Finite Group Databasebeta

← D3×#63861 #13168023

Subgroups — D3×#63861 #13168023

Order 1728.

1222 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723675C211yesmaximal, characteristic, complemented
2D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3#11723430C211yesmaximal, characteristic, complemented
4#11723408C211yesmaximal, characteristic, complemented
5C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
6C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C3×#63861C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723026C211yesmaximal, characteristic, complemented
10#11723023C211yesmaximal, characteristic, complemented
11#11723022C211yesmaximal, characteristic, complemented
12D3×#3724C211yesmaximal, characteristic, complemented
13D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
14D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
15D3×Dic32C211yesmaximal, characteristic, complemented
16C2×#63861—31nomaximal
17D3×#898—31nomaximal
18D3×#879—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
27C3×#3752C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C3×#3750C2211yescharacteristic, complemented
30C32×(C2×D3)⋊C4C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic, complemented
32#88815C2211yescharacteristic, complemented
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88813C2211yescharacteristic, complemented
36#88806C2211yescharacteristic, complemented
37#88806C2211yescharacteristic, complemented
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54C2×C4⋊(C3⋊Dic3)—31no—
55#64107—31no—
56#64088—31no—
57C2×C3×(C2×D3)⋊C4—31no—
58C2×C3×Dic3⋊C4—31no—
59C3×#898—31no—
60C3×D3×C4⋊C4—31no—
61C3×D3×C22⋊C4—31no—
62C3×#879—31no—
63D3×#217—31no—
64D3×#217—31no—
65C2×#3724—31no—
66C2×(C2×D3)⋊Dic3—31no—
67C2×(C2×D3)⋊Dic3—31no—
68#63956—31no—
69#63956—31no—
70C2×Dic32—31no—
71D3×(C2×D3)⋊C4—31no—
72D3×(C2×D3)⋊C4—31no—
73D3×(C2×D3)⋊C4D311yescharacteristic
74D3×C4⋊Dic3—31no—
75D3×C4⋊Dic3—31no—
76D3×C4⋊Dic3—61no—
77D3×Dic3⋊C4—31no—
78D3×Dic3⋊C4—31no—
79D3×Dic3⋊C4D311yescharacteristic, complemented
80C4×D3×Dic3—31no—
81C4×D3×Dic3—31no—
82#63868—31no—
83#63862—31no—
84#63862—31no—
85#63861—31no—
86#63861—31no—
87#63861—31no—
88#63861—31no—
89#63861—31no—
90#63861—31no—
91#63861—31no—
92#63861—31no—
93#63861—31no—
94#63861—61no—
95#63861—61no—
96#63861D311yescharacteristic, direct product factor
97#63859—31no—
98#63858—31no—
99#63858—31no—
100#63848—31no—
101#63848—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C3×D32—22no—
106C2×C3×D32—22no—
107C2×C3×D32—22no—
108C2×C33×C4C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×C4×D3—22no—
121D3×C3⋊Dic3—22no—
122D3×C3⋊Dic3—22no—
123C3×D3×Dic3—22no—
124C3×D3×Dic3—22no—
125C3×D3×Dic3—22no—
126D3×#126—91no—
127C2×#898—91no—
128C2×#879—91no—
129C23×C3×D3—31no—
130C23×C3×D3—31no—
131C22×D32C2×D311yescharacteristic
132C22×C32×C4—31no—
133C22×C3⋊Dic3—31no—
134C22×C3⋊Dic3—31no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—31no—
137C22×C3×Dic3—31no—
138C2×C3×C4×D3—21no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3C2×D311yescharacteristic
143C2×C3×C4×D3C2×D311yescharacteristic
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—61no—
