Finite Group Databasebeta

← #13169347

Subgroups — #13169347

Order 1728.

980 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723676C211yesmaximal, characteristic
2#11723476C211yesmaximal, characteristic
3#11723445C211yesmaximal, characteristic, complemented
4#11723405C211yesmaximal, characteristic, complemented
5C3×#63848C211yesmaximal, characteristic
6C3×#63843C211yesmaximal, characteristic, complemented
7C3×#63839C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic
9#11723023C211yesmaximal, characteristic
10#11723014C211yesmaximal, characteristic, complemented
11#11723012C211yesmaximal, characteristic, complemented
12#11723012C211yesmaximal, characteristic, complemented
13#11722974C211yesmaximal, characteristic
14Dic3×#627C211yesmaximal, characteristic, complemented
15#11722919C211yesmaximal, characteristic
16#10595354—31nomaximal
17#10594446—31nomaximal
18#10594418—31nomaximal
19C2×C32×Dic6C2211yescharacteristic
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C2×C3×#627C2211yescharacteristic
22#88857C2211yescharacteristic
23C3×#3752C2211yescharacteristic
24C3×#3750C2211yescharacteristic
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27C32×Dic3⋊C4C2211yescharacteristic
28#88815C2211yescharacteristic
29#88815C2211yescharacteristic
30#88814C2211yescharacteristic
31#88814C2211yescharacteristic
32#88807C2211yescharacteristic
33#88807C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88803C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×Dic32C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64155—31no—
55#64098—31no—
56#64098—31no—
57C3×Q8×Dic3—31no—
58C3×#944—31no—
59C3×#898—31no—
60C3×#898—31no—
61C3×#888—31no—
62C3×#887—31no—
63C4×#627—31no—
64#63893—31no—
65#63887—31no—
66#63887—31no—
67#63887—31no—
68#63887—61no—
69#63877—31no—
70#63877—31no—
71#63874—31no—
72#63871—31no—
73#63869—31no—
74#63869—31no—
75#63868—31no—
76#63868—31no—
77#63867—31no—
78#63867—31no—
79#63867—31no—
80#63867—31no—
81#63867—31no—
82#63867—31no—
83#63867—61no—
84#63862—31no—
85#63862—31no—
86#63861—31no—
87#63859—31no—
88#63859—31no—
89#63858—31no—
90#63848—31no—
91#63848D311yescharacteristic
92#63847—31no—
93#63847—31no—
94#63847—31no—
95#63847—61no—
96#63846—31no—
97#63846—31no—
98#63843D311yescharacteristic, complemented
99Dic3×Dic6—31no—
100Dic3×Dic6—31no—
101#63839D311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×Dic6—22no—
118Dic3×C3⋊D3—22no—
119C3×#627—22no—
120#5731—91no—
121#5701—91no—
122#5583—91no—
123C2×C32×Q8—31no—
124C2×C4×C3⋊D3—31no—
125C2×C3×Dic6—21no—
126C2×C3×Dic6—31no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6C2×D311yescharacteristic
129C2×C3×Dic6C2×D311yescharacteristic
130C2×#627C2×D311yescharacteristic
131C2×D3×Dic3—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—61no—
134C32×C4⋊C4—31no—
135C32×C4⋊C4—31no—
136#3752—31no—
