Finite Group Databasebeta

← C4×#17988378 #33001124

Subgroups — C4×#17988378 #33001124

Order 18688.

576 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×#14556572C211yesmaximal, characteristic
2C2×#17988378C212yesmaximal
3C4×#14556506C211yesmaximal, characteristic
4#22608050C212yesmaximal
5C4×#100×C73C211yesmaximal, characteristic
6C2×#14556572C2211yescharacteristic
7C22×C4×Dic73C411yescharacteristic, complemented
8C2×#14556506C2212yes—
9#17988475—21no—
10#17988468—21no—
11#17988467C2211yescharacteristic
12#17988459C411yescharacteristic, complemented
13#17988448C411yescharacteristic, complemented
14C4×#11924007—21no—
15C4×C22⋊Dic73—21no—
16C4×C22⋊Dic73—21no—
17C4×C22⋊Dic73C411yescharacteristic, complemented
18#17988378C418yesdirect product factor
19#17988354—21no—
20C2×C4×D4×C73C2211yescharacteristic
21C2×#100×C73C2212yes—
22C4×M16×C73—21no—
23#343×C73—21no—
24C23×Dic73C2×C411yescharacteristic
25C23×Dic73C2×C411yescharacteristic
26#14556572—22no—
27#14556572C2×C414yes—
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×C22⋊Dic73—21no—
31C2×C22⋊Dic73—22no—
32C2×C22⋊Dic73—21no—
33C2×C22⋊Dic73C2×C411yescharacteristic
34C2×C22⋊Dic73C2×C411yescharacteristic
35C2×C4×Dic73—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73—21no—
38C2×C4×Dic73—41no—
39C2×C4×Dic73—41no—
40C2×C4×Dic73—41no—
41#14556506—22no—
42#14556506C2×C414yes—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—41no—
49C22×D4×C73C2311yescharacteristic
50C23×C4×C73C2×C411yescharacteristic
51C23×C4×C73D411yescharacteristic
52C2×M16×C73—22no—
53C4×D4×C73—41no—
54C4×D4×C73—41no—
55C2×C4⋊C4×C73D411yescharacteristic
56C2×C22⋊C4×C73C2×C411yescharacteristic
57C2×C22⋊C4×C73D411yescharacteristic
58C2×C42×C73D411yescharacteristic
59#100×C73—22no—
60#100×C73C2×C414yes—
61#97×C73—41no—
62C4×C8×C73—41no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—42no—
69C22×Dic73—41no—
70C22×Dic73—41no—
71C22×Dic73—41no—
72C22×Dic73—42no—
73C22×Dic73C4212yescomplemented
74#11924007—24no—
75#11924007—42no—
76C22⋊Dic73—21no—
77C22⋊Dic73—24no—
78C22⋊Dic73—24no—
79C22⋊Dic73—42no—
80C22⋊Dic73—42no—
81C22⋊Dic73—41no—
82C22⋊Dic73C4212yescomplemented
83C4×Dic73—42no—
84C4×Dic73—42no—
85C4×Dic73—41no—
86C4×Dic73—41no—
87C4×Dic73—82no—
88C24×C73C22×C411yescharacteristic
89C24×C73C2×D411yescharacteristic
90C2×D4×C73—41no—
91C2×D4×C73—41no—
92C2×D4×C73C22×C412yes—
93C2×D4×C73#4112yes—
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73—42no—
99C22×C4×C73—42no—
100C22×C4×C73C22⋊C411yescharacteristic
101C22×C4×C73C22⋊C411yescharacteristic
102C22×C4×C73C22⋊C411yescharacteristic
103C22×C4×C73C22⋊C411yescharacteristic
104C22×C4×C73C2×D411yescharacteristic
105M16×C73—24no—
106M16×C73—42no—
107C2×C8×C73—42no—
108C4⋊C4×C73—41no—
109C22⋊C4×C73—41no—
110C22⋊C4×C73—41no—
111C42×C73—21no—
112C42×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—41no—
118C23×C73—41no—
119C23×C73—41no—
120C23×C73—41no—
121C23×C73C2×C4211yescharacteristic
122C23×C73C2×C22⋊C411yescharacteristic
123C23×C73#11711yescharacteristic
124C23×C73C4×D412yes—
125D4×C73—42no—
126D4×C73—42no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—22no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73—42no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—81no—
140C2×C4×C73#9911yescharacteristic
141C2×C4×C73#9911yescharacteristic
142C2×C4×C73C4×D412yes—
143C2×Dic73—22no—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—42no—
150C2×Dic73—42no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—42no—
155C2×Dic73—42no—
156C2×Dic73—41no—
157C2×Dic73—44no—
158C2×Dic73—41no—
159C2×Dic73—41no—
160C2×Dic73—82no—
161C2×Dic73—82no—
162C8×C73—44no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—22no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—42no—
171C22×C73—42no—
172C22×C73—41no—
173C22×C73—41no—
174C22×C73—41no—
175C22×C73—41no—
176C22×C73—81no—
177C22×C73C4×C22⋊C411yescharacteristic
178C22×C73C2×#9911yescharacteristic
179C22×C73#41011yescharacteristic
180C4×C73—21no—
181C4×C73—22no—
182C4×C73—41no—
183C4×C73—41no—
184C4×C73—41no—
185C4×C73#35212yescomplemented
186Dic73—42no—
187Dic73—42no—
188Dic73—42no—
189Dic73—81no—
190Dic73—84no—
191C4×#352—731nomaximal, Sylow
