Finite Group Databasebeta

← #33001963

Subgroups — #33001963

Order 18688.

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

normal subgroups only

This group has 512 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#22612596C211yesmaximal, characteristic
2C2×#17988378C212yesmaximal
3#22609919C211yesmaximal, characteristic
4#22608050C212yesmaximal
5C73×#1800C211yesmaximal, characteristic
6C2×#14556572C2211yescharacteristic
7C22×#11924007C411yescharacteristic, complemented
8C2×#14556506C2212yes—
9#17988482—21no—
10#17988481—21no—
11#17988471—21no—
12#17988467C2211yescharacteristic
13#17988460—21no—
14#17988459C411yescharacteristic, complemented
15#17988448C411yescharacteristic, complemented
16#17988447—21no—
17C4×C22⋊Dic73C411yescharacteristic, complemented
18#17988378—24no—
19#17988354—21no—
20C2×C4×D4×C73C2211yescharacteristic
21#423×C73—21no—
22C2×#100×C73C2212yes—
23#343×C73—21no—
24C23×Dic73C2×C411yescharacteristic
25C23×Dic73C2×C411yescharacteristic
26#14556572—21no—
27#14556572—21no—
28#14556572D412yes—
29#14556572Q812yes—
30C2×C4⋊Dic73—41no—
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×#11924007—41no—
36C2×#11924007—41no—
37C2×C22⋊Dic73—21no—
38C2×C22⋊Dic73—22no—
39C2×C22⋊Dic73—21no—
40C2×C22⋊Dic73C2×C411yescharacteristic
41C2×C22⋊Dic73C2×C411yescharacteristic
42C2×C4×Dic73—21no—
43#14556506—22no—
44#14556506—22no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50#14556498—41no—
51C22×D4×C73C2311yescharacteristic
52C23×C4×C73C2×C411yescharacteristic
53C23×C4×C73D411yescharacteristic
54C2×M16×C73—22no—
55C4×D4×C73—41no—
56C4×D4×C73—41no—
57C2×C4⋊C4×C73D411yescharacteristic
58C2×C22⋊C4×C73C2×C411yescharacteristic
59C2×C22⋊C4×C73D411yescharacteristic
60C2×C42×C73D411yescharacteristic
61C4⋊C8×C73—41no—
62C4⋊C8×C73—41no—
63#100×C73—22no—
64#100×C73—22no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—41no—
71C22×Dic73—41no—
72C22×Dic73—41no—
73C22×Dic73—42no—
74C22×Dic73—81no—
75C22×Dic73C4⋊C412yescomplemented
76C4⋊Dic73—82no—
77#11924007—22no—
78#11924007—22no—
79#11924007—42no—
80#11924007—41no—
81#11924007—41no—
82#11924007—81no—
83C22⋊Dic73—21no—
84C22⋊Dic73—22no—
85C22⋊Dic73—22no—
86C22⋊Dic73—41no—
87C22⋊Dic73—42no—
88C22⋊Dic73—42no—
89C22⋊Dic73—81no—
90C22⋊Dic73C4⋊C412yescomplemented
91C4×Dic73—81no—
92C24×C73C22×C411yescharacteristic
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—81no—
105C22×C4×C73—81no—
106C22×C4×C73C22⋊C411yescharacteristic
107C22×C4×C73C22⋊C411yescharacteristic
108C22×C4×C73C22⋊C411yescharacteristic
109C22×C4×C73C22⋊C411yescharacteristic
110C22×C4×C73C2×D411yescharacteristic
111M16×C73—42no—
112M16×C73—42no—
113C2×C8×C73—42no—
114C4⋊C4×C73—41no—
115C22⋊C4×C73—41no—
116C22⋊C4×C73—41no—
117C42×C73—21no—
118C42×C73—21no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73—41no—
124C23×C73—41no—
125C23×C73—41no—
126C23×C73—41no—
127C23×C73C2×C22⋊C411yescharacteristic
