Finite Group Databasebeta

← #19212361

Subgroups — #19212361

Order 5888.

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

normal subgroups only

This group has 656 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#15675884C211yesmaximal, characteristic
2#15673376C211yesmaximal, characteristic, complemented
3#15673158C211yesmaximal, characteristic, complemented
4#15671222C211yesmaximal, characteristic, complemented
5#15671222C211yesmaximal, characteristic, complemented
6#15671218C211yesmaximal, characteristic, complemented
7C23×#1270C211yesmaximal, characteristic, complemented
8C22×#67290C411yescharacteristic
9C2×#10625063C411yescharacteristic
10C2×C42×D23C2211yescharacteristic
11C2×Dic23⋊C8—21no—
12C2×(C2×D23)⋊C8—21no—
13C2×(C2×D23)⋊C8—21no—
14C2×#10624997—21no—
15#13092323C2211yescharacteristic
16#13092322C411yescharacteristic
17#13092320C411yescharacteristic
18#13092293—21no—
19#13092293—21no—
20C22⋊C4×Dic23—21no—
21C22⋊C4×Dic23—21no—
22#13092172C2211yescharacteristic
23#13092172C2211yescharacteristic
24C23×#390C2211yescharacteristic
25C23×#336C2211yescharacteristic
26C23×#336C2211yescharacteristic
27C22×D4×C23C2×C411yescharacteristic
28C22×C22⋊D23—21no—
29C23×Dic23—21no—
30C2×#67290—22no—
31C2×#67290—22no—
32C2×#67290—42no—
33C2×#67290—42no—
34C22×C4×D23C2×C411yescharacteristic
35C22×C4×D23D411yescharacteristic
36C22×C4×D23D411yescharacteristic
37C22×Dic46C2×C411yescharacteristic
38C22×C8×C23—21no—
39C22×C8×C23—21no—
40C2×C4⋊C4×C23C2×C411yescharacteristic
41C2×C22⋊C4×C23—21no—
42C2×C22⋊C4×C23—21no—
43C2×C42×C23C2311yescharacteristic
44C2×C22⋊Dic23—21no—
45C2×C22⋊Dic23—21no—
46C2×(C2×D23)⋊C4—21no—
47C2×C4⋊Dic23C2×C411yescharacteristic
48C2×C4×Dic23—21no—
49C2×C4×Dic23C2×C411yescharacteristic
50C2×C4×Dic23D411yescharacteristic
51C2×C4×Dic23D411yescharacteristic
52C22×C23⋊C8—21no—
53C22×C23⋊C8—21no—
54#10625063—42no—
55C42×D23—42no—
56C23⋊#95—21no—
57C23⋊#95—21no—
58C23⋊#95—21no—
59C23⋊#95—21no—
60(C2×D23)⋊C8—24no—
61(C2×D23)⋊C8—42no—
62#10624997—42no—
63Dic23⋊C8—42no—
64C24×C23—21no—
65C23×D23C22⋊C411yescharacteristic
66C2×D4×C23—21no—
67C2×D4×C23—41no—
68C2×D4×C23—41no—
69C2×D4×C23M1612yes—
70C22×C4×C23—21no—
71C22×C4×C23C22×C411yescharacteristic
72C22×C4×C23C2×D411yescharacteristic
73C22×C4×C23C2×D411yescharacteristic
74C2×C22⋊D23—24no—
75C2×C22⋊D23—42no—
76C2×C22⋊D23—42no—
77C22×Dic23—24no—
78C22×Dic23—21no—
79C22×Dic23—21no—
80C22×Dic23—42no—
81C22×Dic23—42no—
82C22×Dic23C22⋊C411yescharacteristic
83C22×Dic23C22⋊C411yescharacteristic
84C22×Dic23C22⋊C411yescharacteristic
85#67290—48no—
86#67290—48no—
87C2×C4×D23—22no—
88C2×C4×D23—21no—
89C2×C4×D23—21no—
90C2×C4×D23—22no—
91C2×C4×D23—21no—
92C2×C4×D23—21no—
93C2×C4×D23—21no—
94C2×C4×D23—21no—
95C2×C4×D23—22no—
96C2×C4×D23—41no—
97C2×C4×D23—41no—
98C2×C4×D23—41no—
99C2×Dic46—21no—
100C2×Dic46—41no—
101C2×Dic46—41no—
102C2×Dic46M1612yes—
103C2×C8×C23—22no—
104C2×C8×C23—41no—
105C2×C8×C23—41no—
106C2×C8×C23—41no—
107C2×C8×C23—41no—
108C2×C8×C23—41no—
109C4⋊C4×C23—41no—
110C22⋊C4×C23—41no—
111C22⋊C4×C23—41no—
112C22⋊C4×C23—41no—
113C22⋊C4×C23—41no—
114C42×C23—41no—
115C22⋊Dic23—42no—
116C22⋊Dic23—42no—
117(C2×D23)⋊C4—42no—
118C4⋊Dic23—41no—
119C4×Dic23—22no—
120C4×Dic23—22no—
121C4×Dic23—41no—
122C4×Dic23—42no—
123C2×C23⋊C8—22no—
124C2×C23⋊C8—41no—
125C2×C23⋊C8—41no—