137#3752C2×D311yescharacteristic
138C4⋊(C3⋊Dic3)—31no—
139C4⋊(C3⋊Dic3)—31no—
140C4⋊(C3⋊Dic3)—31no—
141#3750—31no—
142#3750—31no—
143#3750—31no—
144#3750—31no—
145#3750—31no—
146#3750—31no—
147#3750—31no—
148#3750—31no—
149#3750—31no—
150#3750—61no—
151#3750—61no—
152#3750—61no—
153#3750—121no—
154#3750C2×D311yescharacteristic
155C4×C3⋊Dic3—31no—
156C4×C3⋊Dic3C2×D311yescharacteristic
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—31no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—31no—
163C3×(C2×D3)⋊C4—61no—
164C3×C4⋊Dic3—21no—
165C3×C4⋊Dic3—31no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3C2×D311yescharacteristic
170C3×C4⋊Dic3C2×D311yescharacteristic
171C3×Dic3⋊C4—21no—
172C3×Dic3⋊C4—31no—
173C3×Dic3⋊C4—31no—
174C3×Dic3⋊C4—31no—
175C3×Dic3⋊C4—31no—
176C3×Dic3⋊C4—31no—
177C3×Dic3⋊C4—31no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4—31no—
180C3×Dic3⋊C4—61no—
181C3×Dic3⋊C4C2×D311yescharacteristic
182C3×Dic3⋊C4C2×D311yescharacteristic
183C3×C4×Dic3—31no—
184C3×C4×Dic3—31no—
185C3×C4×Dic3—31no—
186C3×C4×Dic3—31no—
187C3×C4×Dic3—31no—
188C3×C4×Dic3—31no—
189C3×C4×Dic3—31no—
190C3×C4×Dic3—31no—
191C3×C4×Dic3—31no—
192C3×C4×Dic3—31no—
193C3×C4×Dic3—61no—
194#3724—31no—
195#3724—31no—
196#3724—31no—
197#3724—31no—
198#3724—31no—
199#3724—31no—
200#3724—31no—
201#3724—31no—
202#3724—61no—
203#3724—61no—
204#3724—61no—
205#3724C2×D311yescharacteristic
206Dic3⋊Dic3—31no—
207Dic3⋊Dic3—31no—
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232#3722—31no—
233#3722—31no—
234#3722C2×D311yescharacteristic
235#3722C2×D311yescharacteristic
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—61no—
243Dic32—31no—
244Dic32—31no—
245Dic32—61no—
246Dic32C2×D311yescharacteristic
247Dic32C2×D311yescharacteristic
248Dic32C2×D311yescharacteristic
249Dic32C2×D311yescharacteristic
250C22×C33C2411yescharacteristic
251C2×C3×C3⋊D3—21no—
252C2×C3×C3⋊D3—21no—
253C2×C3×C3⋊D3—21no—
254C33×C4—21no—
255C3⋊(C3⋊Dic3)—21no—
256C3⋊(C3⋊Dic3)—21no—
257C3×C3⋊Dic3—21no—
258C3×C3⋊Dic3—21no—
259C3×C3⋊Dic3—21no—
260C3×C3⋊Dic3—21no—
261C3×C3⋊Dic3—21no—
262C32×Dic3—21no—
263C32×Dic3—21no—
264C32×Dic3—21no—
265C32×Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3#4112yes—
268C3×C4⋊Q8—91no—
269C3×#126—91no—
270C3×C4×Q8—91no—
271#946—91no—
272#946—91no—
273#946—91no—
274#946—181no—
275Q8×Dic3—31no—
276Q8×Dic3—91no—
277#944—31no—
278#898—31no—
279#898—31no—
280#898—91no—
281#898—91no—
282#898—91no—
283#898—91no—
284#897—91no—
285#890—91no—
286#890—91no—
287#889—91no—
288#889—91no—
289#889—91no—
290#889—91no—
291#889—91no—
292#889—91no—
293#889—91no—
294#889—91no—
295#889—91no—
296#889—181no—
297#889—181no—
298#888—31no—
299#887—31no—
300#879—91no—
301#879—91no—
302#879—91no—
303#878—91no—
304#878—91no—
305#877—91no—
306#876—91no—
307#876—91no—
308#872—91no—
309#872—91no—
310#870—91no—
311#870—91no—
312#870—91no—
313#870—91no—
