
26#380×C73C2211yescharacteristic
27C22×Dic146C2×C411yescharacteristic
28C23×Dic73D411yescharacteristic
29C23×Dic73D411yescharacteristic
30C22×#10596831—21no—
31#14556570—21no—
32#14556570—21no—
33#14556570—21no—
34#14556570—21no—
35C2×C4⋊Dic73—22no—
36C2×C4⋊Dic73—21no—
37C2×C4⋊Dic73C2×C411yescharacteristic
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×#11924007—21no—
41C2×#11924007—21no—
42C2×#11924007—21no—
43C2×#11924007C2×C412yes—
44C2×#11924007D412yes—
45C2×C22⋊Dic73—21no—
46C2×C22⋊Dic73—21no—
47C2×C4×Dic73—22no—
48C22⋊#10596831—21no—
49C22⋊#10596831—21no—
50#14556498—22no—
51#14556498—24no—
52#14556498—22no—
53#14556498—22no—
54#14556498—22no—
55#14556498D412yes—
56C23×C4×C73C2311yescharacteristic
57C22×C8×C73—21no—
58C2×C4⋊C4×C73—21no—
59C2×C4⋊C4×C73—21no—
60C2×C22⋊C4×C73—21no—
61C2×C22⋊C4×C73—21no—
62C22⋊C8×C73—21no—
63C22⋊C8×C73—21no—
64#95×C73C2×C412yes—
65#95×C73D412yes—
66C2×Dic146—21no—
67C2×Dic146—21no—
68C2×Dic146—81no—
69C22×Dic73—21no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C22×Dic73—21no—
73C22×Dic73—21no—
74C22×Dic73—21no—
75C22×Dic73—21no—
76C22×Dic73—21no—
77C22×Dic73—21no—
78C22×Dic73—21no—
79C22×Dic73—22no—
80C22×Dic73—81no—
81C22×Dic73C22⋊C412yes—
82C22×Dic73C22⋊C412yes—
83C2×#10596831—41no—
84C2×#10596831—81no—
85C4⋊Dic73—21no—
86C4⋊Dic73—21no—
87C4⋊Dic73—82no—
88C4⋊Dic73—81no—
89#11924007—22no—
90#11924007—22no—
91#11924007—22no—
92#11924007—22no—
93#11924007—41no—
94#11924007—41no—
95C22⋊Dic73—41no—
96C22⋊Dic73—41no—
97C22⋊Dic73—41no—
98C22⋊Dic73—41no—
99C4×Dic73—82no—
100C24×C73C2×D411yescharacteristic
101C22×C4×C73—22no—
102C22×C4×C73—22no—
103C22×C4×C73—81no—
104C22×C4×C73C22×C411yescharacteristic
105C22×C4×C73C2×D411yescharacteristic
106C22×C4×C73C2×D411yescharacteristic
107C22×C4×C73C2×D411yescharacteristic
108C22×C4×C73#4111yescharacteristic
109C22×C4×C73#4111yescharacteristic
110C2×C8×C73—41no—
111C2×C8×C73—81no—
112C4⋊C4×C73—81no—
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
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73—42no—
136C2×C4×C73—42no—
137C2×C4×C73—42no—
138C2×C4×C73—42no—
139C2×C4×C73C4×D411yescharacteristic
140C2×C4×C73C4×D411yescharacteristic
141C2×C4×C73#12111yescharacteristic
142C2×C4×C73#12111yescharacteristic
143C2×Dic73—22no—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—22no—
147C2×Dic73—42no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—42no—
153C2×Dic73—42no—
154C2×Dic73—42no—
155C2×Dic73—42no—
156C2×Dic73—42no—
157C2×Dic73—41no—
158C2×Dic73—41no—
159C2×Dic73—42no—
160C2×Dic73—81no—
161Dic146—81no—
162Dic146—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—82no—
188Dic73—42no—
189Dic73—42no—
190Dic73—82no—
191Dic73—81no—
192Dic73—81no—
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#1520—731no—
207C2×#324—731no—
208#1289—731no—
209#1289D7311yescharacteristic
210C73#920211yescharacteristic, complemented, Sylow
211C2×C22⋊Q8—731no—
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#380C2×D7311yescharacteristic
225#380C2×D7311yescharacteristic
226C4×C22⋊C4—1461no—
227#328—1462no—
228#328—1462no—
