Finite Group Databasebeta

← #34033316

Subgroups — #34033316

Order 18688.

682 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 123 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#22627071C212yesmaximal
2C2×#17989673C212yesmaximal
3#22626940C212yesmaximal
4C2×C4⋊C4×#64408C211yesmaximal, characteristic
5C2×C4⋊#10596842—22no—
6C2×C22⋊#10596842C2214yes—
7(C2×#10596842)⋊C4—22no—
8#17989673—24no—
9C22×C4⋊#64408C2211yescharacteristic
10C22×C4×#64408C411yescharacteristic
11C22×C4×#64408C411yescharacteristic
12C22×C4×#64408C2211yescharacteristic
13C4⋊C4×#64408—22no—
14C4⋊C4×#64408—22no—
15C2×(C2×#64408)⋊C4C411yescharacteristic
16C2×(C2×#64408)⋊C4C2211yescharacteristic
17C2×C4⋊C4×D73C411yescharacteristic
18C22×#10596842—24no—
19C4⋊#10596842—44no—
20C22⋊#10596842—24no—
21C22⋊#10596842—24no—
22C23×#64408C2×C411yescharacteristic
23C23×#64408C2×C411yescharacteristic
24C23×#64408C2×C411yescharacteristic
25C23×#64408C2311yescharacteristic
26C2×C4⋊#64408—22no—
27C2×C4⋊#64408—22no—
28C2×C4⋊#64408D412yes—
29C2×C4⋊#64408Q812yes—
30C2×C4×#64408—21no—
31C2×C4×#64408—21no—
32C2×C4×#64408—22no—
33C2×C4×#64408—21no—
34C2×C4×#64408—21no—
35C2×C4×#64408—22no—
36C2×C4×#64408—42no—
37C2×C4×#64408—42no—
38C2×C4×#64408D412yes—
39C2×C4×#64408D412yes—
40(C2×#64408)⋊C4—22no—
41(C2×#64408)⋊C4—22no—
42C22×C4×D73C2×C411yescharacteristic
43C22×C4×D73C2×C411yescharacteristic
44C22×C4×D73C2×C411yescharacteristic
45C2×C4⋊Dic73C811yescharacteristic, complemented
46C2×#11924007C811yescharacteristic, complemented
47C2×#11924007C811yescharacteristic, complemented
48C4⋊C4×D73—22no—
49C4⋊C4×D73—22no—
50C2×C4⋊C4×C73C811yescharacteristic, complemented
51C2×#10596842—44no—
52C2×#10596842—44no—
53C2×#10596842—44no—
54C22×#64408—21no—
55C22×#64408—21no—
56C22×#64408—22no—
57C22×#64408—22no—
58C22×#64408—21no—
59C22×#64408—21no—
60C22×#64408—21no—
61C22×#64408—21no—
62C22×#64408—41no—
63C22×#64408—41no—
64C22×#64408—41no—
65C22×#64408—41no—
66C22×#64408—41no—
67C22×#64408—41no—
68C22×#64408C22⋊C411yescharacteristic
69C22×#64408C22⋊C411yescharacteristic
70C22×#64408C4⋊C412yes—
71C22×#64408M1612yes—
72C22×#64408C2×D412yes—
73C22×#64408C2×D411yescharacteristic
74C22×#64408C2×Q811yescharacteristic
75C22×#64408#4112yes—
76C4⋊#64408—24no—
77C4⋊#64408—24no—
78C4×#64408—24no—
79C4×#64408—24no—
80C4×#64408—24no—
81C4×#64408—42no—
82C4×#64408—42no—
83C4×#64408—42no—
84C23×D73C22×C411yescharacteristic
85C22×Dic73C2×C811yescharacteristic
86C22×Dic73C2×C811yescharacteristic
87C22×Dic73C2×C811yescharacteristic
88C2×C4×D73—21no—
89C2×C4×D73—21no—
90C2×C4×D73—21no—
91C2×C4×D73—21no—
92C2×C4×D73—21no—
93C2×C4×D73—21no—
94C2×C4×D73—41no—
95C2×C4×D73—41no—
96C2×C4×D73—41no—
97C2×C4×D73—41no—
98C2×C4×D73C22⋊C412yes—
99C2×C4×D73C4⋊C412yes—
100C2×C4×D73M1612yes—
101C2×C4×D73M1612yes—
102C4⋊Dic73—22no—
103#11924007—22no—
104#11924007—22no—
105C22×C4×C73C2×C811yescharacteristic
106C22×C4×C73C2×C811yescharacteristic
107C22×C4×C73C2×C811yescharacteristic
108C4⋊C4×C73—22no—
109C23×C73C22×C811yescharacteristic
110C22×D73—21no—
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114C22×D73C2×C22⋊C411yescharacteristic
115C22×D73C2×C4⋊C411yescharacteristic
116C22×D73#11711yescharacteristic
117C22×D73C2×M1611yescharacteristic
118C22×D73C2×M1611yescharacteristic
119C22×D73C2×M1611yescharacteristic
120C2×#64408—24no—
