Finite Group Databasebeta

← #72229143

Subgroups — #72229143

Order 5832.

1860 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 1860 conjugacy classes of subgroups — too many to draw. Only its 105 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#72228915C212yesmaximal, complemented
2C2×#13091503C211yesmaximal, characteristic
3#14518830—32nomaximal
4#14518795—32nomaximal
5#14517113—32nomaximal
6#13091503C412yescomplemented
7C2×H(3,𝔽3)2C2211yescharacteristic
8C2×C3⋊(C3⋊((C3⋊D3)⋊C3))D312yes—
9C2×C3×C3⋊((C3⋊D3)⋊C3)—32no—
10C3⋊(C3⋊#1084)D312yescomplemented
11C3×C3⋊#1084—32no—
12C3×C3⋊((C3⋊Dic3)⋊C3)—32no—
13C3×C3⋊((C3⋊Dic3)⋊C3)—32no—
14C3×C3⋊((C3⋊Dic3)⋊C3)—62no—
15C2×#92301D312yes—
16C2×#92258—61no—
17#11757604—34no—
18#11757604—64no—
19#11757604—62no—
20H(3,𝔽3)2C2×C411yescharacteristic, complemented, Sylow
21#10620155—91no—
22#10620154—92no—
23#10620150—91no—
24#10619901—96no—
25#10619883—92no—
26#10619883—94no—
27((C3⋊D3)⋊C3)⋊Dic3—96no—
28C2×C32×H(3,𝔽3)—22no—
29C2×C32×H(3,𝔽3)C2×D312yes—
30C2×C32×H(3,𝔽3)C2×D312yes—
31C3⋊(C3⋊((C3⋊D3)⋊C3))Dic314yescomplemented
32C3×C3⋊((C3⋊D3)⋊C3)—34no—
33C2×C32⋊H(3,𝔽3)—22no—
34C2×C32⋊H(3,𝔽3)—21no—
35C2×C32⋊H(3,𝔽3)—24no—
36C2×C32⋊H(3,𝔽3)—42no—
37C2×C32⋊H(3,𝔽3)—42no—
38C2×C32⋊H(3,𝔽3)C2×D312yes—
39#92301Dic314yescomplemented
40#92258—62no—
41C2×C3⋊(C3⋊(C3⋊D3))C3⋊D311yescharacteristic
42C2×C3×C3⋊(C3⋊D3)—32no—
43C2×C32×C3⋊D3—91no—
44C3×C3⋊(C3⋊Dic3)—32no—
45C3×C3⋊(C3⋊Dic3)—32no—
46C3×C3⋊(C3⋊Dic3)—62no—
47C32×C3⋊Dic3—92no—
48C32×C3⋊Dic3—92no—
49C32×C3⋊Dic3—182no—
50C2×C3⋊((C3⋊D3)⋊C3)—32no—
51C2×C3⋊((C3⋊D3)⋊C3)—34no—
52C2×C3⋊((C3⋊D3)⋊C3)—62no—
53C2×C3⋊((C3⋊D3)⋊C3)—62no—
54C2×C3⋊((C3⋊D3)⋊C3)—96no—
55C2×C3×(C3⋊D3)⋊C3—96no—
56C3⋊#1084—32no—
57C3⋊#1084—34no—
58C3⋊#1084—62no—
59C3⋊#1084—64no—
60C3⋊#1084—96no—
61C3⋊#1084—186no—
62C3×#1084—96no—
63C3×#1084—186no—
64C3⋊((C3⋊Dic3)⋊C3)—36no—
65C3⋊((C3⋊Dic3)⋊C3)—36no—
66C3⋊((C3⋊Dic3)⋊C3)—66no—
67C3×(C3⋊Dic3)⋊C3—94no—
68C3×(C3⋊Dic3)⋊C3—92no—
69C3×(C3⋊Dic3)⋊C3—184no—
70C3×(C3⋊Dic3)⋊C3—182no—
71C32×H(3,𝔽3)—22no—
72C32×H(3,𝔽3)C4×D312yescomplemented
73C32×H(3,𝔽3)C2×Dic312yescomplemented
74C32⋊H(3,𝔽3)—22no—
75C32⋊H(3,𝔽3)—21no—
76C32⋊H(3,𝔽3)—24no—
77C32⋊H(3,𝔽3)—42no—
78C32⋊H(3,𝔽3)—42no—
