Finite Group Databasebeta

← #13175885

Subgroups — #13175885

Order 1728.

1664 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723919C211yesmaximal, characteristic, complemented
2C3×#64087C211yesmaximal, characteristic, complemented
3C32×#67⋊C4C211yesmaximal, characteristic
4#11723640C211yesmaximal, characteristic, complemented
5#67⋊(C3⋊Dic3)C211yesmaximal, characteristic
6#67×C3⋊Dic3C211yesmaximal, characteristic
7C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#11723496C211yesmaximal, characteristic, complemented
9#11723487C211yesmaximal, characteristic, complemented
10D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
11#11723443C211yesmaximal, characteristic, complemented
12#11723415C211yesmaximal, characteristic, complemented
13#11723401C211yesmaximal, characteristic, complemented
14#11723400C211yesmaximal, characteristic, complemented
15#11723389C211yesmaximal, characteristic, complemented
16#10596014—31nomaximal
17#10594146—34nomaximal
18C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#6308C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C33×C22⋊C4C2211yescharacteristic
29#88864C2211yescharacteristic
30C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
31#88857C2211yescharacteristic
32#88857C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40#88807C2211yescharacteristic
41#88806C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×C4×D4—31no—
54D4×C3⋊Dic3—31no—
55D4×C3⋊Dic3—31no—
56C2×C4⋊(C3⋊Dic3)—31no—
57C2×C4⋊(C3⋊Dic3)—31no—
58#64133—31no—
59#64133—31no—
60#64099—31no—
61#64099—31no—
62#64087—31no—
63#64087—31no—
64#64087—31no—
65#64087—34no—
66#64087—64no—
67#64087D311yescharacteristic, complemented
68#64078—31no—
69C4×#634—31no—
70C3×#67⋊C4D314yes—
71C3×#878—34no—
72#67⋊Dic3—34no—
73Dic3×#67—34no—
74C2×Dic3⋊Dic3—34no—
75#63964—34no—
76#63896—34no—
77D3×C4⋊Dic3—34no—
78#63887—34no—
79#63866—34no—
80#63851—34no—
81#63846—34no—
82#63845—34no—
83#63837—34no—
84C23×C33C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C33×C4C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C3⋊(C3⋊Dic3)—41no—
89C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
90C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93#6308—41no—
94C2×C3×C3⋊Dic3—41no—
95C2×C3×C3⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C3×#634—41no—
100C32×#67Q814yescomplemented
101C2×C32×Dic3—22no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C32×C4×D3—22no—
106#6293—22no—
107D3×C3⋊Dic3—41no—
108D3×C3⋊Dic3—41no—
109#5636—91no—
110#5543—94no—
111C2×C32×D4—31no—
112C22×C32×C4—31no—
113C22×C32×C4—31no—
114C22×C3⋊Dic3—31no—
115C22×C3⋊Dic3—34no—
116C22×C3⋊Dic3—31no—
117C22×C3⋊Dic3—31no—
118C22×C3⋊Dic3—64no—
119C22×C3⋊Dic3C2×D311yescharacteristic
120C2×#634—31no—
121C2×#634—31no—
122C2×#634—34no—
123C2×#634—64no—
124C2×#634C2×D311yescharacteristic
125C2×C3×#67C2×D314yes—