121C2×#64408—24no—
122C2×#64408—21no—
123C2×#64408—21no—
124C2×#64408—22no—
125C2×#64408—21no—
126C2×#64408—22no—
127C2×#64408—21no—
128C2×#64408—22no—
129C2×#64408—22no—
130C2×#64408—41no—
131C2×#64408—41no—
132C2×#64408—42no—
133C2×#64408—42no—
134C2×#64408—42no—
135C2×#64408—41no—
136C2×#64408—41no—
137C2×#64408—41no—
138C2×#64408—41no—
139C2×#64408—42no—
140C2×#64408—42no—
141C2×#64408#9912yes—
142C2×#64408#10112yes—
143C2×#64408#12112yes—
144C2×#64408C22⋊Q812yes—
145#10596842—84no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—41no—
150C2×C4×C73—41no—
151C2×C4×C73C22⋊C812yes—
152C2×C4×C73C4⋊C812yescomplemented
153C2×Dic73—21no—
154C2×Dic73—21no—
155C2×Dic73—21no—
156C2×Dic73—41no—
157C2×Dic73—41no—
158C2×Dic73C22⋊C812yes—
159C2×Dic73C4⋊C812yescomplemented
160C4×D73—22no—
161C4×D73—22no—
162C4×D73—22no—
163C4×D73—22no—
164C4×D73—22no—
165C4×D73—22no—
166C4×D73—42no—
167C4×D73—42no—
168C4×D73—41no—
169C4×D73—41no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73C2×C22⋊C811yescharacteristic
173C22×C73C2×C4⋊C811yescharacteristic
174C22×C73#43111yescharacteristic
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—21no—
182C2×D73—21no—
183C2×D73—21no—
184C2×D73—21no—
185C2×D73#38011yescharacteristic
186C2×D73#40711yescharacteristic
187C2×D73C2×#9911yescharacteristic
188C2×D73#41011yescharacteristic
189C2×D73C2×#10111yescharacteristic
190C2×D73#41311yescharacteristic
191C2×D73#42311yescharacteristic
192C2×D73#43211yescharacteristic
193#64408—22no—
194#64408—22no—
195#64408—22no—
196#64408—22no—
197#64408—42no—
198#64408—42no—
199C4×C73—22no—
200C4×C73—22no—
201C4×C73—41no—
202Dic73—22no—
203Dic73—22no—
204Dic73—41no—
205#8560—731nomaximal, Sylow
206C2×C73—21no—
207C2×C73—21no—
208C2×C73#145911yescharacteristic
209C2×C73#146111yescharacteristic
210C2×C73#179711yescharacteristic
211D73—21no—
212D73—21no—
213D73#146311yescharacteristic
214D73#146411yescharacteristic
215D73#179911yescharacteristic
216D73#180111yescharacteristic
217C2×C4×C4⋊C4—731no—
218#1797—732no—
219C2×#324—732no—
220#1280—732no—
221C73#856011yescharacteristic, complemented, Sylow
222C22×C4⋊C4—731no—
223C22×C4⋊C4—731no—
224C22×C42—731no—
225C22×C42—731no—
226C22×C42—731no—
227C2×C4⋊C8—1462no—
228C2×C22⋊C8—734no—
229C4×C4⋊C4—1462no—
230C4×C4⋊C4—1462no—
231C2×#95—731no—
232C2×#95—731no—
233#336—1462no—
234#324—1464no—
235C23×C4—731no—
236C23×C4—731no—
237C23×C4—731no—
238C23×C4—731no—
239C23×C4—731no—
240C23×C4—731no—
241C23×C4—731no—
242C22×C8—1464no—
243C2×C4⋊C4—732no—
244C2×C4⋊C4—732no—
245C2×C4⋊C4—731no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—731no—
248C2×C4⋊C4—1462no—
249C2×C4⋊C4—1462no—
250C2×C4⋊C4—1462no—
251C2×C4⋊C4—1462no—
252C2×C4⋊C4#1059684211yescharacteristic, complemented
253C2×C42—2922no—
254C2×C42—2922no—
255C2×C42—732no—
256C2×C42—732no—
257C2×C42—1461no—
258C2×C42—1461no—
259C2×C42—1461no—
260C2×C42—1461no—
261C2×C42—1462no—
262C2×C42—1462no—
263C4⋊C8—2924no—
264C22⋊C8—1464no—
265C22⋊C8—1464no—
266#95—1462no—
267#95—1462no—
268C24—731no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—2921no—
272C22×C4—2921no—
273C22×C4—2921no—
274C22×C4—2921no—
275C22×C4—2921no—
276C22×C4—2921no—
277C22×C4—2921no—
278C22×C4—2921no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—732no—
282C22×C4—731no—
283C22×C4—732no—
284C22×C4—732no—
