Finite Group Databasebeta

← #33001968

Subgroups — #33001968

Order 18688.

544 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14556578C211yesmaximal, characteristic
2C2×#17988381C212yesmaximal
3#22609919C211yesmaximal, characteristic
4#22608055C212yesmaximal
5C73×#1799C211yesmaximal, characteristic
6C2×#14556578C2211yescharacteristic
7C2×C4×Dic146C411yescharacteristic, complemented
8C2×#14556506C2212yes—
9#17988492C411yescharacteristic, complemented
10#17988490C2211yescharacteristic
11#17988481—21no—
12#17988481—21no—
13#17988452C411yescharacteristic, complemented
14#17988447—21no—
15C4×C22⋊Dic73—21no—
16C4×C22⋊Dic73—21no—
17C42×Dic73C411yescharacteristic, complemented
18#17988381—24no—
19#17988354—21no—
20C2×C4×D4×C73C2211yescharacteristic
21C2×#99×C73C2212yes—
22#380×C73—21no—
23#342×C73—21no—
24C22×Dic146C2×C411yescharacteristic
25#14556578—21no—
26#14556578—21no—
27#14556578D412yes—
28#14556578Q812yes—
29C4×Dic146—41no—
30C4×Dic146—41no—
31C2×C4⋊Dic73—41no—
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×#11924007—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C22⋊Dic73—21no—
37C2×C22⋊Dic73—21no—
38C2×C22⋊Dic73—22no—
39C2×C4×Dic73—21no—
40C2×C4×Dic73—21no—
41C2×C4×Dic73—21no—
42C2×C4×Dic73C2×C411yescharacteristic
43C2×C4×Dic73C2×C411yescharacteristic
44#14556506—22no—
45#14556506—22no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50#14556498—41no—
51C22×D4×C73C2311yescharacteristic
52C23×C4×C73D411yescharacteristic
53C23×C4×C73D411yescharacteristic
54C4×D4×C73—41no—
55C4×D4×C73—41no—
56C2×C4⋊C4×C73—41no—
57C2×C4⋊C4×C73C2×C411yescharacteristic
58C2×C22⋊C4×C73—22no—
59C2×C22⋊C4×C73D411yescharacteristic
60C2×C22⋊C4×C73D411yescharacteristic
61C2×C42×C73C2×C411yescharacteristic
62#99×C73—22no—
63#99×C73—22no—
64#95×C73—41no—
65C2×Dic146—21no—
66C2×Dic146—41no—
67C2×Dic146—41no—
68C2×Dic146C4⋊C412yescomplemented
69C22×Dic73—21no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C22×Dic73—21no—
73C22×Dic73—42no—
74C4⋊Dic73—41no—
75C4⋊Dic73—82no—
76#11924007—42no—
77C22⋊Dic73—22no—
78C22⋊Dic73—22no—
79C22⋊Dic73—22no—
80C22⋊Dic73—22no—
81C22⋊Dic73—42no—
82C22⋊Dic73—42no—
83C22⋊Dic73—42no—
84C22⋊Dic73—42no—
85C4×Dic73—21no—
86C4×Dic73—42no—
87C4×Dic73—42no—
88C4×Dic73—41no—
89C4×Dic73—41no—
90C4×Dic73—41no—
91C4×Dic73C4⋊C412yescomplemented
92C24×C73C2×D411yescharacteristic
93C24×C73C2×D411yescharacteristic
94C2×D4×C73—41no—
95C2×D4×C73—41no—
96C2×D4×C73C2×D411yescharacteristic
97C2×D4×C73C2×Q811yescharacteristic
98C2×D4×C73#4111yescharacteristic
99C2×D4×C73#4111yescharacteristic
100C22×C4×C73—21no—
101C22×C4×C73—21no—
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73—42no—
105C22×C4×C73—42no—
106C22×C4×C73—42no—
107C22×C4×C73C22⋊C411yescharacteristic
108C22×C4×C73C22⋊C411yescharacteristic
109C22×C4×C73C22⋊C411yescharacteristic
110C22×C4×C73C22⋊C411yescharacteristic
111C22×C4×C73C22×C411yescharacteristic
112C4⋊C4×C73—41no—
113C4⋊C4×C73—82no—
114C22⋊C4×C73—41no—
115C22⋊C4×C73—41no—
116C22⋊C4×C73—42no—
117C22⋊C4×C73—42no—