149C2×D3×Dic3—61no—
150C2×D3×Dic3C2×D311yescharacteristic
151C2×D3×Dic3C2×D311yescharacteristic
152C2×D3×Dic3C2×D311yescharacteristic
153C32×C4⋊C4—31no—
154C32×C22⋊C4—31no—
155#3757—31no—
156#3757—31no—
157#3752—31no—
158#3752—31no—
159#3752C2×D311yescharacteristic
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)—31no—
162C4⋊(C3⋊Dic3)—31no—
163C4⋊(C3⋊Dic3)—31no—
164C4⋊(C3⋊Dic3)—31no—
165C4⋊(C3⋊Dic3)—61no—
166C4⋊(C3⋊Dic3)—61no—
167C4⋊(C3⋊Dic3)—61no—
168C4⋊(C3⋊Dic3)—121no—
169C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
170#3750—31no—
171#3750—31no—
172#3750C2×D311yescharacteristic, complemented
173C4×C3⋊Dic3—31no—
174C4×C3⋊Dic3—31no—
175C3×#217—31no—
176C3×#217—31no—
177C3×#217—31no—
178C3×(C2×D3)⋊C4—21no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—61no—
187C3×(C2×D3)⋊C4C2×D311yescharacteristic
188C3×(C2×D3)⋊C4C2×D311yescharacteristic
189C3×C4⋊Dic3—31no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—61no—
193C3×Dic3⋊C4—21no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—61no—
202C3×Dic3⋊C4C2×D311yescharacteristic, complemented
203C3×Dic3⋊C4C2×D311yescharacteristic, complemented
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—61no—
212#3724—61no—
213#3724C2×D311yescharacteristic, complemented
214#3724C2×D311yescharacteristic, complemented
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3C2×D311yescharacteristic, complemented
224#3722—31no—
225#3722—31no—
226#3722C2×D311yescharacteristic
227(C2×D3)⋊Dic3—31no—
228(C2×D3)⋊Dic3—31no—
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—61no—
240(C2×D3)⋊Dic3—61no—
241(C2×D3)⋊Dic3—61no—
242(C2×D3)⋊Dic3—61no—
243(C2×D3)⋊Dic3C2×D311yescharacteristic
244(C2×D3)⋊Dic3C2×D311yescharacteristic
245(C2×D3)⋊Dic3C2×D311yescharacteristic
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—61no—
254Dic32—61no—
255Dic32C2×D311yescharacteristic, complemented
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3#4112yes—
264C2×C32×D3#4112yes—
265C2×C32×D3#4112yes—
266C3×D32—44no—
267C33×C4—21no—
268C3⋊(C3⋊Dic3)—21no—
269C3⋊(C3⋊Dic3)—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C32×Dic3—21no—
279C3×#126—91no—
280C2×C3×C4⋊C4—91no—
281C2×C3×C22⋊C4—91no—
282C2×#217—91no—
283C2×#217—91no—
284C2×(C2×D3)⋊C4—31no—
285C2×(C2×D3)⋊C4—91no—
286C2×(C2×D3)⋊C4—91no—
287C2×C4⋊Dic3—91no—
288C2×C4⋊Dic3—91no—
289C2×C4⋊Dic3—181no—
290C2×Dic3⋊C4—31no—
291C2×Dic3⋊C4—91no—
292C2×Dic3⋊C4—91no—
293C2×C4×Dic3—91no—
294C2×C4×Dic3—91no—
295#898—31no—
296#898—91no—
297#898—91no—
298#898—91no—
299#898—91no—
300#898—91no—
301#898—91no—
302#898—91no—
303#898—91no—
304#898—91no—
305#898—91no—
306#898—181no—
307D3×C4⋊C4—31no—
308D3×C4⋊C4—91no—
309D3×C4⋊C4—91no—
310D3×C22⋊C4—31no—
311D3×C22⋊C4—91no—
312D3×C22⋊C4—91no—
313#879—31no—
314#879—91no—
315#879—91no—
316#879—91no—
317#879—91no—
318#879—91no—
319#879—91no—
320#879—91no—
321#879—91no—
322#879—91no—
323#879—91no—
324#879—181no—
325#876—91no—
326C42×D3—91no—
327C23×C32—31no—
328C23×C32—31no—
329C22×C3⋊D3C22×D311yescharacteristic
330C22×C3×D3—21no—
331C22×C3×D3—21no—
332C22×C3×D3—31no—
333C22×C3×D3—31no—
334C22×C3×D3—61no—
335C22×C3×D3—62no—
336C22×C3×D3—62no—
337C22×C3×D3—62no—
338C22×C3×D3—62no—
339C22×C3×D3—62no—
340C22×C3×D3—62no—