314C4×Dic6—91no—
315C4×Dic6—91no—
316C22×C3⋊D3C22×D311yescharacteristic
317C22×C3×D3—31no—
318C22×C3×D3—31no—
319C22×C3×D3—61no—
320C32×Q8—62no—
321C2×C32×C4—21no—
322C2×C32×C4—21no—
323C2×C32×C4—21no—
324C2×C32×C4—31no—
325C2×C32×C4—31no—
326C2×C32×C4—31no—
327C2×C32×C4—31no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—41no—
331C2×C32×C4C22×D311yescharacteristic
332C2×C32×C4C22×D311yescharacteristic
333C2×C32×C4C22×D311yescharacteristic
334C2×C3⋊Dic3—31no—
335C2×C3⋊Dic3—31no—
336C2×C3⋊Dic3—31no—
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—31no—
340C2×C3⋊Dic3—61no—
341C2×C3⋊Dic3—61no—
342C2×C3⋊Dic3—61no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—121no—
347C2×C3⋊Dic3—121no—
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350C2×C3⋊Dic3C22×D311yescharacteristic
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C4×C3⋊D3—62no—
354C2×C3×Dic3—21no—
355C2×C3×Dic3—21no—
356C2×C3×Dic3—21no—
357C2×C3×Dic3—21no—
358C2×C3×Dic3—21no—
359C2×C3×Dic3—21no—
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—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—61no—
371C2×C3×Dic3—61no—
372C2×C3×Dic3—61no—
373C2×C3×Dic3—61no—
374C2×C3×Dic3—61no—
375C2×C3×Dic3C22×D311yescharacteristic
376C2×C3×Dic3C22×D311yescharacteristic
377C2×C3×Dic3C22×D311yescharacteristic
378C2×C3×Dic3C22×D311yescharacteristic
379C2×C3×Dic3C22×D311yescharacteristic
380C2×C3×Dic3C22×D311yescharacteristic
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C3×Dic6—22no—
388C3×Dic6—22no—
389C3×Dic6—42no—
390C3×Dic6—62no—
391C3×Dic6—62no—
392#627—22no—
393D3×Dic3—62no—
394D3×Dic3—62no—
395D3×Dic3—122no—
396#541—271noSylow
397C2×C33C2×#4111yescharacteristic
398C2×C332−1+411yescharacteristic
399C2×C332−1+411yescharacteristic
400C3×C3⋊D3—41no—
401C2×C3×Q8—31no—
402C2×C3×Q8—31no—
403C2×C3×Q8—61no—
404C2×C3×Q8—91no—
405C22×Dic3—91no—
406C2×C4×D3—91no—
407C2×C4×D3—91no—
408C2×C4×D3—181no—
409C2×Dic6—31no—
410C2×Dic6—31no—
411C2×Dic6D3211yescharacteristic
412C3×C4⋊C4—31no—
413C3×C4⋊C4—31no—
414C3×C4⋊C4—31no—
415C3×C4⋊C4—31no—
416C3×C4⋊C4—61no—
417C3×C4⋊C4—61no—
418C3×C4⋊C4—91no—
419C3×C4⋊C4—91no—
420C3×C4⋊C4—91no—
421C3×C4⋊C4—91no—
422C3×C4⋊C4—91no—
423C3×C4⋊C4—91no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4—91no—
426C3×C22⋊C4—91no—
427C3×C42—91no—
428C3×C42—91no—
429C3×C42—91no—
430C3×C42—91no—
431C3×C42—91no—
432#217—91no—
433#217—91no—
434#217—91no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—181no—
449C4⋊Dic3—31no—
450C4⋊Dic3—31no—
451C4⋊Dic3—31no—
452C4⋊Dic3—31no—
453C4⋊Dic3—91no—
454C4⋊Dic3—91no—
455C4⋊Dic3—91no—
456C4⋊Dic3—91no—
457C4⋊Dic3—91no—
458C4⋊Dic3—91no—
459C4⋊Dic3—91no—
460C4⋊Dic3—91no—
461C4⋊Dic3—91no—
462C4⋊Dic3—91no—
463C4⋊Dic3—91no—
464C4⋊Dic3—181no—
465C4⋊Dic3—181no—
466C4⋊Dic3—181no—
467C4⋊Dic3D3211yescharacteristic
468Dic3⋊C4—31no—
469Dic3⋊C4—31no—
470Dic3⋊C4—31no—