118C42×C73—21no—
119C42×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73—41no—
125C23×C73—41no—
126C23×C73—41no—
127C23×C73—41no—
128C23×C73C2×C22⋊C411yescharacteristic
129C23×C73#12111yescharacteristic
130C23×C73#12111yescharacteristic
131C23×C73C22⋊Q811yescharacteristic
132C23×C73C22⋊Q811yescharacteristic
133D4×C73—41no—
134D4×C73—41no—
135D4×C73—41no—
136D4×C73—41no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—22no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—42no—
144C2×C4×C73—42no—
145C2×C4×C73—41no—
146C2×C4×C73—41no—
147C2×C4×C73—41no—
148C2×C4×C73—81no—
149C2×C4×C73—81no—
150C2×C4×C73—82no—
151C2×C4×C73—82no—
152C2×C4×C73—82no—
153C2×C4×C73#9911yescharacteristic
154C2×C4×C73#9911yescharacteristic
155C2×C4×C73C2×C4⋊C411yescharacteristic
156C2×C4×C73#11711yescharacteristic
157C2×Dic73—22no—
158C2×Dic73—22no—
159C2×Dic73—22no—
160C2×Dic73—41no—
161C2×Dic73—41no—
162C2×Dic73—41no—
163C2×Dic73—41no—
164C2×Dic73—41no—
165C2×Dic73—41no—
166C2×Dic73—41no—
167C2×Dic73—41no—
168C2×Dic73—41no—
169C2×Dic73—82no—
170C2×Dic73—82no—
171C2×Dic73—82no—
172Dic146—42no—
173Dic146—42no—
174C22×C73—21no—
175C22×C73—21no—
176C22×C73—21no—
177C22×C73—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—41no—
188C22×C73—81no—
189C22×C73—81no—
190C22×C73#38011yescharacteristic
191C22×C73C2×#9911yescharacteristic
192C22×C73#41011yescharacteristic
193C4×C73—21no—
194C4×C73—21no—
195C4×C73—21no—
196C4×C73—41no—
197C4×C73—41no—
198C4×C73—41no—
199C4×C73—162no—
200C4×C73#35412yescomplemented
201Dic73—42no—
202Dic73—42no—
203Dic73—42no—
204Dic73—81no—
205Dic73—162no—
206#12798—731nomaximal, Sylow
207C2×C73—21no—
208C2×C73—21no—
209C2×C73—41no—
210C2×C73—41no—
211C2×C73—41no—
212C2×C73—41no—
213C2×C73#179911yescharacteristic
214C2×C73C2×#35411yescharacteristic
215C2×C73#212611yescharacteristic
216C4×#124—731no—
217C2×#354—732no—
218#1799—731no—
219#1799D7311yescharacteristic
220#1393—732no—
221C73#1279811yescharacteristic, complemented, Sylow
222C2×#124—731no—
223C2×C4×Q8—731no—
224C2×C4×D4C2×D7311yescharacteristic
225C2×#99—732no—
226C2×#99C2×D7312yes—
227#391—731no—
228#390—731no—
229#388—1461no—
230#388—1461no—
231#382—731no—
232#380—21no—
233#380—1461no—
234C4×C22⋊C4—1461no—
235C4×C22⋊C4—1461no—
236C43—731no—
237#354—1464no—
238#342—21no—
239#342—1461no—
240C22×Q8—731no—
241C22×D4C22×D7311yescharacteristic
242C23×C4D29211yescharacteristic
243C23×C4C22⋊D7311yescharacteristic
244#124—732no—
245#124—732no—
246#124—1461no—
247#124—1461no—
248C4×Q8—2921no—
249C4×Q8—2921no—
250C4×D4—41no—
251C4×D4—41no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—2921no—
254C2×C4⋊C4—731no—
255C2×C4⋊C4—1461no—
256C2×C4⋊C4C4×D7311yescharacteristic
257C2×C22⋊C4—22no—
258C2×C22⋊C4—1462no—
259C2×C22⋊C4—1461no—
260C2×C22⋊C4—1461no—
261C2×C22⋊C4—1461no—
262C2×C22⋊C4—1461no—
263C2×C22⋊C4D29211yescharacteristic
264C2×C22⋊C4C22⋊D7311yescharacteristic
265C2×C42—731no—
266C2×C42—731no—
267C2×C42—1461no—
268C2×C42—1461no—
269C2×C42—1461no—
270C2×C42C4×D7311yescharacteristic
271#99—22no—