192C2×C73—21no—
193C2×C73—21no—
194C2×C73—42no—
195C2×C73—41no—
196C2×C73—41no—
197C2×C73C4×#9911yescharacteristic
198C2×C73C2×#35211yescharacteristic
199C2×C73#212011yescharacteristic
200C4×#123—731no—
201C2×#352—732no—
202C4×#100D7311yescharacteristic
203C4×#99—731no—
204#1390—732no—
205C73C4×#35211yescharacteristic, complemented, Sylow
206C2×#123—731no—
207C2×C4×D4C2×D7311yescharacteristic
208C22×C42—731no—
209C2×#100C2×D7312yes—
210C2×#99—732no—
211C4×M16—21no—
212#388—1461no—
213#387—1461no—
214#386—731no—
215#385—731no—
216#381—731no—
217C4×C4⋊C4—1461no—
218C4×C22⋊C4—731no—
219C4×C22⋊C4—1461no—
220C4×C22⋊C4—1461no—
221#352—738no—
222#343—21no—
223#342—1461no—
224C22×D4C22×D7311yescharacteristic
225C23×C4—731no—
226C23×C4—731no—
227C23×C4C4×D7311yescharacteristic
228C23×C4D29211yescharacteristic
229C2×M16—22no—
230#123—734no—
231#123—1462no—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—1461no—
235C2×C4⋊C4—1461no—
236C2×C4⋊C4C22⋊D7311yescharacteristic
237C2×C22⋊C4—731no—
238C2×C22⋊C4—731no—
239C2×C22⋊C4—1461no—
240C2×C22⋊C4—1462no—
241C2×C22⋊C4—1461no—
242C2×C22⋊C4C4×D7311yescharacteristic
243C2×C22⋊C4D29211yescharacteristic
244C2×C42—2921no—
245C2×C42—2921no—
246C2×C42—2921no—
247C2×C42—1461no—
248C2×C42—1461no—
249C2×C42—1461no—
250C2×C42C22⋊D7311yescharacteristic
251#100—22no—
252#100C4×D7314yes—
253#99—734no—
254#99—1462no—
255#97—41no—
256C4×C8—41no—
257#95—2921no—
258#95—1461no—
259#95—1461no—
260#95—1461no—
261#95—1461no—
262#95—1461no—
263C24C2×C4×D7311yescharacteristic
264C24C2×D29211yescharacteristic
265C2×D4—41no—
266C2×D4—41no—
267C2×D4C2×C4×D7312yes—
268C2×D4#1192402812yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—2921no—
276C22×C4—2921no—
277C22×C4—2921no—
278C22×C4—2922no—
279C22×C4—2922no—
280C22×C4—732no—
281C22×C4—1461no—
282C22×C4—1461no—
283C22×C4—1461no—
284C22×C4—1461no—
285C22×C4—1461no—
286C22×C4#1192400511yescharacteristic
287C22×C4#1192400511yescharacteristic
288C22×C4#1192400511yescharacteristic
289C22×C4#1192400511yescharacteristic
290C22×C4C2×C22⋊D7311yescharacteristic
291M16—24no—
292M16—42no—
293C2×C8—42no—
294C4⋊C4—41no—
295C4⋊C4—2922no—
296C4⋊C4—1464no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—2922no—
300C22⋊C4—2922no—
301C22⋊C4—2921no—
302C22⋊C4—732no—
303C22⋊C4—1464no—
304C22⋊C4—1461no—
305C22⋊C4—1464no—
306C42—21no—
307C42—21no—
308C42—2922no—
309C42—2922no—
310C42—2921no—
311C42—2921no—
312C42—5842no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C42×D7311yescharacteristic
322C23C2×#1192400511yescharacteristic
323C23#1455654811yescharacteristic
324C23C4×D29212yes—
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2922no—
343C2×C4—2921no—
344C2×C4—2922no—
345C2×C4—2921no—
346C2×C4—2921no—
347C2×C4—2921no—
348C2×C4—2922no—
349C2×C4—2922no—
350C2×C4—2921no—
351C2×C4—2921no—
352C2×C4—2924no—
353C2×C4—2921no—
354C2×C4—5842no—
355C2×C4—5842no—
356C2×C4—1462no—
357C2×C4—1462no—
358C2×C4—1462no—
359C2×C4#1455650511yescharacteristic
360C2×C4#1455650511yescharacteristic
361C2×C4C4×C22⋊D7312yes—
362C8—44no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22C4×#1192400511yescharacteristic
378C22C2×#1455650511yescharacteristic
379C22#1798856011yescharacteristic
380C4—22no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—2922no—
386C4—2922no—
387C4—2922no—
388C4—5841no—
389C4—5844no—
390C4#1798837812yesdirect product factor
391C2—21no—
392C2—21no—
393C2—42no—
394C2—41no—
395C2—41no—
396C2C4×#1455650511yescharacteristic
397C2C2×#1798837811yescharacteristic
398C2#2261157311yescharacteristic
subgroupG/H
centerC2×C4#14556505
commutatorC23×C73C2×C42
FrattiniC22×D4C22×D73
FittingC4×#100×C73C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenterC4×#100D73
hypocenterC73C4×#352
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
7. C22×C4×Dic73C4semidirect
12. #17988459C4semidirect
13. #17988448C4semidirect
17. C4×C22⋊Dic73C4semidirect
18. #17988378C4direct (N × H)
73. C22×Dic73C42semidirect
82. C22⋊Dic73C42semidirect
185. C4×C73#352semidirect
205. C73C4×#352semidirect
390. C4#17988378direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#145565722
C2×#179883782
C4×#145565062
#226080502
C4×#100×C732
C4×#35273