Finite Group Databasebeta

← #32981051

Subgroups — #32981051

Order 18688.

534 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 103 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#22618960C211yesmaximal, characteristic
2#22613215C211yesmaximal, characteristic
3#22608379C212yesmaximal, complemented
4#22607825C212yesmaximal, complemented
5C4×#100×C73C211yesmaximal, characteristic
6C2×C4×Dic146C2211yescharacteristic
7#17988659—24no—
8#17988644C2212yes—
9#17988551—21no—
10C2×C22⋊#10596831—21no—
11#17988525—21no—
12#17988512C411yescharacteristic
13#17988512C411yescharacteristic
14#17988501—21no—
15#17988499C411yescharacteristic
16#17988499C411yescharacteristic
17C4×C22⋊Dic73—21no—
18C4×C22⋊Dic73—21no—
19#17988433C2211yescharacteristic
20#17988319—24no—
21C2×C4×D4×C73C2211yescharacteristic
22C2×#100×C73—21no—
23C4×M16×C73C2212yes—
24#343×C73—21no—
25C22×Dic146C2×C411yescharacteristic
26C2×#11924012—22no—
27C22×#10596831—22no—
28C4×Dic146—22no—
29C4×Dic146—22no—
30C2×C4⋊Dic73C2×C411yescharacteristic
31C2×#11924007—21no—
32C2×C22⋊Dic73—21no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73—21no—
38C4⋊#10596831D414yes—
39C22⋊#10596831—22no—
40C22⋊#10596831—22no—
41C22⋊#10596831—22no—
42#14556502—22no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498C2×C411yescharacteristic
49#14556498C2×C411yescharacteristic
50C22×D4×C73D411yescharacteristic
51C23×C4×C73D411yescharacteristic
52C23×C4×C73D411yescharacteristic
53C2×M16×C73—22no—
54C4×D4×C73—22no—
55C4×D4×C73—22no—
56C2×C4⋊C4×C73D411yescharacteristic
57C2×C22⋊C4×C73C2×C411yescharacteristic
58C2×C22⋊C4×C73C2×C411yescharacteristic
59C2×C42×C73C2311yescharacteristic
60#100×C73—24no—
61#97×C73—22no—
62C4×C8×C73—22no—
63C2×Dic146—22no—
64C2×Dic146—42no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69#11924012—82no—
70C2×#10596831—24no—
71C2×#10596831—82no—
72C4⋊Dic73—22no—
73#11924007—42no—
74C22⋊Dic73—42no—
75C22⋊Dic73—42no—
76C22⋊Dic73—42no—
77C22⋊Dic73—42no—
78C4×Dic73—42no—
79C4×Dic73—41no—
80C4×Dic73—41no—
81C24×C73C22⋊C411yescharacteristic
82C24×C73C22⋊C411yescharacteristic
83C2×D4×C73—22no—
84C2×D4×C73—22no—
85C2×D4×C73—41no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—42no—
91C22×C4×C73—42no—
92C22×C4×C73C22⋊C411yescharacteristic
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22×C411yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96C22×C4×C73C2×D411yescharacteristic
97M16×C73—24no—
98M16×C73—42no—
99C2×C8×C73—42no—
100C4⋊C4×C73—22no—
101C22⋊C4×C73—22no—
102C22⋊C4×C73—22no—
103C42×C73C2×D412yes—
104C42×C73#4112yes—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—41no—
111C23×C73—41no—
112C23×C73—41no—
113C23×C73—41no—
114C23×C73#10412yes—
115C23×C73C2×C22⋊C411yescharacteristic
116D4×C73—44no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—22no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—41no—
123C2×C4×C73—42no—
124C2×C4×C73—42no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—81no—
128C2×C4×C73—81no—
129C2×C4×C73C4×D412yes—
130C2×C4×C73#12011yescharacteristic
131C2×C4×C73#12112yes—
132C2×C4×C73#12311yescharacteristic
133C2×Dic73—22no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145Dic146—24no—
146Dic146—42no—
147C8×C73—44no—
148#10596831—44no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—22no—
152C22×C73—42no—
153C22×C73—42no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—81no—
160C22×C73—81no—
161C22×C73#38611yescharacteristic
162C22×C73C2×#10411yescharacteristic
163C22×C73#42111yescharacteristic
164C4×C73—22no—
165C4×C73—21no—
166C4×C73—22no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73#45512yes—