285C22×C4—732no—
286C22×C4—731no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—732no—
290C22×C4—731no—
291C22×C4—732no—
292C22×C4—732no—
293C22×C4—732no—
294C22×C4—1461no—
295C22×C4—1461no—
296C22×C4—1461no—
297C22×C4—1461no—
298C22×C4—1461no—
299C22×C4—1461no—
300C22×C4—1461no—
301C22×C4—1461no—
302C22×C4—1461no—
303C22×C4—1461no—
304C22×C4—1462no—
305C22×C4—1462no—
306C22×C4—1461no—
307C22×C4—1461no—
308C22×C4C2×#1059684211yescharacteristic
309C22×C4C2×#1059684211yescharacteristic
310C22×C4C2×#1059684211yescharacteristic
311C2×C8—2924no—
312C2×C8—2924no—
313C2×C8—2924no—
314C4⋊C4—22no—
315C4⋊C4—1462no—
316C4⋊C4—1462no—
317C4⋊C4—1464no—
318C4⋊C4—1464no—
319C4⋊C4—1462no—
320C42—2922no—
321C42—2922no—
322C42—2922no—
323C42—1464no—
324C42—1464no—
325C42—1464no—
326C23—731no—
327C23—731no—
328C23—731no—
329C23—731no—
330C23—731no—
331C23—731no—
332C23—1461no—
333C23—1461no—
334C23—1461no—
335C23—1461no—
336C23C22×#1059684211yescharacteristic
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—2922no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—2922no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2921no—
349C2×C4—2921no—
350C2×C4—2922no—
351C2×C4—2922no—
352C2×C4—2921no—
353C2×C4—2922no—
354C2×C4—2922no—
355C2×C4—2921no—
356C2×C4—2921no—
357C2×C4—2922no—
358C2×C4—2921no—
359C2×C4—732no—
360C2×C4—732no—
361C2×C4—732no—
362C2×C4—732no—
363C2×C4—732no—
364C2×C4—732no—
365C2×C4—1462no—
366C2×C4—1462no—
367C2×C4—1462no—
368C2×C4—1462no—
369C2×C4—1462no—
370C2×C4—1462no—
371C2×C4—1462no—
372C2×C4—1462no—
373C2×C4—1461no—
374C2×C4—1461no—
375C2×C4—1462no—
376C2×C4—1461no—
377C2×C4—1461no—
378C2×C4—1462no—
379C2×C4—1461no—
380C2×C4—1464no—
381C2×C4—1464no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4C22⋊#1059684212yes—
385C2×C4C4⋊#1059684212yescomplemented
386C8—5844no—
387C22—21no—
388C22—21no—
389C22—731no—
390C22—731no—
391C22—731no—
392C22—731no—
393C22—731no—
394C22—731no—
395C22—731no—
396C22—731no—
397C22—1461no—
398C22—1461no—
399C22—1461no—
400C22—1461no—
401C22—1461no—
402C22—1461no—
403C22—1461no—
404C22—1461no—
405C22—1461no—
406C22—1461no—
407C22C2×C22⋊#1059684211yescharacteristic
408C22C2×C4⋊#1059684211yescharacteristic
409C22#1798970011yescharacteristic
410C4—22no—
411C4—22no—
412C4—41no—
413C4—2922no—
414C4—2922no—
415C4—2921no—
416C4—1462no—
417C4—1462no—
418C4—1462no—
419C4—1462no—
420C4—1462no—
421C4—1462no—
422C2—21no—
423C2—21no—
424C2—731no—
425C2—731no—
426C2—731no—
427C2—731no—
428C2—1461no—
429C2—1461no—
430C2#2262704411yescharacteristic
431C2#2262704611yescharacteristic
432C2#2262707111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10596842
commutatorC23×C73C22×C8
FrattiniC23C22×#10596842
FittingC2×C4⋊C4×C73C8
socleC22×C73C2×C22⋊C8
prime radicalC23×D73C22×C4
cosocleC23×#64408C23
hypercenterC2×C4⋊C4#10596842
hypocenterC73#8560
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
45. C2×C4⋊Dic73C8semidirect
46. C2×#11924007C8semidirect
47. C2×#11924007C8semidirect
50. C2×C4⋊C4×C73C8semidirect
152. C2×C4×C73C4⋊C8semidirect
159. C2×Dic73C4⋊C8semidirect
221. C73#8560semidirect
252. C2×C4⋊C4#10596842semidirect
385. C2×C4C4⋊#10596842semidirect

Maximal subgroups

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

subgroupindex
#226270712
C2×#179896732
#226269402
C2×C4⋊C4×#644082
#856073