126C2×C23⋊C8—41no—
127C2×C23⋊C8—41no—
128C2×C23⋊C8—41no—
129#7612—231nomaximal, Sylow
130C23×C23—22no—
131C23×C23—41no—
132C23×C23—41no—
133C23×C23—41no—
134C23×C23—41no—
135C23×C23—41no—
136C23×C23—41no—
137C23×C23C2×C22⋊C411yescharacteristic
138C22×D23—21no—
139C22×D23—21no—
140C22×D23—21no—
141C22×D23—21no—
142C22×D23—21no—
143C22×D23—21no—
144C22×D23#10012yes—
145D4×C23—42no—
146D4×C23—42no—
147C2×C4×C23—21no—
148C2×C4×C23—21no—
149C2×C4×C23—21no—
150C2×C4×C23—21no—
151C2×C4×C23—21no—
152C2×C4×C23—21no—
153C2×C4×C23—41no—
154C2×C4×C23—41no—
155C2×C4×C23—41no—
156C2×C4×C23C2×M1611yescharacteristic
157C2×C4×C23C2×M1611yescharacteristic
158C2×C4×C23#13511yescharacteristic
159C2×C4×C23#13511yescharacteristic
160C2×C4×C23AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C23#13711yescharacteristic
162C22⋊D23—48no—
163C2×Dic23—21no—
164C2×Dic23—21no—
165C2×Dic23—21no—
166C2×Dic23—21no—
167C2×Dic23—22no—
168C2×Dic23—21no—
169C2×Dic23—21no—
170C2×Dic23—21no—
171C2×Dic23—48no—
172C2×Dic23—41no—
173C2×Dic23—41no—
174C2×Dic23—41no—
175C2×Dic23—41no—
176C2×Dic23—41no—
177C2×Dic23#9912yes—
178C2×Dic23#10412yes—
179C4×D23—24no—
180C4×D23—24no—
181C4×D23—42no—
182C4×D23—42no—
183C4×D23—42no—
184C4×D23—42no—
185Dic46—42no—
186Dic46—42no—
187C8×C23—42no—
188C8×C23—81no—
189C23⋊C8—42no—
190C23⋊C8—81no—
191#2297—231no—
192#1797—231no—
193#1749—231no—
194#1272—231no—
195#1272—231no—
196#1270—231no—
197#1270D2311yescharacteristic, complemented
198C22×C23—42no—
199C22×C23—42no—
200C22×C23—42no—
201C22×C23—81no—
202C22×C23—81no—
203C22×C23—81no—
204C22×C23—81no—
205C22×C23#40711yescharacteristic
206C22×C23C2×#9911yescharacteristic
207C22×C23C2×#10011yescharacteristic
208C22×C23#41611yescharacteristic
209C22×C23#41711yescharacteristic
210C22×C23C2×#10411yescharacteristic
211C22×C23#42111yescharacteristic
212C2×D23—22no—
213C2×D23—22no—
214C2×D23—22no—
215C2×D23—41no—
216C2×D23—41no—
217C2×D23—41no—
218C2×D23—41no—
219C4×C23—21no—
220C4×C23—21no—
221C4×C23—21no—
222C4×C23—21no—
223C4×C23—21no—
224C4×C23—21no—
225C4×C23—81no—
226Dic23—22no—
227Dic23—22no—
228Dic23—42no—
229Dic23—41no—
230Dic23—81no—
231C22×#41—231no—
232C2×#117—231no—
233C22×C42—231no—
234C2×C4⋊C8—461no—
235C2×C22⋊C8—461no—
236C2×C22⋊C8—461no—
237C2×#97—461no—
238#391—231no—
239#391—231no—
240#390—231no—
241#390C2×D2311yescharacteristic
242#386—461no—
243#386—461no—
244C4×C22⋊C4—461no—
245C4×C22⋊C4—461no—
246#336—231no—
247#336—231no—
248#336C2×D2311yescharacteristic
249#336C2×D2311yescharacteristic
250C2×C23—82no—
251C2×C23#146211yescharacteristic
252C2×C23#148811yescharacteristic
253C2×C23#148911yescharacteristic
254C2×C23#150111yescharacteristic
255C2×C23#151311yescharacteristic
256C2×C23#153011yescharacteristic
257C2×C23#155111yescharacteristic
258D23—42no—
259C2×#41—462no—
260C2×#41—462no—
261C2×#41—922no—
262C2×#41—922no—
263C22×Q8—231no—
264C22×D4—461no—
265C22×D4C4×D2311yescharacteristic
266C23×C4—231no—
267C23×C4—231no—
268C23×C4—231no—
269C23×C4—461no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—461no—
273C22×C8—461no—
274#117—922no—
275C2×C4⋊C4—231no—
276C2×C4⋊C4C4×D2311yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—461no—
280C2×C22⋊C4—461no—
281C2×C22⋊C4—461no—
282C2×C42—231no—
283C2×C42—231no—
284C2×C42—231no—
285C2×C42—461no—
286C2×C42—922no—