471Dic3⋊C4—31no—
472Dic3⋊C4—31no—
473Dic3⋊C4—31no—
474Dic3⋊C4—31no—
475Dic3⋊C4—31no—
476Dic3⋊C4—61no—
477Dic3⋊C4—91no—
478Dic3⋊C4—91no—
479Dic3⋊C4—91no—
480Dic3⋊C4—91no—
481Dic3⋊C4—91no—
482Dic3⋊C4—91no—
483Dic3⋊C4—91no—
484Dic3⋊C4—91no—
485Dic3⋊C4—91no—
486Dic3⋊C4—91no—
487Dic3⋊C4—91no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495Dic3⋊C4—91no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—181no—
503Dic3⋊C4—181no—
504Dic3⋊C4—181no—
505Dic3⋊C4—181no—
506Dic3⋊C4—181no—
507Dic3⋊C4—181no—
508Dic3⋊C4—181no—
509Dic3⋊C4—181no—
510Dic3⋊C4—181no—
511Dic3⋊C4—361no—
512Dic3⋊C4D3211yescharacteristic
513C4×Dic3—31no—
514C4×Dic3—31no—
515C4×Dic3—31no—
516C4×Dic3—31no—
517C4×Dic3—31no—
518C4×Dic3—31no—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—31no—
522C4×Dic3—31no—
523C4×Dic3—61no—
524C4×Dic3—91no—
525C4×Dic3—91no—
526C4×Dic3—91no—
527C4×Dic3—181no—
528C22×C32—21no—
529C22×C32—21no—
530C22×C32—21no—
531C22×C32—41no—
532C22×C32C23×D311yescharacteristic
533C22×C32C23×D311yescharacteristic
534C22×C32C23×D311yescharacteristic
535C2×C3⋊D3—21no—
536C2×C3⋊D3—21no—
537C2×C3⋊D3—21no—
538C2×C3×D3—62no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—61no—
542C2×C3×D3—61no—
543C2×C3×D3—61no—
544C2×C3×D3—61no—
545C2×C3×D3—121no—
546C2×C3×D3—121no—
547C32×C4—21no—
548C32×C4—21no—
549C32×C4—21no—
550C32×C4—32no—
551C32×C4—41no—
552C32×C4—41no—
553C32×C4—41no—
554C32×C4—61no—
555C32×C4—61no—
556C32×C4—61no—
557C32×C4—61no—
558C32×C4—61no—
559C32×C4—81no—
560C3⋊Dic3—21no—
561C3⋊Dic3—21no—
562C3⋊Dic3—21no—
563C3⋊Dic3—21no—
564C3⋊Dic3—21no—
565C3⋊Dic3—61no—
566C3⋊Dic3—62no—
567C3⋊Dic3—61no—
568C3⋊Dic3—61no—
569C3⋊Dic3—61no—
570C3⋊Dic3—61no—
571C3⋊Dic3—61no—
572C3⋊Dic3—121no—
573C3⋊Dic3—121no—
574C3⋊Dic3—122no—
575C3⋊Dic3—121no—
576C3⋊Dic3—121no—
577C3⋊Dic3—121no—
578C3⋊Dic3—241no—
579C3×Dic3—21no—
580C3×Dic3—21no—
581C3×Dic3—21no—
582C3×Dic3—21no—
583C3×Dic3—21no—
584C3×Dic3—21no—
585C3×Dic3—21no—
586C3×Dic3—21no—
587C3×Dic3—21no—
588C3×Dic3—21no—
589C3×Dic3—22no—
590C3×Dic3—41no—
591C3×Dic3—41no—
592C3×Dic3—41no—
593C3×Dic3—41no—
594C3×Dic3—41no—
595C3×Dic3—62no—
596C3×Dic3—61no—
597C3×Dic3—61no—
598C3×Dic3—61no—
599C3×Dic3—61no—
600C3×Dic3—61no—
601C3×Dic3—61no—
602C3×Dic3—61no—
603C3×Dic3—61no—
604C3×Dic3—61no—
605C3×Dic3—61no—
606C3×Dic3—121no—
607C3×Dic3—121no—
608C3×Dic3—121no—
609C3×Dic3—121no—
610C3×Dic3#23512yes—
611C3×Dic3#23712yes—
612C4⋊Q8—91no—
613#126—91no—
614#126—271no—
615#126—271no—
616#126—271no—
617#125—271no—
618#125—271no—
619#125—271no—
620#125—271no—
621#125—271no—
622C22⋊Q8—271no—
623C22⋊Q8—271no—
624C4×Q8—91no—
625C4×Q8—271no—
626#117—271no—
627C33#54111yescharacteristic, complemented, Sylow
628C23×C3—91no—
629C22×D3—31no—
630C22×D3—31no—
631C22×D3—61no—
632C3×Q8—62no—
633C3×Q8—62no—
634C3×Q8—122no—
635C3×Q8—182no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—31no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—31no—