128C23×C73C2×C4⋊C411yescharacteristic
129C23×C73#11711yescharacteristic
130C23×C73#12111yescharacteristic
131C23×C73C22⋊Q811yescharacteristic
132D4×C73—41no—
133D4×C73—41no—
134D4×C73—41no—
135D4×C73—41no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—41no—
142C2×C4×C73—42no—
143C2×C4×C73—41no—
144C2×C4×C73—41no—
145C2×C4×C73—41no—
146C2×C4×C73—81no—
147C2×C4×C73—81no—
148C2×C4×C73—81no—
149C2×C4×C73#9911yescharacteristic
150C2×C4×C73#9911yescharacteristic
151C2×C4×C73#12111yescharacteristic
152C2×C4×C73C22⋊Q811yescharacteristic
153C2×Dic73—22no—
154C2×Dic73—22no—
155C2×Dic73—41no—
156C2×Dic73—41no—
157C2×Dic73—42no—
158C2×Dic73—41no—
159C2×Dic73—41no—
160C2×Dic73—42no—
161C2×Dic73—41no—
162C2×Dic73—41no—
163C2×Dic73—41no—
164C2×Dic73—41no—
165C2×Dic73—41no—
166C2×Dic73—41no—
167C2×Dic73—82no—
168C2×Dic73—82no—
169C2×Dic73—82no—
170C2×Dic73—82no—
171C8×C73—82no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—21no—
175C22×C73—21no—
176C22×C73—21no—
177C22×C73—21no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—42no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—81no—
188C22×C73#38011yescharacteristic
189C22×C73C2×#9911yescharacteristic
190C22×C73#41011yescharacteristic
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—21no—
195C4×C73—41no—
196C4×C73—41no—
197C4×C73—41no—
198Dic73—42no—
199Dic73—42no—
200Dic73—81no—
201Dic73—81no—
202Dic73—162no—
203#12796—731nomaximal, Sylow
204C2×C73—21no—
205C2×C73—21no—
206C2×C73—41no—
207C2×C73—41no—
208C2×C73—41no—
209C2×C73—41no—
210C2×C73#179911yescharacteristic
211C2×C73#212111yescharacteristic
212C2×C73#212311yescharacteristic
213#2322—731no—
214C2×#352—732no—
215#1800D7311yescharacteristic
216#1799—731no—
217#1390—732no—
218C73#1279611yescharacteristic, complemented, Sylow
219C2×#123—731no—
220C2×C4×D4C2×D7311yescharacteristic
221C22×C4⋊C4—731no—
222#423—21no—
223C2×#100C2×D7312yes—
224C2×#99—732no—
225#389—1461no—
226#388—1461no—
227#387—1461no—
228#386—731no—
229#385—731no—
230#385—1461no—
231#381—731no—
232#380—1461no—
233C4×C22⋊C4—731no—
234#352—1464no—
235#343—21no—
236#342—1461no—
237C22×D4C22×D7311yescharacteristic
238C23×C4—731no—
239C23×C4—731no—
240C23×C4C4×D7311yescharacteristic
241C23×C4D29211yescharacteristic
242C2×M16—22no—
243#123—732no—
244#123—732no—
245#123—1461no—
246#123—1461no—
247C4×D4—41no—
248C4×D4—41no—
249C2×C4⋊C4—2921no—
250C2×C4⋊C4—2921no—
251C2×C4⋊C4—2921no—
252C2×C4⋊C4—1461no—
253C2×C4⋊C4—1461no—
254C2×C4⋊C4—1461no—
255C2×C4⋊C4—1461no—
256C2×C4⋊C4C22⋊D7311yescharacteristic
257C2×C22⋊C4—731no—
258C2×C22⋊C4—731no—
259C2×C22⋊C4—1462no—
260C2×C22⋊C4—1461no—
261C2×C22⋊C4—1461no—
262C2×C22⋊C4C4×D7311yescharacteristic
263C2×C22⋊C4D29211yescharacteristic
264C2×C42—1461no—
265C2×C42C22⋊D7311yescharacteristic
266C4⋊C8—41no—
267C4⋊C8—41no—
268#100—22no—
269#100—22no—
270#99—1462no—
271#99—1462no—
272#95—2921no—
273#95—1461no—