341C22×C3×D3C22×D311yescharacteristic
342C22×C3×D3C22×D311yescharacteristic
343C22×C3×D3C22×D311yescharacteristic
344C22×C3×D3C22×D311yescharacteristic
345C2×D32—22no—
346C2×D32—22no—
347C2×D32—22no—
348C2×C32×C4—21no—
349C2×C32×C4—21no—
350C2×C32×C4—21no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—41no—
356C2×C32×C4—62no—
357C2×C32×C4C22×D311yescharacteristic
358C2×C32×C4C22×D311yescharacteristic
359C2×C32×C4C22×D311yescharacteristic
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—61no—
372C2×C3⋊Dic3—62no—
373C2×C3⋊Dic3—62no—
374C2×C3⋊Dic3—121no—
375C2×C3⋊Dic3—121no—
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3×Dic3—21no—
382C2×C3×Dic3—21no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—21no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—62no—
401C2×C3×Dic3—62no—
402C2×C3×Dic3—62no—
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C3×C4×D3—24no—
412C3×C4×D3—22no—
413C3×C4×D3—22no—
414C3×C4×D3—62no—
415C3×C4×D3—62no—
416C3×C4×D3—62no—
417D3×Dic3—22no—
418D3×Dic3—22no—
419D3×Dic3—22no—
420D3×Dic3—62no—
421D3×Dic3—62no—
422D3×Dic3—62no—
423D3×Dic3—62no—
424D3×Dic3—122no—
425D3×Dic3—122no—
426C2×#126—271noSylow
427C2×C33C2×#4111yescharacteristic
428C2×C33C2×#4111yescharacteristic
429C2×C33C2×#4111yescharacteristic
430C3×C3⋊D3—41no—
431C32×D3—41no—
432C32×D3#12614yescomplemented
433C24×C3—91no—
434C23×D3—31no—
435C23×D3—31no—
436C22×C3×C4—31no—
437C22×C3×C4—31no—
438C22×C3×C4—61no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C22×C3×C4—91no—
442C22×Dic3—31no—
443C22×Dic3—31no—
444C22×Dic3—31no—
445C22×Dic3—91no—
446C22×Dic3—91no—
447C22×Dic3—91no—
448C22×Dic3—91no—
449C22×Dic3—181no—
450C22×Dic3—181no—
451C2×C4×D3—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3D3211yescharacteristic
457C3×C4⋊C4—31no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—61no—
460C3×C4⋊C4—91no—
461C3×C4⋊C4—91no—
462C3×C4⋊C4—91no—
463C3×C4⋊C4—91no—
464C3×C4⋊C4—91no—
465C3×C22⋊C4—31no—
466C3×C22⋊C4—31no—
467C3×C22⋊C4—61no—
468C3×C22⋊C4—91no—
469C3×C22⋊C4—91no—
470C3×C22⋊C4—91no—
471C3×C22⋊C4—91no—
472C3×C22⋊C4—91no—
473C3×C42—91no—
474#217—31no—
475#217—31no—
476#217—31no—
477#217—91no—
478#217—91no—
479#217—91no—
480#217—91no—
481#217—91no—
482#217—91no—
483#217—91no—
484#217—91no—
485#217—181no—
486#217—181no—
487(C2×D3)⋊C4—31no—
488(C2×D3)⋊C4—31no—
489(C2×D3)⋊C4—31no—
490(C2×D3)⋊C4—31no—
491(C2×D3)⋊C4—31no—
492(C2×D3)⋊C4—31no—
493(C2×D3)⋊C4—31no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—91no—
496(C2×D3)⋊C4—91no—
497(C2×D3)⋊C4—91no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—181no—
506(C2×D3)⋊C4—181no—
507(C2×D3)⋊C4D3211yescharacteristic
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—31no—
511C4⋊Dic3—61no—
512C4⋊Dic3—91no—
513C4⋊Dic3—91no—
514C4⋊Dic3—91no—
515C4⋊Dic3—91no—
516C4⋊Dic3—91no—
517C4⋊Dic3—91no—
518C4⋊Dic3—91no—
519C4⋊Dic3—91no—
520C4⋊Dic3—181no—
521C4⋊Dic3—181no—
522C4⋊Dic3—181no—
523C4⋊Dic3—181no—
524C4⋊Dic3—181no—
525C4⋊Dic3—361no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—61no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—181no—
545Dic3⋊C4—181no—
546Dic3⋊C4D3211yescharacteristic, complemented
547C4×Dic3—31no—
548C4×Dic3—31no—