650C2×C3×C4—31no—
651C2×C3×C4—41no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—91no—
659C2×C3×C4—91no—
660C2×C3×C4—91no—
661C2×C3×C4—91no—
662C2×C3×C4—91no—
663C2×C3×C4C2×D3211yescharacteristic
664C2×C3×C4C2×D3211yescharacteristic
665C2×C3×C4C2×D3211yescharacteristic
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—31no—
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—91no—
682C2×Dic3—91no—
683C2×Dic3—91no—
684C2×Dic3—91no—
685C2×Dic3—91no—
686C2×Dic3—91no—
687C2×Dic3—181no—
688C2×Dic3—181no—
689C2×Dic3—181no—
690C2×Dic3—181no—
691C2×Dic3—181no—
692C2×Dic3—181no—
693C2×Dic3—182no—
694C2×Dic3—361no—
695C2×Dic3—361no—
696C2×Dic3C2×D3211yescharacteristic
697C2×Dic3C2×D3211yescharacteristic
698C2×Dic3C2×D3211yescharacteristic
699C2×Dic3C2×D3211yescharacteristic
700C2×Dic3C2×D3211yescharacteristic
701C2×Dic3C2×D3211yescharacteristic
702C4×D3—182no—
703C4×D3—182no—
704C4×D3—362no—
705Dic6—22no—
706Dic6—62no—
707Dic6—62no—
708C2×C32—21no—
709C2×C32—21no—
710C2×C32—21no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—21no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—41no—
718C2×C32—41no—
719C2×C32—41no—
720C2×C32C2×#23511yescharacteristic
721C2×C32C2×#23711yescharacteristic
722C2×C32#100711yescharacteristic
723C2×C32#100711yescharacteristic
724C2×C32#100711yescharacteristic
725C2×C32D3×#4111yescharacteristic
726C2×C32#101011yescharacteristic
727C2×C32#101011yescharacteristic
728C2×C32#101011yescharacteristic
729C3⋊D3—41no—
730C3×D3—122no—
731C3×D3—121no—
732C3×D3—121no—
733C2×Q8—31no—
734C2×Q8—91no—
735C22×C4—271no—
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—91no—
739C4⋊C4—91no—
740C4⋊C4—91no—
741C4⋊C4—91no—
742C4⋊C4—91no—
743C4⋊C4—91no—
744C4⋊C4—271no—
745C4⋊C4—271no—
746C4⋊C4—271no—
747C4⋊C4—271no—
748C4⋊C4—271no—
749C4⋊C4—271no—
750C4⋊C4—271no—
751C4⋊C4—271no—
752C4⋊C4—271no—
753C4⋊C4—271no—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4—91no—
759C22⋊C4—271no—
760C22⋊C4—271no—
761C22⋊C4—271no—
762C42—91no—
763C42—91no—
764C42—91no—
765C42—91no—
766C42—91no—
767C42—271no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—41no—
772C22×C3—181no—
773C22×C3—181no—
774C22×C3—181no—
775C22×C3C22×D3211yescharacteristic
776C22×C3C22×D3211yescharacteristic
777C22×C3C22×D3211yescharacteristic
778C2×D3—62no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—61no—
783C2×D3—61no—
784C2×D3—61no—
785C2×D3—121no—
786C2×D3—121no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—32no—
791C3×C4—32no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—62no—
796C3×C4—61no—
797C3×C4—61no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—61no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—81no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4—121no—
811C3×C4—121no—
812C3×C4—181no—
813C3×C4—181no—