126C22×C3×Dic3—34no—
127C22×C3×Dic3C2×D314yes—
128C2×C3×C4×D3C2×D314yes—
129C2×C3×Dic6—34no—
130C2×#627—34no—
131C2×D3×Dic3—34no—
132C2×D3×Dic3—34no—
133C32×C4⋊C4—31no—
134C32×C22⋊C4—24no—
135C32×C22⋊C4—31no—
136C32×C22⋊C4C2×D314yes—
137C32×C22⋊C4C2×D311yescharacteristic
138C32×C42—31no—
139#3757—31no—
140#3757—34no—
141#3757—31no—
142#3757—31no—
143#3757—64no—
144#3757C2×D311yescharacteristic
145C4⋊(C3⋊Dic3)—31no—
146C4⋊(C3⋊Dic3)—34no—
147C4⋊(C3⋊Dic3)—31no—
148C4⋊(C3⋊Dic3)—31no—
149C4⋊(C3⋊Dic3)—31no—
150C4⋊(C3⋊Dic3)—31no—
151C4⋊(C3⋊Dic3)—31no—
152C4⋊(C3⋊Dic3)—31no—
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—64no—
155C4⋊(C3⋊Dic3)C2×D311yescharacteristic
156#3750—31no—
157#3750—31no—
158#3750—34no—
159#3750—34no—
160#3750—31no—
161#3750—31no—
162#3750—64no—
163#3750—64no—
164#3750C2×D311yescharacteristic
165#3750C2×D311yescharacteristic
166C4×C3⋊Dic3—31no—
167C4×C3⋊Dic3—31no—
168C3×#217—34no—
169C3×(C2×D3)⋊C4C2×D314yes—
170C3×C4⋊Dic3—34no—
171C3×Dic3⋊C4—34no—
172C3×Dic3⋊C4—34no—
173C3×Dic3⋊C4C2×D314yes—
174C3×C4×Dic3C2×D314yes—
175#3724—34no—
176Dic3⋊Dic3—34no—
177Dic3⋊Dic3—34no—
178Dic3⋊Dic3—34no—
179Dic3⋊Dic3—34no—
180Dic3⋊Dic3—34no—
181Dic3⋊Dic3—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185(C2×D3)⋊Dic3—34no—
186Dic32—34no—
187Dic32—34no—
188C22×C33—21no—
189C22×C33—21no—
190C22×C33C2×Q812yes—
191C22×C33C2411yescharacteristic
192C2×C32×D3—21no—
193C2×C32×D3—21no—
194C2×C32×D3C2×Q812yes—
195C33×C4—21no—
196C33×C4—21no—
197C3⋊(C3⋊Dic3)—21no—
198C3⋊(C3⋊Dic3)—21no—
199C3⋊(C3⋊Dic3)—21no—
200C3⋊(C3⋊Dic3)—21no—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3—21no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3C2×Q812yes—
207C32×Dic3#4112yes—
208C3×C22⋊Q8—91no—
209C3×C4×D4—34no—
210#946—91no—
211#944—91no—
212D4×Dic3—94no—
213D4×Dic3—94no—
214C4×#67—91no—
215C2×C4⋊Dic3—94no—
216C2×C4⋊Dic3—94no—
217#924—94no—
218#924—94no—
219C2×Dic3⋊C4—91no—
220#896—91no—
221#896—91no—
222D3×C4⋊C4—91no—
223#890—94no—
224#890—94no—
225#889—91no—
226#889—91no—
227#887—91no—
228#67⋊C4—91no—
229#67⋊C4C3⋊D311yescharacteristic
230#878—34no—
231#878—94no—
232#878—94no—
233#878—91no—
234#878—94no—
235#878—91no—
236#878—184no—
237#869—94no—
238C4×Dic6—94no—
239C23×C32—24no—
240C23×C32—31no—
241C23×C32C22×D314yes—
242C23×C32C22×D311yescharacteristic
243C22×C3×D3C22×D314yes—
244C32×D4—34no—
245C2×C32×C4—24no—
246C2×C32×C4—24no—
247C2×C32×C4—31no—
248C2×C32×C4—31no—
249C2×C32×C4—31no—
250C2×C32×C4—62no—
251C2×C32×C4—62no—
252C2×C32×C4C22×D314yes—
253C2×C32×C4C22×D314yes—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—34no—
261C2×C3⋊Dic3—34no—
262C2×C3⋊Dic3—34no—
263C2×C3⋊Dic3—34no—
264C2×C3⋊Dic3—41no—
265C2×C3⋊Dic3—64no—
266C2×C3⋊Dic3—64no—
267C2×C3⋊Dic3—64no—
268C2×C3⋊Dic3—64no—
269C2×C3⋊Dic3—121no—
270C2×C3⋊Dic3—121no—
271C2×C3⋊Dic3—121no—
272C2×C3⋊Dic3—124no—
273C2×C3⋊Dic3—128no—