79C32⋊H(3,𝔽3)C2×Dic312yescomplemented
80#6294—272no—
81#6294—272no—
82#6294—276no—
83#6289—272no—
84#6289—276no—
85Dic3×C3⋊D3—272no—
86D3×C3⋊Dic3—272no—
87((C3⋊D3)⋊C3)⋊C4—276no—
88((C3⋊D3)⋊C3)⋊C4—2712no—
89C2×C34—22no—
90C2×C34—22no—
91C2×C34—41no—
92C2×C34D3212yes—
93C2×C34D3211yescharacteristic
94C2×C34C2×C3⋊D311yescharacteristic
95C3⋊(C3⋊(C3⋊D3))C3⋊Dic312yescomplemented
96C3×C3⋊(C3⋊D3)—34no—
97C32×C3⋊D3—92no—
98C2×C3×H(3,𝔽3)—24no—
99C2×C3×H(3,𝔽3)—22no—
100C2×C3×H(3,𝔽3)—22no—
101C2×C3×H(3,𝔽3)—24no—
102C2×C3×H(3,𝔽3)—22no—
103C2×C3×H(3,𝔽3)—22no—
104C2×C3×H(3,𝔽3)—36no—
105C2×C3×H(3,𝔽3)—36no—
106C2×C3×H(3,𝔽3)—42no—
107C2×C3×H(3,𝔽3)—44no—
108C2×C3×H(3,𝔽3)—42no—
109C2×C3×H(3,𝔽3)—42no—
110C2×C3×H(3,𝔽3)—41no—
111C2×C3×H(3,𝔽3)—44no—
112C2×C3×H(3,𝔽3)—42no—
113C2×C3×H(3,𝔽3)—42no—
114C2×C3×H(3,𝔽3)—66no—
115C2×C3×H(3,𝔽3)—66no—
116C2×C3×H(3,𝔽3)—66no—
117C2×C3×H(3,𝔽3)—126no—
118C2×C3×H(3,𝔽3)D3212yes—
119C2×C3×H(3,𝔽3)D3214yes—
120C3⋊((C3⋊D3)⋊C3)—34no—
121C3⋊((C3⋊D3)⋊C3)—38no—
122C3⋊((C3⋊D3)⋊C3)—64no—
123C3⋊((C3⋊D3)⋊C3)—64no—
124C3⋊((C3⋊D3)⋊C3)—912no—
125C3×(C3⋊D3)⋊C3—912no—
126C2×C3⋊(C3⋊D3)—32no—
127C2×C3⋊(C3⋊D3)—61no—
128C2×C3⋊(C3⋊D3)—96no—
129C2×C3⋊(C3⋊D3)—541no—
130C2×C3×C3⋊D3—96no—
131C2×C3×C3⋊D3—92no—
132C2×C3×C3⋊D3—92no—
133C2×C3×C3⋊D3—272no—
134C2×C3×C3⋊D3—542no—
135C2×C32×D3—272no—
136C2×C32×D3—541no—
137C3⋊(C3⋊Dic3)—32no—
138C3⋊(C3⋊Dic3)—32no—
139C3⋊(C3⋊Dic3)—62no—
140C3×C3⋊Dic3—96no—
141C3×C3⋊Dic3—96no—
142C3×C3⋊Dic3—92no—
143C3×C3⋊Dic3—92no—
144C3×C3⋊Dic3—94no—
145C3×C3⋊Dic3—92no—
146C3×C3⋊Dic3—182no—
147C3×C3⋊Dic3—184no—
148C3×C3⋊Dic3—182no—
149C3×C3⋊Dic3—186no—
150C3×C3⋊Dic3—272no—
151C3×C3⋊Dic3—276no—
152C3×C3⋊Dic3—542no—
153C3×C3⋊Dic3—546no—
154C32×Dic3—272no—
155C32×Dic3—276no—
156C32×Dic3—272no—
157C32×Dic3—546no—
158C32×Dic3—542no—
159C2×(C3⋊D3)⋊C3—912no—
160C2×(C3⋊D3)⋊C3—96no—
161C2×(C3⋊D3)⋊C3—542no—
162C2×(C3⋊D3)⋊C3—542no—
163#1084—96no—
164#1084—186no—
165#1084—2712no—
166#1084—542no—
167#1084—5412no—
168#1084—544no—
169(C3⋊Dic3)⋊C3—912no—
170(C3⋊Dic3)⋊C3—96no—
171(C3⋊Dic3)⋊C3—186no—
172(C3⋊Dic3)⋊C3—1812no—
173C34—22no—
174C34—22no—
175C34—41no—
176C34D3×Dic312yescomplemented
177C34#62411yescharacteristic, complemented
