Finite Group Databasebeta

← #14673224

Subgroups — #14673224

Order 2816.

508 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×#10622179C211yesmaximal, characteristic
2C2×#10622177C211yesmaximal, characteristic
3#13069030C211yesmaximal, characteristic
4#13069005C211yesmaximal, characteristic
5#13068896C211yesmaximal, characteristic
6#13066734C211yesmaximal, characteristic
7C11×#2717C211yesmaximal, characteristic
8C2×C11×#124C2211yescharacteristic
9C2×C11×#123C2211yescharacteristic
10#10623329C2211yescharacteristic
11C11×#397—21no—
12C11×#397—21no—
13C11×#395—21no—
14C11×#387—21no—
15C11×#386C2211yescharacteristic
16C11×#385—21no—
17C11×#380—21no—
18#10622838—21no—
19C2×#66898C2211yescharacteristic
20C2×#66898C2211yescharacteristic
21C2×#66897C2211yescharacteristic
22#10622824—21no—
23#10622823—21no—
24#10622179—22no—
25#10622177—22no—
26#10622165—21no—
27#10622165—21no—
28#10622161—21no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11C2311yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C11×#124—21no—
34C11×#124—21no—
35C11×#124—21no—
36C11×#124—21no—
37C11×#123—21no—
38C11×#123—21no—
39C11×#123—21no—
40C11×#123—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4D411yescharacteristic
50C2×C11×C22⋊C4D411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—21no—
56D4×Dic11—41no—
57D4×Dic11—41no—
58#66979—21no—
59C2×Dic11⋊C4—41no—
60C2×#4318—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95—21no—
67#66899—41no—
68#66899—41no—
69#66898—21no—
70#66898—21no—
71#66898—21no—
72#66898D412yes—
73#66897—21no—
74#66897—21no—
75C11⋊#95—41no—
76C11⋊#95—41no—
77C11⋊#95—41no—
78#13425—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11C2×D411yescharacteristic
88C2×D4×C11#4111yescharacteristic
89C2×D4×C11#4111yescharacteristic
90C2×D4×C11#4111yescharacteristic
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—42no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—81no—
114C11×C4⋊C4—81no—
115C11×C22⋊C4—21no—
116C11×C22⋊C4—21no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—21no—
126C42×C11—21no—
127C22⋊Dic11—22no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—41no—
131C22⋊Dic11—41no—
132C22⋊Dic11—41no—
133C22⋊Dic11—41no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136Dic11⋊C4—82no—
137C4×Dic11—41no—
138#4318—41no—
139#4318—41no—
140C2×C11⋊C8—41no—
141#2717D1111yescharacteristic
142C2×#354—111no—
143C2×#352—111no—
144#1890—111no—
145#1885—111no—
146#1867—111no—
147#1390—111no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11#12011yescharacteristic
157C23×C11#12111yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12311yescharacteristic
160C23×C11#12411yescharacteristic
161Q8×C11—42no—
162Q8×C11—81no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—41no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12311yescharacteristic
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—81no—
197C2×Dic11—81no—
198C2×Dic11—81no—
199C2×Dic11—81no—
200C2×Dic11—81no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205C11⋊C8—81no—
206C2×#124C2×D1111yescharacteristic
207C2×#123C2×D1111yescharacteristic
208#518—111no—
209#419—221no—
210C2×#100—111no—
211C2×#99—111no—
212C2×#99—111no—
213#397—21no—
214#397—21no—
215#395—21no—
216#387—21no—
217#386C2×D1111yescharacteristic
218#385—21no—
219#385—221no—
220#381—221no—
221#380—21no—
222#354—222no—
223#352—222no—
224#342—221no—
225#342—221no—
226#339—221no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11#39411yescharacteristic
244C22×C11B(4,𝔽2)11yescharacteristic
245C22×C11#45811yescharacteristic
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—42no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11—81no—
253C4×C11—81no—
254Dic11—82no—
255Dic11—81no—
256Dic11—81no—
257Dic11—161no—
258C22×Q8C22⋊D1111yescharacteristic
259C22×D4C22×D1111yescharacteristic
260C23×C4C22⋊D1111yescharacteristic
261C23×C4C22⋊D1111yescharacteristic
262C2×M16—221no—
263#124—21no—
264#124—21no—
265#124—21no—
266#124—21no—
267#123—21no—
268#123—21no—
269#123—21no—
270#123—21no—
271C4×D4—441no—
272C4×D4—441no—
273#117—221no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—441no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—221no—
284C2×C22⋊C4—221no—
285C2×C22⋊C4—221no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4C22⋊D1111yescharacteristic
288C2×C22⋊C4C22⋊D1111yescharacteristic
289C2×C42C22⋊D1111yescharacteristic
290#103—441no—
291#103—441no—
292#100—221no—
293#100—221no—
294#99—112no—
295#99—221no—
296#99—221no—
297#99—221no—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—441no—
305#95—441no—
306#95—441no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—41no—
310C2×C11—41no—
311C2×C11—41no—
312C2×C11—41no—
313C2×C11#204411yescharacteristic
314C2×C11#219711yescharacteristic
315C2×C11#220111yescharacteristic
316C24C2×C22⋊D1111yescharacteristic
317C24C2×C22⋊D1111yescharacteristic
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—41no—
321C2×Q8—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4D4×D1111yescharacteristic
325C2×D4#434111yescharacteristic
326C2×D4#434111yescharacteristic
327C2×D4#434111yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—441no—
345C22×C4—441no—
346C22×C4C2×C22⋊D1111yescharacteristic
347M16—441no—
348M16—441no—
349C2×C8—441no—
350C4⋊C4—42no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—81no—
354C4⋊C4—81no—
355C4⋊C4—221no—
356C4⋊C4—221no—
357C4⋊C4—882no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—42no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—222no—
369C22⋊C4—441no—
370C22⋊C4—441no—
371C22⋊C4—441no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—441no—
375C42—21no—
376C42—21no—
377C42—441no—
378C11#1342511yescharacteristic, complemented, Sylow
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23#6698811yescharacteristic
388C23#6698911yescharacteristic
389C23#6699111yescharacteristic
390C23#6699211yescharacteristic
391C23#6700611yescharacteristic
392Q8—42no—
393Q8—81no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—881no—
426C2×C4—881no—
427C2×C4—881no—
428C2×C4—881no—
429C2×C4—881no—
430C2×C4—881no—
431C2×C4—881no—
432C2×C4—881no—
433C2×C4—881no—
434C2×C4#6698811yescharacteristic
435C2×C4#6699211yescharacteristic
436C8—881no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—81no—
452C22—81no—
453C22#1062283511yescharacteristic
454C22#1062285611yescharacteristic
455C22#1062285711yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4—882no—
465C4—881no—
466C4—881no—
467C4—1761no—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—41no—
474C2#1306986411yescharacteristic
475C2#1307060611yescharacteristic
476C2#1307062911yescharacteristic
subgroupG/H
centerC22#10622857
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#2717C2
socleC22×C11B(4,𝔽2)
hypercenter#2717D11
hypocenterC11#13425
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2717

Complements

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

NH ≅ G/Ntype
378. C11#13425semidirect

Maximal subgroups

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

subgroupindex
C2×#106221792
C2×#106221772
#130690302
#130690052
#130688962
#130667342
C11×#27172
#1342511