549C4×Dic3—91no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C4×Dic3—91no—
553C4×Dic3—91no—
554C4×Dic3—91no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—181no—
559C4×Dic3—181no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—32no—
564C22×C32—32no—
565C22×C32—32no—
566C22×C32—41no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32C23×D311yescharacteristic
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3×D3—21no—
577C2×C3×D3—21no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—22no—
585C2×C3×D3—41no—
586C2×C3×D3—41no—
587C2×C3×D3—41no—
588C2×C3×D3—61no—
589C2×C3×D3—61no—
590C2×C3×D3—61no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—61no—
594C2×C3×D3—121no—
595C2×C3×D3—121no—
596C2×C3×D3—121no—
597C2×C3×D3—124no—
598C2×C3×D3—124no—
599C2×C3×D3#23512yes—
600C2×C3×D3#23512yes—
601C2×C3×D3#23712yes—
602C2×C3×D3#23712yes—
603C2×C3×D3#23712yes—
604C2×C3×D3#23912yes—
605D32—44no—
606C32×C4—21no—
607C32×C4—22no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—41no—
611C32×C4—41no—
612C32×C4—42no—
613C32×C4—61no—
614C32×C4—61no—
615C32×C4—61no—
616C32×C4—61no—
617C3⋊Dic3—21no—
618C3⋊Dic3—21no—
619C3⋊Dic3—21no—
620C3⋊Dic3—21no—
621C3⋊Dic3—21no—
622C3⋊Dic3—61no—
623C3⋊Dic3—61no—
624C3⋊Dic3—61no—
625C3⋊Dic3—61no—
626C3⋊Dic3—61no—
627C3⋊Dic3—61no—
628C3⋊Dic3—121no—
629C3⋊Dic3—121no—
630C3⋊Dic3—121no—
631C3⋊Dic3—121no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—241no—
635C3⋊Dic3—241no—
636C3×Dic3—22no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—121no—
659C3×Dic3—121no—
660C3×Dic3—121no—
661C3×Dic3—121no—
662C3×Dic3—121no—
663#126—91no—
664#126—271no—
665#126—271no—
666#126—271no—
667#126—271no—
668#126—271no—
669#126—271no—
670#126—271no—
671C2×C4⋊C4—91no—
672C2×C4⋊C4—271no—
673C2×C4⋊C4—271no—
674C2×C22⋊C4—91no—
675C2×C22⋊C4—271no—
676C2×C22⋊C4—271no—
677C2×C42—271no—
678C33C2×#12611yescharacteristic, complemented, Sylow
679C23×C3—31no—
680C23×C3—31no—
681C23×C3—31no—
682C23×C3—31no—
683C23×C3—61no—
684C23×C3—61no—
685C23×C3—91no—
686C23×C3—182no—
687C23×C3—182no—
688C23×C3—182no—
689C22×D3—31no—
690C22×D3—31no—
691C22×D3—61no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—62no—
698C22×D3C2×D3211yescharacteristic
699C22×D3C2×D3211yescharacteristic
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—41no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—62no—
717C2×C3×C4—62no—
718C2×C3×C4—64no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—91no—
724C2×C3×C4—182no—
725C2×C3×C4—182no—
726C2×C3×C4—182no—
727C2×C3×C4C2×D3211yescharacteristic
728C2×C3×C4C2×D3211yescharacteristic
729C2×C3×C4C2×D3211yescharacteristic
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—62no—
746C2×Dic3—62no—
747C2×Dic3—62no—
748C2×Dic3—91no—
749C2×Dic3—91no—
750C2×Dic3—91no—
751C2×Dic3—91no—
752C2×Dic3—91no—
753C2×Dic3—91no—
754C2×Dic3—181no—
755C2×Dic3—181no—
756C2×Dic3—181no—
757C2×Dic3—181no—
758C2×Dic3—181no—
759C2×Dic3—181no—
760C2×Dic3—182no—
761C2×Dic3—182no—
762C2×Dic3—182no—
763C2×Dic3—182no—
764C2×Dic3—361no—
765C2×Dic3—361no—
766C2×Dic3—362no—
767C2×Dic3—362no—
768C2×Dic3C2×D3211yescharacteristic
769C2×Dic3C2×D3211yescharacteristic
770C2×Dic3C2×D3211yescharacteristic
771C2×Dic3C2×D3211yescharacteristic