274C2×C3⋊Dic3C22×D311yescharacteristic
275C2×C3⋊Dic3C22×D311yescharacteristic
276C2×C3⋊Dic3C22×D311yescharacteristic
277C2×C3⋊Dic3C22×D311yescharacteristic
278#634—41no—
279#634—62no—
280#634—121no—
281#634—124no—
282#634—128no—
283C3×#67Dic6116yescomplemented
284C2×C3×Dic3—28no—
285C2×C3×Dic3—34no—
286C2×C3×Dic3—34no—
287C2×C3×Dic3—34no—
288C2×C3×Dic3—34no—
289C2×C3×Dic3—124no—
290C2×C3×Dic3C22×D314yes—
291C2×C3×Dic3C22×D314yes—
292C2×C3×Dic3C22×D314yes—
293C3×C4×D3—28no—
294C3×Dic6—124no—
295#627—68no—
296D3×Dic3—124no—
297D3×Dic3—124no—
298#554—271noSylow
299C2×C33—22no—
300C2×C33C22×Q811yescharacteristic
301C2×C33C2×#4111yescharacteristic
302C2×C33H(5,𝔽2)11yescharacteristic
303C32×D3—22no—
304C2×C3×Q8—91no—
305C2×C3×D4—34no—
306C22×C3×C4—34no—
307C22×C3×C4—34no—
308C22×C3×C4—91no—
309C2×#67C2×C3⋊D311yescharacteristic
310C22×Dic3—34no—
311C22×Dic3—94no—
312C22×Dic3—94no—
313C22×Dic3—94no—
314C22×Dic3—91no—
315C22×Dic3—184no—
316C22×Dic3C2×C3⋊D311yescharacteristic
317C2×C4×D3—91no—
318C2×C4×D3—91no—
319C2×C4×D3C2×C3⋊D311yescharacteristic
320C2×Dic6—34no—
321C2×Dic6—94no—
322C2×Dic6—91no—
323C2×Dic6—94no—
324C2×Dic6—91no—
325C2×Dic6—184no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C22⋊C4—24no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—91no—
333C3×C22⋊C4D3214yes—
334C3×C22⋊C4C2×C3⋊D311yescharacteristic
335C3×C42—34no—
336#217—34no—
337#217—94no—
338#217—94no—
339#217—94no—
340#217—91no—
341#217—184no—
342(C2×D3)⋊C4—91no—
343(C2×D3)⋊C4—91no—
344(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
345C4⋊Dic3—34no—
346C4⋊Dic3—94no—
347C4⋊Dic3—94no—
348C4⋊Dic3—94no—
349C4⋊Dic3—94no—
350C4⋊Dic3—94no—
351C4⋊Dic3—94no—
352C4⋊Dic3—94no—
353C4⋊Dic3—94no—
354C4⋊Dic3—91no—
355C4⋊Dic3—91no—
356C4⋊Dic3—184no—
357Dic3⋊C4—34no—
358Dic3⋊C4—34no—
359Dic3⋊C4—94no—
360Dic3⋊C4—94no—
361Dic3⋊C4—94no—
362Dic3⋊C4—94no—
363Dic3⋊C4—91no—
364Dic3⋊C4—91no—
365Dic3⋊C4—91no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—184no—
374Dic3⋊C4—184no—
375Dic3⋊C4C2×C3⋊D311yescharacteristic
376C4×Dic3—94no—
377C4×Dic3—94no—
378C4×Dic3—91no—
379C4×Dic3—91no—
380C4×Dic3C2×C3⋊D311yescharacteristic
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—24no—
384C22×C32—28no—
385C22×C32—24no—
386C22×C32—24no—
387C22×C32—32no—
388C22×C32—44no—
389C22×C32—44no—
390C22×C32—61no—
391C22×C32—61no—
392C22×C32C2×Dic618yes—
393C22×C32D3×Q812yes—
394C22×C32C23×D314yes—
395C22×C32C23×D311yescharacteristic
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3C2×Dic618yes—
399C32×C4—21no—
400C32×C4—21no—
401C32×C4—24no—
402C32×C4—24no—
403C32×C4—32no—
404C32×C4—32no—
405C32×C4—44no—
406C32×C4—44no—
407C32×C4—61no—
408C3⋊Dic3—21no—
409C3⋊Dic3—21no—
410C3⋊Dic3—21no—
411C3⋊Dic3—21no—
412C3⋊Dic3—68no—
413C3⋊Dic3—61no—
414C3⋊Dic3—61no—
415C3⋊Dic3—61no—
416C3⋊Dic3—61no—
417C3⋊Dic3—64no—
418C3⋊Dic3—64no—