287C2×C42C22×D2311yescharacteristic
288C4⋊C8—922no—
289C22⋊C8—464no—
290C22⋊C8—922no—
291#97—922no—
292#95—461no—
293#95—461no—
294#95—461no—
295#95—461no—
296C23#761211yescharacteristic, complemented, Sylow
297C24—21no—
298C24—231no—
299#41—928no—
300#41—928no—
301C2×Q8—232no—
302C2×Q8—461no—
303C2×Q8—921no—
304C2×Q8—921no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—464no—
309C2×D4—922no—
310C2×D4—922no—
311C2×D4#6726212yes—
312C22×C4—21no—
313C22×C4—231no—
314C22×C4—231no—
315C22×C4—231no—
316C22×C4—462no—
317C22×C4—462no—
318C22×C4—462no—
319C22×C4—461no—
320C22×C4—461no—
321C22×C4—464no—
322C22×C4—461no—
323C22×C4—461no—
324C22×C4—461no—
325C22×C4—461no—
326C22×C4—461no—
327C22×C4—461no—
328C22×C4—921no—
329C22×C4—921no—
330C22×C4—921no—
331C22×C4—922no—
332C22×C4—922no—
333C22×C4C2×C4×D2311yescharacteristic
334C22×C4D4×D2311yescharacteristic
335C22×C4D4×D2311yescharacteristic
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—462no—
343C2×C8—921no—
344C2×C8—921no—
345C2×C8—921no—
346C2×C8—921no—
347C2×C8—921no—
348C4⋊C4—41no—
349C4⋊C4—921no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—922no—
355C22⋊C4—922no—
356C22⋊C4—922no—
357C42—41no—
358C42—462no—
359C42—462no—
360C42—921no—
361C42—922no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—232no—
370C23—461no—
371C23—461no—
372C23—461no—
373C23—461no—
374C23—461no—
375C23—461no—
376C23C22⋊C4×D2311yescharacteristic
377Q8—922no—
378Q8—922no—
379D4—42no—
380D4—42no—
381D4—928no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—232no—
392C2×C4—232no—
393C2×C4—464no—
394C2×C4—464no—
395C2×C4—461no—
396C2×C4—461no—
397C2×C4—461no—
398C2×C4—461no—
399C2×C4—462no—
400C2×C4—461no—
401C2×C4—461no—
402C2×C4—461no—
403C2×C4—922no—
404C2×C4—922no—
405C2×C4—922no—
406C2×C4—922no—
407C2×C4—928no—
408C2×C4—921no—
409C2×C4—921no—
410C2×C4—921no—
411C2×C4—921no—
412C2×C4—921no—
413C2×C4C2×#6726211yescharacteristic
414C2×C4M16×D2311yescharacteristic
415C2×C4#1062508211yescharacteristic
416C2×C4#1062508311yescharacteristic
417C2×C4#1062508611yescharacteristic
418C2×C4#1062508711yescharacteristic
419C8—42no—
420C8—81no—
421C8—922no—
422C8—1841no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—462no—
431C22—462no—
432C22—462no—
433C22—921no—
434C22—921no—
435C22—921no—
436C22—921no—
437C22#1309237911yescharacteristic
438C22#99×D2311yescharacteristic
439C22#100×D2311yescharacteristic
440C22#1309241011yescharacteristic
441C22#1309241511yescharacteristic
442C22#104×D2311yescharacteristic
443C22#1309243211yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—462no—
452C4—462no—
453C4—921no—
454C4—922no—
455C4—1841no—
456C2—82no—
457C2—922no—
458C2#1567172211yescharacteristic
459C2#1567182811yescharacteristic
460C2#1567183311yescharacteristic
461C2#1567188511yescharacteristic
462C2#1567193711yescharacteristic
463C2#1567200611yescharacteristic
464C2#1567208911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D23
commutatorC22×C4×C23C22×C4
FrattiniC2×C42C22×D23
FittingC23×#1270C2
socleC23×C23C2×C22⋊C4
hypercenter#1270D23
hypocenterC23#7612
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #15673376C2semidirect
3. #15673158C2semidirect
4. #15671222C2semidirect
5. #15671222C2semidirect
6. #15671218C2semidirect
7. C23×#1270C2semidirect
197. #1270D23semidirect
296. C23#7612semidirect