772C4×D3—22no—
773C4×D3—62no—
774C4×D3—62no—
775C4×D3—62no—
776C4×D3—182no—
777C4×D3—182no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—34no—
788C2×C32—41no—
789C2×C32—41no—
790C2×C32—41no—
791C2×C32—121no—
792C2×C32C2×#23511yescharacteristic
793C2×C32C2×#23511yescharacteristic
794C2×C32C2×#23711yescharacteristic
795C2×C32C2×#23711yescharacteristic
796C2×C32C2×#23711yescharacteristic
797C2×C32C2×#23911yescharacteristic
798C2×C32D3×#4111yescharacteristic
799C2×C32D3×#4111yescharacteristic
800C2×C32D3×#4111yescharacteristic
801C3⋊D3—41no—
802C3×D3—24no—
803C3×D3—41no—
804C3×D3—41no—
805C3×D3—81no—
806C3×D3—121no—
807C3×D3—121no—
808C3×D3—241no—
809C3×D3#87914yescomplemented
810C3×D3#89814yescomplemented
811C24—91no—
812C22×C4—31no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—91no—
816C22×C4—271no—
817C22×C4—271no—
818C4⋊C4—31no—
819C4⋊C4—91no—
820C4⋊C4—91no—
821C4⋊C4—91no—
822C4⋊C4—91no—
823C4⋊C4—91no—
824C4⋊C4—271no—
825C4⋊C4—271no—
826C4⋊C4—271no—
827C4⋊C4—271no—
828C4⋊C4—271no—
829C4⋊C4—271no—
830C22⋊C4—31no—
831C22⋊C4—91no—
832C22⋊C4—91no—
833C22⋊C4—91no—
834C22⋊C4—91no—
835C22⋊C4—91no—
836C22⋊C4—271no—
837C22⋊C4—271no—
838C22⋊C4—271no—
839C22⋊C4—271no—
840C22⋊C4—271no—
841C22⋊C4—271no—
842C42—91no—
843C42—271no—
844C42—271no—
845C42—271no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—32no—
850C22×C3—32no—
851C22×C3—32no—
852C22×C3—32no—
853C22×C3—32no—
854C22×C3—32no—
855C22×C3—41no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—61no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—61no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—121no—
868C22×C3—181no—
869C22×C3—181no—
870C22×C3—181no—
871C22×C3—364no—
872C22×C3C22×D3211yescharacteristic
873C22×C3C22×D3211yescharacteristic
874C22×C3C22×D3211yescharacteristic
875C2×D3—21no—
876C2×D3—21no—
877C2×D3—21no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—61no—
883C2×D3—61no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—124no—
888C2×D3—124no—
889C2×D3#379512yes—
890C2×D3#379912yes—
891C2×D3#380512yes—
892C3×C4—22no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—42no—
899C3×C4—62no—
900C3×C4—61no—
901C3×C4—61no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—61no—
907C3×C4—61no—
908C3×C4—121no—
909C3×C4—121no—
910C3×C4—121no—
911C3×C4—181no—
912C3×C4—181no—
913C3×C4—181no—
914C3×C4—181no—
915C3×C4—181no—
916Dic3—21no—
917Dic3—21no—
918Dic3—21no—
919Dic3—21no—
920Dic3—61no—
921Dic3—61no—
922Dic3—61no—
923Dic3—61no—
924Dic3—61no—
925Dic3—61no—
926Dic3—61no—
927Dic3—61no—
928Dic3—61no—
929Dic3—61no—
930Dic3—121no—
931Dic3—121no—
932Dic3—121no—
933Dic3—121no—
934Dic3—121no—
935Dic3—181no—
936Dic3—181no—
937Dic3—181no—
938Dic3—181no—
939Dic3—181no—
940Dic3—181no—
941Dic3—361no—
942Dic3—361no—
943Dic3—361no—
944Dic3—361no—
945Dic3—361no—
946Dic3—361no—
947Dic3—721no—
948Dic3—721no—
949C32—21no—
950C32—21no—
951C32—21no—
952C32—41no—
953C32C2×#87911yescharacteristic, complemented
954C32C2×#89811yescharacteristic, complemented
955C32D3×#12611yescharacteristic, complemented
956C23—31no—
957C23—31no—
958C23—91no—
959C23—182no—
960C23—182no—
961C23—182no—
962C2×C4—31no—
963C2×C4—31no—
964C2×C4—31no—
965C2×C4—31no—
966C2×C4—62no—