178C34C2×C3⋊Dic311yescharacteristic, complemented
179C3×H(3,𝔽3)—24no—
180C3×H(3,𝔽3)—22no—
181C3×H(3,𝔽3)—24no—
182C3×H(3,𝔽3)—22no—
183C3×H(3,𝔽3)—22no—
184C3×H(3,𝔽3)—22no—
185C3×H(3,𝔽3)—36no—
186C3×H(3,𝔽3)—36no—
187C3×H(3,𝔽3)—42no—
188C3×H(3,𝔽3)—44no—
189C3×H(3,𝔽3)—42no—
190C3×H(3,𝔽3)—42no—
191C3×H(3,𝔽3)—41no—
192C3×H(3,𝔽3)—44no—
193C3×H(3,𝔽3)—42no—
194C3×H(3,𝔽3)—42no—
195C3×H(3,𝔽3)—66no—
196C3×H(3,𝔽3)—66no—
197C3×H(3,𝔽3)—66no—
198C3×H(3,𝔽3)—126no—
199C3×H(3,𝔽3)D3×Dic312yes—
200C3×H(3,𝔽3)D3×Dic314yescomplemented
201C2×C3⋊Dic3—811no—
202C4×C3⋊D3—812no—
203#624—816no—
204#624—811no—
205#624—819no—
206D3×Dic3—812no—
207D3×Dic3—816no—
208D3×Dic3—814no—
209D3×Dic3—812no—
210C2×C33—22no—
211C2×C33—21no—
212C2×C33—22no—
213C2×C33—24no—
214C2×C33—32no—
215C2×C33—36no—
216C2×C33—32no—
217C2×C33—36no—
218C2×C33—42no—
219C2×C33—42no—
220C2×C33—62no—
221C2×C33—66no—
222C2×C33—62no—
223C2×C33—66no—
224C2×C33—62no—
225C2×C33—66no—
226C2×C33—122no—
227C2×C33—126no—
228C2×C33—181no—
229C2×C33—181no—
230C2×C33—182no—
231C2×C33—362no—
232C2×C33—362no—
233C2×C33—361no—
234C2×C33—361no—
235C2×C33D3×C3⋊D312yes—
236C2×C33#111312yes—
237C2×C33#111312yes—
238C3⋊(C3⋊D3)—34no—
239C3⋊(C3⋊D3)—62no—
240C3⋊(C3⋊D3)—912no—
241C3⋊(C3⋊D3)—542no—
242C3×C3⋊D3—94no—
243C3×C3⋊D3—94no—
244C3×C3⋊D3—912no—
245C3×C3⋊D3—274no—
246C3×C3⋊D3—544no—
247C32×D3—274no—
248C32×D3—542no—
249C2×H(3,𝔽3)—26no—
250C2×H(3,𝔽3)—312no—
251C2×H(3,𝔽3)—612no—
252C2×H(3,𝔽3)—64no—
253C2×H(3,𝔽3)—62no—
254C2×H(3,𝔽3)—66no—
255C2×H(3,𝔽3)—612no—
256C2×H(3,𝔽3)—62no—
257C2×H(3,𝔽3)—126no—
258C2×H(3,𝔽3)—1212no—
259C2×H(3,𝔽3)—122no—
260C2×H(3,𝔽3)—124no—
261C2×H(3,𝔽3)—122no—
262C2×H(3,𝔽3)—182no—
263C2×H(3,𝔽3)—362no—
264C2×H(3,𝔽3)—362no—
265C2×H(3,𝔽3)—361no—
266C2×H(3,𝔽3)—364no—
267C2×H(3,𝔽3)—362no—
268C2×H(3,𝔽3)((C3⋊D3)⋊C3)⋊C216yes—
269(C3⋊D3)⋊C3—924no—
270(C3⋊D3)⋊C3—912no—
271(C3⋊D3)⋊C3—544no—
272(C3⋊D3)⋊C3—544no—
273C22×C32—811no—
274C2×C3⋊D3—91no—
275C2×C3⋊D3—96no—
276C2×C3⋊D3—272no—
277C2×C3⋊D3—542no—
278C2×C3⋊D3—542no—
279C2×C3⋊D3—542no—
280C2×C3⋊D3—819no—
281C2×C3×D3—274no—
282C2×C3×D3—272no—
283C2×C3×D3—272no—
284C2×C3×D3—542no—
285C2×C3×D3—542no—
286C2×C3×D3—816no—
287C32×C4—812no—
288C3⋊Dic3—92no—
289C3⋊Dic3—92no—
290C3⋊Dic3—94no—
291C3⋊Dic3—92no—