274#95—1461no—
275#95—1461no—
276#95—1461no—
277#95—1461no—
278C24C2×C4×D7311yescharacteristic
279C24C2×D29211yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4D4×D7311yescharacteristic
283C2×D4Q8×D7311yescharacteristic
284C2×D4#1192402711yescharacteristic
285C2×D4#1192402911yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4—2921no—
293C22×C4—2921no—
294C22×C4—2921no—
295C22×C4—2922no—
296C22×C4—5841no—
297C22×C4—732no—
298C22×C4—1461no—
299C22×C4—1461no—
300C22×C4—1461no—
301C22×C4—1461no—
302C22×C4—1461no—
303C22×C4#1192400511yescharacteristic
304C22×C4#1192400511yescharacteristic
305C22×C4#1192400511yescharacteristic
306C22×C4#1192400511yescharacteristic
307C22×C4C2×C22⋊D7311yescharacteristic
308M16—42no—
309M16—42no—
310C2×C8—42no—
311C4⋊C4—41no—
312C4⋊C4—2922no—
313C4⋊C4—2921no—
314C4⋊C4—2921no—
315C4⋊C4—5841no—
316C4⋊C4—5842no—
317C4⋊C4—1462no—
318C4⋊C4—1462no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—2921no—
322C22⋊C4—2922no—
323C22⋊C4—2922no—
324C22⋊C4—5841no—
325C22⋊C4—732no—
326C22⋊C4—1461no—
327C22⋊C4—1462no—
328C22⋊C4—1462no—
329C42—21no—
330C42—21no—
331C42—5841no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C2×#1192400511yescharacteristic
341C23C4⋊C4×D7311yescharacteristic
342C23#1455654911yescharacteristic
343C23#1455656611yescharacteristic
344C23#1455657111yescharacteristic
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—2921no—
363C2×C4—2922no—
364C2×C4—2921no—
365C2×C4—2921no—
366C2×C4—2921no—
367C2×C4—2922no—
368C2×C4—2921no—
369C2×C4—2921no—
370C2×C4—2921no—
371C2×C4—2921no—
372C2×C4—2921no—
373C2×C4—2921no—
374C2×C4—5842no—
375C2×C4—5842no—
376C2×C4—5842no—
377C2×C4—5842no—
378C2×C4—1462no—
379C2×C4—1462no—
380C2×C4#1455650511yescharacteristic
381C2×C4#1455650511yescharacteristic
382C2×C4#1455656211yescharacteristic
383C2×C4#1455656711yescharacteristic
384C8—82no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22#1798844411yescharacteristic
402C22C2×#1455650511yescharacteristic
403C22#1798856011yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—2922no—
412C4—2922no—
413C4—5841no—
414C4—5841no—
415C4—11682no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2—41no—
421C2—41no—
422C2#2260991611yescharacteristic
423C2#2261157811yescharacteristic
424C2#2261158611yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC24×C73C22×C4
FrattiniC22×D4C22×D73
FittingC73×#1800C2
socleC22×C73C2×#99
prime radical, cosocleC22×D4×C73C23
hypercenter#1800D73
hypocenterC73#12796
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
7. C22×#11924007C4semidirect
14. #17988459C4semidirect
15. #17988448C4semidirect
17. C4×C22⋊Dic73C4semidirect
75. C22×Dic73C4⋊C4semidirect
90. C22⋊Dic73C4⋊C4semidirect
218. C73#12796semidirect

Maximal subgroups

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

subgroupindex
#226125962
C2×#179883782
#226099192
#226080502
C73×#18002
#1279673