170Dic73—42no—
171Dic73—81no—
172Dic73—81no—
173Dic73—81no—
174#9029—731nomaximal, Sylow
175C2×C73—21no—
176C2×C73—21no—
177C2×C73—42no—
178C2×C73—81no—
179C2×C73#187111yescharacteristic
180C2×C73#188511yescharacteristic
181C2×C73#189111yescharacteristic
182#2973—731no—
183#2398—731no—
184C4×#100D7311yescharacteristic
185#1491—732no—
186#1300—732no—
187C73#902911yescharacteristic, complemented, Sylow
188C2×C4×Q8—731no—
189C2×C4×D4C2×D7311yescharacteristic
190#435—1464no—
191#432—732no—
192C2×#100—21no—
193#407—1461no—
194C2×C22⋊C8—1461no—
195C4×M16C2×D7312yes—
196#400—1461no—
197#397—731no—
198#397—731no—
199#394—1461no—
200#393—731no—
201#393—731no—
202C4×C22⋊C4—1461no—
203C4×C22⋊C4—1461no—
204#376—731no—
205#343—21no—
206Q8⋊C8—1464no—
207C22×Q8—731no—
208C22×D4C22⋊D7311yescharacteristic
209C23×C4D29211yescharacteristic
210C23×C4D29211yescharacteristic
211C2×M16—22no—
212C2×M16—1462no—
213C22×C8—1462no—
214C4×Q8—1462no—
215C4×Q8—1462no—
216C4×D4—22no—
217C4×D4—22no—
218C2×C4⋊C4—731no—
219C2×C4⋊C4—1461no—
220C2×C4⋊C4C22⋊D7311yescharacteristic
221C2×C22⋊C4—1461no—
222C2×C22⋊C4—1461no—
223C2×C22⋊C4—1461no—
224C2×C22⋊C4—1461no—
225C2×C22⋊C4C4×D7311yescharacteristic
226C2×C22⋊C4C4×D7311yescharacteristic
227C2×C42—1461no—
228C2×C42—1461no—
229C2×C42C22×D7311yescharacteristic
230C4⋊C8—734no—
231#100—24no—
232C22⋊C8—1462no—
233C22⋊C8—1462no—
234C22⋊C8—1462no—
235#97—22no—
236#97—1462no—
237C4×C8—22no—
238#95—731no—
239#95—731no—
240#95—1461no—
241#95—1461no—
242#95—1461no—
243#95—1461no—
244#95—1461no—
245C24#1192400511yescharacteristic
246C24#1192400511yescharacteristic
247C2×Q8—2922no—
248C2×Q8—1462no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4#1192400511yescharacteristic
263C22×C4#1192400511yescharacteristic
264C22×C4C2×C4×D7311yescharacteristic
265C22×C4C2×C22⋊D7311yescharacteristic
266C22×C4C2×D29211yescharacteristic
267M16—24no—
268M16—42no—
269M16—5842no—
270C2×C8—42no—
271C2×C8—5842no—
272C2×C8—1464no—
273C4⋊C4—22no—
274C4⋊C4—2922no—
275C4⋊C4—1462no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—2922no—
279C22⋊C4—2922no—
280C22⋊C4—2922no—
281C22⋊C4—2922no—
282C42—2922no—
283C42—2921no—
284C42—2921no—
285C42D4×D7312yes—
286C42#1192402712yes—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#1455651912yes—
297C23C2×#1192400511yescharacteristic
298Q8—2922no—
299Q8—1464no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—2921no—
314C2×C4—2921no—
315C2×C4—2921no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—2921no—
320C2×C4—2921no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—1462no—
325C2×C4#1455655112yes—
326C2×C4#1455656111yescharacteristic
327C2×C4#1455656312yes—
328C2×C4#1455657511yescharacteristic
329C8—44no—
330C8—2924no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22#1798846411yescharacteristic
344C22C2×#1455651911yescharacteristic
345C22#1798860511yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—2922no—
352C4—5841no—
353C4—5841no—
354C4—5841no—
355C4#1798876712yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#2261023111yescharacteristic
361C2#2261031711yescharacteristic
362C2#2261034711yescharacteristic
subgroupG/H
centerC2×C4#14556561
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC4×#100×C73C2
socleC22×C73#386
prime radicalC22×D4×C73D4
cosocleC2×C42×C73C23
hypercenterC4×#100D73
hypocenterC73#9029
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. #22608379C2semidirect
4. #22607825C2semidirect
187. C73#9029semidirect

Maximal subgroups

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

subgroupindex
#226189602
#226132152
#226083792
#226078252
C4×#100×C732
#902973