272#99—22no—
273#99—1462no—
274#99—1462no—
275#95—41no—
276#95—2921no—
277#95—1461no—
278#95—1461no—
279#95—1461no—
280#95—1461no—
281C24C2×C22⋊D7311yescharacteristic
282C24C2×D29211yescharacteristic
283C2×Q8—2921no—
284C2×Q8—2921no—
285C2×Q8—732no—
286C2×Q8—1461no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4D4×D7311yescharacteristic
290C2×D4Q8×D7311yescharacteristic
291C2×D4#1192402711yescharacteristic
292C2×D4#1192402911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—2922no—
301C22×C4—1461no—
302C22×C4—1461no—
303C22×C4—1461no—
304C22×C4—1461no—
305C22×C4#1192400511yescharacteristic
306C22×C4#1192400511yescharacteristic
307C22×C4#1192400511yescharacteristic
308C22×C4#1192400511yescharacteristic
309C22×C4C2×C4×D7311yescharacteristic
310C4⋊C4—41no—
311C4⋊C4—82no—
312C4⋊C4—2921no—
313C4⋊C4—2922no—
314C4⋊C4—5842no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—2922no—
320C22⋊C4—2922no—
321C22⋊C4—2922no—
322C22⋊C4—2922no—
323C22⋊C4—1462no—
324C22⋊C4—1462no—
325C22⋊C4—1462no—
326C22⋊C4—1462no—
327C42—21no—
328C42—21no—
329C42—2921no—
330C42—2922no—
331C42—2922no—
332C42—2921no—
333C42—2921no—
334C42—732no—
335C42—1461no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23C2×#1192400511yescharacteristic
345C23#1455656211yescharacteristic
346C23#1455656611yescharacteristic
347C23#1455656711yescharacteristic
348C23#1455657111yescharacteristic
349Q8—2922no—
350Q8—2922no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—41no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—2921no—
372C2×C4—2921no—
373C2×C4—2921no—
374C2×C4—2921no—
375C2×C4—2921no—
376C2×C4—2921no—
377C2×C4—2921no—
378C2×C4—2921no—
379C2×C4—2921no—
380C2×C4—5842no—
381C2×C4—5842no—
382C2×C4—5842no—
383C2×C4—1462no—
384C2×C4—1462no—
385C2×C4—1462no—
386C2×C4#1455650511yescharacteristic
387C2×C4#1455650511yescharacteristic
388C2×C4C4⋊C4×D7311yescharacteristic
389C2×C4#1455654911yescharacteristic
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22—81no—
406C22#1798844411yescharacteristic
407C22C2×#1455650511yescharacteristic
408C22#1798856011yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—162no—
416C4—2922no—
417C4—2922no—
418C4—2922no—
419C4—5841no—
420C4—11682no—
421C4#1798838112yescomplemented
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2—41no—
427C2—41no—
428C2#2260991611yescharacteristic
429C2C2×#1798838111yescharacteristic
430C2#2261159411yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC22×D4C22×D73
FittingC73×#1799C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenter#1799D73
hypocenterC73#12798
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic146C4semidirect
9. #17988492C4semidirect
13. #17988452C4semidirect
17. C42×Dic73C4semidirect
68. C2×Dic146C4⋊C4semidirect
91. C4×Dic73C4⋊C4semidirect
200. C4×C73#354semidirect
221. C73#12798semidirect
421. C4#17988381semidirect

Maximal subgroups

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

subgroupindex
C4×#145565782
C2×#179883812
#226099192
#226080552
C73×#17992
#1279873