229#324—1462no—
230C22×Q8—731no—
231C23×C4—731no—
232C23×C4—731no—
233C23×C4C22×D7311yescharacteristic
234C22×C8—21no—
235C22×C8—1461no—
236C22⋊Q8—1461no—
237C22⋊Q8—1461no—
238C22⋊Q8—1461no—
239C22⋊Q8—1461no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—732no—
243C2×C4⋊C4—732no—
244C2×C4⋊C4—731no—
245C2×C4⋊C4—1461no—
246C2×C4⋊C4—1462no—
247C2×C4⋊C4—1461no—
248C2×C4⋊C4—1461no—
249C2×C4⋊C4—1461no—
250C2×C4⋊C4—1461no—
251C2×C4⋊C4—1461no—
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—1462no—
263#95—1462no—
264#95—1462no—
265#95—1462no—
266#95—1464no—
267#95C4×D7312yes—
268#95D29212yes—
269C24D4×D7311yescharacteristic
270C2×Q8—5841no—
271C2×Q8—1461no—
272C2×Q8—1461no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—81no—
276C22×C4—5841no—
277C22×C4—732no—
278C22×C4—732no—
279C22×C4—1461no—
280C22×C4—1461no—
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×D29211yescharacteristic
294C22×C4#1192402811yescharacteristic
295C22×C4#1192402911yescharacteristic
296C2×C8—41no—
297C2×C8—81no—
298C2×C8—2921no—
299C2×C8—5841no—
300C4⋊C4—81no—
301C4⋊C4—81no—
302C4⋊C4—2921no—
303C4⋊C4—2921no—
304C4⋊C4—5841no—
305C4⋊C4—5842no—
306C4⋊C4—1461no—
307C4⋊C4—1461no—
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#1455656111yescharacteristic
325C23#1455657611yescharacteristic
326C23#1455661011yescharacteristic
327C23#1455661211yescharacteristic
328C23#1455662011yescharacteristic
329C23#1455662311yescharacteristic
330Q8—5841no—
331Q8—5841no—
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—42no—
343C2×C4—42no—
344C2×C4—2922no—
345C2×C4—2921no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2921no—
349C2×C4—2922no—
350C2×C4—2922no—
351C2×C4—2922no—
352C2×C4—2922no—
353C2×C4—2922no—
354C2×C4—2921no—
355C2×C4—2921no—
356C2×C4—2922no—
357C2×C4—5841no—
358C2×C4—1462no—
359C2×C4—1462no—
360C2×C4—1462no—
361C2×C4—1462no—
362C2×C4#1455655311yescharacteristic
363C2×C4C4×D29211yescharacteristic
364C2×C4#1455656411yescharacteristic
365C2×C4#1455656611yescharacteristic
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#1798846511yescharacteristic
379C22#1798858011yescharacteristic
380C22#1798859411yescharacteristic
381C22#1798875011yescharacteristic
382C22#1798875211yescharacteristic
383C22#1798893011yescharacteristic
384C22#1798893111yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—82no—
391C4—2922no—
392C4—2922no—
393C4—5842no—
394C4—5841no—
395C4—5841no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#2261024211yescharacteristic
403C2#2261046711yescharacteristic
404C2#2261047211yescharacteristic
subgroupG/H
centerC22#17988465
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1289C2
socleC22×C73#386
prime radicalC24×C73C2×D4
cosocleC23×C4×C73C23
hypercenter#1289D73
hypocenterC73#9202
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
11. #17988527C4semidirect
13. #17988508C4semidirect
210. C73#9202semidirect

Maximal subgroups

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

subgroupindex
#226157472
#226125332
#226085042
#226085022
C2×#179883122
#226077982
C73×#12892
#920273