292C3⋊Dic3—182no—
293C3⋊Dic3—182no—
294C3⋊Dic3—184no—
295C3⋊Dic3—272no—
296C3⋊Dic3—276no—
297C3⋊Dic3—542no—
298C3⋊Dic3—546no—
299C3×Dic3—276no—
300C3×Dic3—2718no—
301C3×Dic3—276no—
302C3×Dic3—276no—
303C3×Dic3—272no—
304C3×Dic3—272no—
305C3×Dic3—546no—
306C3×Dic3—542no—
307C3×Dic3—546no—
308C3×Dic3—5418no—
309C3×Dic3—814no—
310C3×Dic3—812no—
311C3×Dic3—1624no—
312C3×Dic3—1622no—
313C33—22no—
314C33—21no—
315C33—22no—
316C33—24no—
317C33—32no—
318C33—36no—
319C33—32no—
320C33—36no—
321C33—42no—
322C33—42no—
323C33—62no—
324C33—66no—
325C33—62no—
326C33—66no—
327C33—62no—
328C33—66no—
329C33—122no—
330C33—126no—
331C33—181no—
332C33—181no—
333C33—182no—
334C33—362no—
335C33—362no—
336C33—361no—
337C33—361no—
338C33D3×C3⋊Dic312yes—
339C33#629412yes—
340C33#629412yes—
341H(3,𝔽3)—26no—
342H(3,𝔽3)—312no—
343H(3,𝔽3)—612no—
344H(3,𝔽3)—64no—
345H(3,𝔽3)—62no—
346H(3,𝔽3)—66no—
347H(3,𝔽3)—612no—
348H(3,𝔽3)—62no—
349H(3,𝔽3)—126no—
350H(3,𝔽3)—122no—
351H(3,𝔽3)—1212no—
352H(3,𝔽3)—124no—
353H(3,𝔽3)—122no—
354H(3,𝔽3)—182no—
355H(3,𝔽3)—362no—
356H(3,𝔽3)—362no—
357H(3,𝔽3)—361no—
358H(3,𝔽3)—364no—
359H(3,𝔽3)—362no—
360H(3,𝔽3)((C3⋊D3)⋊C3)⋊C416yescomplemented
361C2×Dic3—2432no—
362C2×Dic3—2432no—
363C4×D3—2432no—
364C4×D3—2436no—
365C2×C32—22no—
366C2×C32—26no—
367C2×C32—32no—
368C2×C32—32no—
369C2×C32—34no—
370C2×C32—62no—
371C2×C32—62no—
372C2×C32—62no—
373C2×C32—62no—
374C2×C32—62no—
375C2×C32—64no—
376C2×C32—62no—
377C2×C32—62no—
378C2×C32—64no—
379C2×C32—62no—
380C2×C32—91no—
381C2×C32—99no—
382C2×C32—96no—
383C2×C32—122no—
384C2×C32—122no—
385C2×C32—124no—
386C2×C32—122no—
387C2×C32—124no—
388C2×C32—122no—
389C2×C32—122no—
390C2×C32—124no—
391C2×C32—122no—
392C2×C32—182no—
393C2×C32—186no—
394C2×C32—186no—
395C2×C32—1818no—
396C2×C32—361no—
397C2×C32—366no—
398C2×C32—369no—
399C2×C32—812no—
400C2×C32((C3⋊D3)⋊C3)⋊D316yes—
401C2×C32#6643212yes—
402C2×C32C3⋊#111311yescharacteristic
403C3⋊D3—92no—
404C3⋊D3—912no—
405C3⋊D3—274no—
406C3⋊D3—544no—
407C3⋊D3—544no—
408C3⋊D3—544no—
409C3⋊D3—8118no—
410C3×D3—278no—
411C3×D3—274no—
412C3×D3—274no—
413C3×D3—544no—
414C3×D3—544no—
415C3×D3—8112no—
416C22×C3—812no—
417C22×C3—812no—
418C2×D3—272no—
419C2×D3—541no—
420C2×D3—816no—