814C3×C4—181no—
815C3×C4—181no—
816C3×C4—181no—
817Dic3—21no—
818Dic3—21no—
819Dic3—21no—
820Dic3—21no—
821Dic3—21no—
822Dic3—62no—
823Dic3—61no—
824Dic3—61no—
825Dic3—61no—
826Dic3—61no—
827Dic3—61no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—61no—
833Dic3—121no—
834Dic3—121no—
835Dic3—121no—
836Dic3—121no—
837Dic3—182no—
838Dic3—181no—
839Dic3—181no—
840Dic3—181no—
841Dic3—181no—
842Dic3—181no—
843Dic3—181no—
844Dic3—361no—
845Dic3—361no—
846Dic3—361no—
847Dic3—361no—
848Dic3—361no—
849Dic3—362no—
850Dic3—721no—
851Dic3#380412yes—
852C32—21no—
853C32—21no—
854C32—21no—
855C32—41no—
856C32#558311yescharacteristic, complemented
857C32#570111yescharacteristic, complemented
858C32#573111yescharacteristic, complemented
859C23—91no—
860Q8—62no—
861Q8—182no—
862C2×C4—31no—
863C2×C4—31no—
864C2×C4—31no—
865C2×C4—31no—
866C2×C4—31no—
867C2×C4—31no—
868C2×C4—91no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—91no—
872C2×C4—91no—
873C2×C4—271no—
874C2×C4—271no—
875C2×C4—542no—
876C2×C4D3311yescharacteristic
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—41no—
887C2×C3—41no—
888C2×C3—41no—
889C2×C3—361no—
890C2×C3#6429711yescharacteristic
891C2×C3D3×#23511yescharacteristic
892C2×C3#6430911yescharacteristic
893C2×C3D3×#23711yescharacteristic
894C2×C3#6431511yescharacteristic
895C2×C3#6431511yescharacteristic
896C2×C3#6431511yescharacteristic
897C2×C3#6431611yescharacteristic
898C2×C3C2×#380411yescharacteristic
899D3—122no—
900D3—121no—
901D3—121no—
902C22—181no—
903C22—181no—
904C22—181no—
905C22C2×D3311yescharacteristic
906C4—21no—
907C4—32no—
908C4—61no—
909C4—61no—
910C4—61no—
911C4—61no—
912C4—61no—
913C4—181no—
914C4—181no—
915C4—181no—
916C4—181no—
917C4—181no—
918C4—541no—
919C4—541no—
920C3—21no—
921C3—21no—
922C3—21no—
923C3—41no—
924C3#1059441811yescharacteristic, complemented
925C3#1059444611yescharacteristic, complemented
926C3#1059535411yescharacteristic, complemented
927C2—361no—
928C2#1172439411yescharacteristic
929C2#1172439711yescharacteristic
930C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×C4D33
hypocenterC33#541
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #11723445C2semidirect
4. #11723405C2semidirect
6. C3×#63843C2semidirect
7. C3×#63839C2semidirect
10. #11723014C2semidirect
11. #11723012C2semidirect
12. #11723012C2semidirect
14. Dic3×#627C2semidirect
98. #63843D3semidirect
101. #63839D3semidirect
627. C33#541semidirect
856. C32#5583semidirect
857. C32#5701semidirect
858. C32#5731semidirect
924. C3#10594418semidirect
925. C3#10594446semidirect
926. C3#10595354semidirect

Maximal subgroups

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

subgroupindex
#117236762
#117234762
#117234452
#117234052
C3×#638482
C3×#638432
C3×#638392
#117230252
#117230232
#117230142
#117230122
#117229742
Dic3×#6272
#117229192
#105953543
#105944463
#105944183