967C2×C4—91no—
968C2×C4—91no—
969C2×C4—91no—
970C2×C4—91no—
971C2×C4—91no—
972C2×C4—182no—
973C2×C4—182no—
974C2×C4—182no—
975C2×C4—271no—
976C2×C4—271no—
977C2×C4—542no—
978C2×C4—542no—
979C2×C4D3311yescharacteristic
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—34no—
990C2×C3—34no—
991C2×C3—41no—
992C2×C3—41no—
993C2×C3—41no—
994C2×C3—64no—
995C2×C3—121no—
996C2×C3—121no—
997C2×C3—241no—
998C2×C3—361no—
999C2×C3C2×#379511yescharacteristic
1000C2×C3C2×#379911yescharacteristic
1001C2×C3D3×#23511yescharacteristic
1002C2×C3D3×#23511yescharacteristic
1003C2×C3D3×#23711yescharacteristic
1004C2×C3D3×#23711yescharacteristic
1005C2×C3D3×#23711yescharacteristic
1006C2×C3D3×#23911yescharacteristic
1007C2×C3C2×#380511yescharacteristic
1008D3—41no—
1009D3—121no—
1010D3—121no—
1011D3—241no—
1012D3#6386114yesdirect product factor
1013C22—32no—
1014C22—32no—
1015C22—32no—
1016C22—61no—
1017C22—61no—
1018C22—61no—
1019C22—181no—
1020C22—181no—
1021C22—181no—
1022C22—364no—
1023C22C2×D3311yescharacteristic
1024C4—21no—
1025C4—61no—
1026C4—61no—
1027C4—61no—
1028C4—61no—
1029C4—181no—
1030C4—181no—
1031C4—181no—
1032C4—181no—
1033C4—181no—
1034C4—541no—
1035C4—541no—
1036C3—21no—
1037C3—21no—
1038C3—21no—
1039C3—41no—
1040C3D3×#87911yescharacteristic, complemented
1041C3D3×#89811yescharacteristic, complemented
1042C3C2×#6386111yescharacteristic, complemented
1043C2—34no—
1044C2—121no—
1045C2—361no—
1046C2D3×#379511yescharacteristic
1047C2D3×#379911yescharacteristic
1048C2D3×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×D32C22
hypercenterC2×C4D33
hypocenterC33C2×#126
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723675C2semidirect
2. D3×C4⋊(C3⋊Dic3)C2semidirect
3. #11723430C2semidirect
4. #11723408C2semidirect
6. C3×D3×Dic3⋊C4C2semidirect
7. C3×#63861C2semidirect
8. #11723027C2semidirect
9. #11723026C2semidirect
10. #11723023C2semidirect
11. #11723022C2semidirect
12. D3×#3724C2semidirect
15. D3×Dic32C2semidirect
26. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
28. C3×C4⋊(C3⋊Dic3)C22semidirect
29. C3×#3750C22semidirect
31. C32×Dic3⋊C4C22semidirect
32. #88815C22semidirect
35. #88813C22semidirect
36. #88806C22semidirect
37. #88806C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×#3724C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
79. D3×Dic3⋊C4D3semidirect
96. #63861D3direct (N × H)
169. C4⋊(C3⋊Dic3)C2×D3semidirect
172. #3750C2×D3semidirect
202. C3×Dic3⋊C4C2×D3semidirect
203. C3×Dic3⋊C4C2×D3semidirect
213. #3724C2×D3semidirect
214. #3724C2×D3semidirect
223. Dic3⋊Dic3C2×D3semidirect
255. Dic32C2×D3semidirect
432. C32×D3#126semidirect
546. Dic3⋊C4D32semidirect
678. C33C2×#126semidirect
809. C3×D3#879semidirect
810. C3×D3#898semidirect
953. C32C2×#879semidirect
954. C32C2×#898semidirect
955. C32D3×#126semidirect
1012. D3#63861direct (N × H)
1040. C3D3×#879semidirect
1041. C3D3×#898semidirect
1042. C3C2×#63861semidirect

Maximal subgroups

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

subgroupindex
#117236752
D3×C4⋊(C3⋊Dic3)2
#117234302
#117234082
C3×D3×(C2×D3)⋊C42
C3×D3×Dic3⋊C42
C3×#638612
#117230272
#117230262
#117230232
#117230222
D3×#37242
D3×(C2×D3)⋊Dic32
D3×Dic322
C2×#638613
D3×#8983
D3×#8793