421C2×D3—4861no—
422C3×C4—816no—
423C3×C4—812no—
424Dic3—276no—
425Dic3—272no—
426Dic3—272no—
427Dic3—542no—
428Dic3—546no—
429Dic3—812no—
430Dic3—814no—
431Dic3—1622no—
432Dic3—1624no—
433C32—22no—
434C32—26no—
435C32—32no—
436C32—32no—
437C32—34no—
438C32—62no—
439C32—62no—
440C32—62no—
441C32—62no—
442C32—62no—
443C32—62no—
444C32—64no—
445C32—62no—
446C32—62no—
447C32—64no—
448C32—91no—
449C32—96no—
450C32—99no—
451C32—122no—
452C32—122no—
453C32—124no—
454C32—122no—
455C32—124no—
456C32—122no—
457C32—122no—
458C32—124no—
459C32—122no—
460C32—182no—
461C32—186no—
462C32—186no—
463C32—1818no—
464C32—361no—
465C32—366no—
466C32—369no—
467C32((C3⋊D3)⋊C3)⋊Dic316yescomplemented
468C32#1061990112yescomplemented
469C32#1062015511yescharacteristic
470C2×C4—7291noSylow
471C2×C3—21no—
472C2×C3—32no—
473C2×C3—36no—
474C2×C3—62no—
475C2×C3—66no—
476C2×C3—92no—
477C2×C3—182no—
478C2×C3—184no—
479C2×C3—181no—
480C2×C3—362no—
481C2×C3—362no—
482C2×C3—814no—
483C2×C3—814no—
484C2×C3#1175809012yes—
485D3—274no—
486D3—542no—
487D3—8112no—
488D3—4862no—
489C22—811no—
490C4—812no—
491C3—21no—
492C3—36no—
493C3—32no—
494C3—62no—
495C3—66no—
496C3—92no—
497C3—181no—
498C3—182no—
499C3—184no—
500C3—362no—
501C3—362no—
502C3#1451883212yes—
503C2—812no—
504C2#7221438511yescharacteristic
subgroupG/H
center, hypercenterC2#72214385
commutator, hypocenterH(3,𝔽3)2C2×C4
Frattini, socleC2×C32C3⋊#1113
Fitting, cosocleC2×H(3,𝔽3)2C22
prime radicalC2×#13091503C2
LCSG ▷ H(3,𝔽3)2
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #72228915C2semidirect
6. #13091503C4semidirect
10. C3⋊(C3⋊#1084)D3semidirect
20. H(3,𝔽3)2C2×C4semidirect
31. C3⋊(C3⋊((C3⋊D3)⋊C3))Dic3semidirect
39. #92301Dic3semidirect
72. C32×H(3,𝔽3)C4×D3semidirect
73. C32×H(3,𝔽3)C2×Dic3semidirect
79. C32⋊H(3,𝔽3)C2×Dic3semidirect
95. C3⋊(C3⋊(C3⋊D3))C3⋊Dic3semidirect
176. C34D3×Dic3semidirect
177. C34#624semidirect
178. C34C2×C3⋊Dic3semidirect
200. C3×H(3,𝔽3)D3×Dic3semidirect
360. H(3,𝔽3)((C3⋊D3)⋊C3)⋊C4semidirect
467. C32((C3⋊D3)⋊C3)⋊Dic3semidirect
468. C32#10619901semidirect

Maximal subgroups

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

subgroupindex
#722289152
C2×#130915032
#145188303
#145187953
#145171133