419C3⋊Dic3—64no—
420C3⋊Dic3—64no—
421C3⋊Dic3—124no—
422C3⋊Dic3—124no—
423C3⋊Dic3—124no—
424C3×Dic3—24no—
425C3×Dic3—64no—
426C3×Dic3—64no—
427C3×Dic3—64no—
428C3×Dic3—64no—
429C3×Dic3C2×Dic618yes—
430C3×Dic3#23718yes—
431C4⋊Q8—271no—
432#125—271no—
433#125—271no—
434C22⋊Q8—91no—
435C22⋊Q8—271no—
436C22⋊Q8—271no—
437C22⋊Q8—271no—
438C22⋊Q8—271no—
439C22⋊Q8—271no—
440C4×Q8—271no—
441C4×D4—31no—
442C4×D4—271no—
443C4×D4—271no—
444C2×C4⋊C4—271no—
445C2×C4⋊C4—271no—
446C33#55411yescharacteristic, complemented, Sylow
447C23×C3—24no—
448C23×C3—34no—
449C23×C3C2×D3214yes—
450C23×C3C22×C3⋊D311yescharacteristic
451C22×D3C22×C3⋊D311yescharacteristic
452C3×Q8—361no—
453C3×D4—316no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—34no—
457C2×C3×C4—34no—
458C2×C3×C4—34no—
459C2×C3×C4—68no—
460C2×C3×C4—68no—
461C2×C3×C4—91no—
462C2×C3×C4—91no—
463C2×C3×C4—91no—
464C2×C3×C4—91no—
465C2×C3×C4—361no—
466C2×C3×C4C2×D3214yes—
467C2×C3×C4C2×D3214yes—
468C2×C3×C4C22×C3⋊D311yescharacteristic
469C2×C3×C4C22×C3⋊D311yescharacteristic
470#67#63414yescomplemented
471C2×Dic3—22no—
472C2×Dic3—34no—
473C2×Dic3—34no—
474C2×Dic3—34no—
475C2×Dic3—34no—
476C2×Dic3—94no—
477C2×Dic3—94no—
478C2×Dic3—94no—
479C2×Dic3—94no—
480C2×Dic3—91no—
481C2×Dic3—91no—
482C2×Dic3—91no—
483C2×Dic3—91no—
484C2×Dic3—124no—
485C2×Dic3—184no—
486C2×Dic3—184no—
487C2×Dic3—184no—
488C2×Dic3—184no—
489C2×Dic3—364no—
490C2×Dic3—364no—
491C2×Dic3—364no—
492C2×Dic3—361no—
493C2×Dic3—368no—
494C2×Dic3C22×C3⋊D311yescharacteristic
495C2×Dic3C22×C3⋊D311yescharacteristic
496C2×Dic3C22×C3⋊D311yescharacteristic
497C4×D3—22no—
498C4×D3—361no—
499C4×D3—361no—
500Dic6—124no—
501Dic6—188no—
502Dic6—182no—
503Dic6—364no—
504Dic6—361no—
505Dic6—368no—
506C2×C32—22no—
507C2×C32—24no—
508C2×C32—24no—
509C2×C32—24no—
510C2×C32—28no—
511C2×C32—48no—
512C2×C32—62no—
513C2×C32C22×Dic614yes—
514C2×C32C2×#23714yes—
515C2×C32#100411yescharacteristic
516C2×C32C2×D3×Q811yescharacteristic
517C2×C32D3×#4111yescharacteristic
518C2×C32#100914yes—
519C3×D3—28no—
520C2×Q8—91no—
521C2×Q8—271no—
522C2×Q8—271no—
523C2×D4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—91no—
527C22×C4—271no—
528C22×C4—271no—
529C22×C4—271no—
530C4⋊C4—31no—
531C4⋊C4—91no—
532C4⋊C4—91no—
533C4⋊C4—91no—
534C4⋊C4—271no—
535C4⋊C4—271no—
536C4⋊C4—271no—
537C4⋊C4—271no—
538C4⋊C4—271no—
539C4⋊C4—271no—
540C4⋊C4—271no—
541C4⋊C4—271no—
542C4⋊C4—271no—
543C4⋊C4—271no—
544C4⋊C4—271no—
545C4⋊C4—271no—
546C22⋊C4—31no—
547C22⋊C4—91no—
548C22⋊C4—271no—
549C22⋊C4—271no—
550C22⋊C4—271no—
551C22⋊C4D3×C3⋊D311yescharacteristic
552C42—31no—
553C42—271no—
554C42—271no—
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—24no—
560C22×C3—28no—
561C22×C3—38no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—64no—
565C22×C3—64no—
566C22×C3D3×Dic618yes—
567C22×C3C2×#63412yes—
568C22×C3C22×D3214yes—
569C22×C3C23×C3⋊D311yescharacteristic
570C2×D3—21no—
571C2×D3—21no—
572C2×D3C2×#63412yes—
573C3×C4—24no—
574C3×C4—24no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—38no—
578C3×C4—38no—
579C3×C4—44no—
580C3×C4—44no—
581C3×C4—64no—
582C3×C4—181no—
583C3×C4—181no—
584C3×C4—181no—
585C3×C4—181no—
586Dic3—21no—
587Dic3—64no—
588Dic3—64no—
589Dic3—64no—
590Dic3—64no—
591Dic3—188no—
592Dic3—184no—
593Dic3—184no—
594Dic3—184no—
595Dic3—184no—
596Dic3—181no—
597Dic3—181no—
598Dic3—181no—
599Dic3—181no—
600Dic3—364no—
601Dic3—364no—
602Dic3—364no—
603Dic3C2×#63412yes—
604Dic3#383012yes—
605C32—24no—
606C32#554314yescomplemented
607C32#563611yescharacteristic, complemented
608C23—31no—
609C23C2×D3×C3⋊D311yescharacteristic
610Q8—361no—
611Q8—542no—
612Q8—1081no—
613D4—34no—
614C2×C4—31no—
615C2×C4—31no—
616C2×C4—31no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—91no—
620C2×C4—91no—
621C2×C4—91no—
622C2×C4—91no—
623C2×C4—271no—
624C2×C4—271no—
625C2×C4—271no—
626C2×C4—271no—
627C2×C4—361no—
628C2×C4—1081no—
629C2×C4—1081no—
630C2×C4—1081no—
631C2×C4C2×D3×C3⋊D311yescharacteristic
632C2×C4C2×D3×C3⋊D311yescharacteristic
633C2×C3—28no—
634C2×C3—22no—
635C2×C3—24no—
636C2×C3—24no—
637C2×C3—24no—
638C2×C3—48no—
639C2×C3—68no—
640C2×C3C2×D3×Dic614yes—
641C2×C3D3×#23714yes—
642C2×C3#6431414yes—
643C2×C3C22×#63411yescharacteristic
644C2×C3C2×#383011yescharacteristic
645C2×C3#6436611yescharacteristic
646D3—22no—
647C22—21no—
648C22—21no—
649C22—32no—
650C22—61no—
651C22—61no—
652C22D3×#63412yes—
653C22C22×D3×C3⋊D311yescharacteristic
654C4—21no—
655C4—21no—
656C4—32no—
657C4—32no—
658C4—61no—
659C4—181no—
660C4—181no—
661C4—181no—
662C4—181no—
663C4—541no—
664C4—541no—
665C4—541no—
666C4—541no—
667C3—24no—
668C3#1059414614yescomplemented
669C3#1059601411yescharacteristic, complemented
670C2—22no—
671C2—62no—
672C2C2×D3×#63411yescharacteristic
673C2D3×#383011yescharacteristic
674C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×C32×#67C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723919C2semidirect
2. C3×#64087C2semidirect
4. #11723640C2semidirect
7. C2×Dic3⋊(C3⋊Dic3)C2semidirect
8. #11723496C2semidirect
9. #11723487C2semidirect
10. D3×C4⋊(C3⋊Dic3)C2semidirect
11. #11723443C2semidirect
12. #11723415C2semidirect
13. #11723401C2semidirect
14. #11723400C2semidirect
15. #11723389C2semidirect
67. #64087D3semidirect
100. C32×#67Q8semidirect
283. C3×#67Dic6semidirect
446. C33#554semidirect
470. #67#634semidirect
606. C32#5543semidirect
607. C32#5636semidirect
668. C3#10594146semidirect
669. C3#10596014semidirect

Maximal subgroups

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

subgroupindex
#117239192
C3×#640872
C32×#67⋊C42
#117236402
#67⋊(C3⋊Dic3)2
#67×C3⋊Dic32
C2×Dic3⋊(C3⋊Dic3)2
#117234962
#117234872
D3×C4⋊(C3⋊Dic3)2
#117234432
#117234152
#117234012
#117234002
#117233892
#105960143
#105941463