Finite Group Databasebeta

← #13169385

Subgroups — #13169385

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723675C211yesmaximal, characteristic, complemented
2#11723471C211yesmaximal, characteristic
3#11723411C211yesmaximal, characteristic, complemented
4#11723403C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×#63848C211yesmaximal, characteristic, complemented
7C3×#63837C211yesmaximal, characteristic, complemented
8#11723003C211yesmaximal, characteristic
9#11723003C211yesmaximal, characteristic
10#11722974C211yesmaximal, characteristic, complemented
11#11722973C211yesmaximal, characteristic, complemented
12#11722940C211yesmaximal, characteristic, complemented
13Dic3×#627C211yesmaximal, characteristic, complemented
14#11722921C211yesmaximal, characteristic, complemented
15#11722920C211yesmaximal, characteristic, complemented
16#10594450—31nomaximal
17#10594421—31nomaximal
18#10593865—31nomaximal
19C2×#6292C2211yescharacteristic
20C2×#6289C2211yescharacteristic
21C2×Dic3×C3⋊D3C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25#88859C2211yescharacteristic
26C3×#3752C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×C4⋊Dic3C2211yescharacteristic
30C32×Dic3⋊C4C2211yescharacteristic
31C32×C4×Dic3C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2211yescharacteristic
35#88813C2211yescharacteristic
36#88807C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64107—31no—
55#64107—31no—
56C4×C4⋊(C3⋊D3)—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#888—31no—
60C3×#887—31no—
61C3×#869—31no—
62C3×C4×Dic6—31no—
63#63918D311yescharacteristic, complemented
64C4×#627—31no—
65#63907—31no—
66#63907—31no—
67#63895—31no—
68#63893—31no—
69#63888—31no—
70#63887—31no—
71#63880—31no—
72#63880—31no—
73#63880—61no—
74#63878—31no—
75#63878—31no—
76#63871—31no—
77#63871—31no—
78#63864—31no—
79#63864—31no—
80#63861—31no—
81#63858—31no—
82#63852—31no—
83#63852—31no—
84#63849—31no—
85#63849—31no—
86#63848—31no—
87#63848—31no—
88#63848—31no—
89#63848—31no—
90#63848—31no—
91#63848—61no—
92#63848—61no—
93#63848D311yescharacteristic, complemented
94#63843—31no—
95Dic3×Dic6—31no—
96Dic3×Dic6—31no—
97Dic3×Dic6—31no—
98#63837—31no—
99#63837D311yescharacteristic, complemented
100#63836—31no—
101#63836—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
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
117#6292—22no—
118#6289—22no—
119Dic3×C3⋊D3—22no—
120C3×#627—22no—
121C3×#627—22no—
122C3×#627—22no—
123#5732—91no—
124#5702—91no—
125#5584—91no—
126C2×C4⋊(C3⋊D3)—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—31no—
129C2×C3×Dic6—31no—
130C2×C3×Dic6—31no—
131C2×C3×Dic6—31no—
132C2×C3×Dic6—31no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×#627C2×D311yescharacteristic
136C2×#627C2×D311yescharacteristic
137C2×#627C2×D311yescharacteristic
138C2×#626—31no—
139C2×#626—31no—
140C2×#626—61no—
141C2×#624—31no—
142C2×#624—31no—
143C2×#624—61no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—61no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C42—31no—
150#3752—31no—
151#3752—31no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—61no—
158#3752—61no—
159#3752—61no—
160#3752—121no—
161#3752C2×D311yescharacteristic
162C4⋊(C3⋊Dic3)—31no—
163C4⋊(C3⋊Dic3)—31no—
164C4⋊(C3⋊Dic3)C2×D311yescharacteristic
165#3750—31no—
166#3750C2×D311yescharacteristic
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—61no—
176C3×C4⋊Dic3—21no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—61no—
184C3×C4⋊Dic3C2×D311yescharacteristic
185C3×C4⋊Dic3C2×D311yescharacteristic
186C3×Dic3⋊C4—21no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—61no—
194C3×Dic3⋊C4C2×D311yescharacteristic
195C3×Dic3⋊C4C2×D311yescharacteristic
196C3×C4×Dic3—21no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3C2×D311yescharacteristic
204C3×C4×Dic3C2×D311yescharacteristic
205#3724—31no—
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—61no—
215Dic3⋊Dic3—61no—
216Dic3⋊Dic3—61no—
217Dic3⋊Dic3C2×D311yescharacteristic
218Dic3⋊Dic3C2×D311yescharacteristic
219Dic3⋊Dic3C2×D311yescharacteristic
220Dic3⋊Dic3C2×D311yescharacteristic
221#3722—31no—
222#3722—31no—
223#3722—31no—
224#3722—31no—
225#3722—31no—
226#3722—31no—
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—61no—
232#3722—61no—
233#3722—61no—
234#3722—61no—
235#3722C2×D311yescharacteristic
236#3722C2×D311yescharacteristic
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—61no—
249Dic32—61no—
250Dic32C2×D311yescharacteristic
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3⋊(C3⋊D3)—21no—
255C2×C3⋊(C3⋊D3)—21no—
256C2×C3⋊(C3⋊D3)—21no—
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C33×C4—21no—
261C3⋊(C3⋊Dic3)—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3#4112yes—
272C32×Dic3#4112yes—
273C3×C4⋊Q8—91no—
274C3×#126—91no—
275C3×C4×Q8—91no—
276#947—91no—
277#947—91no—
278#946—91no—
279#946—91no—
280Q8×Dic3—91no—
281Q8×Dic3—91no—
282#898—31no—
283#898—31no—
284#898—91no—
285#898—91no—
286#898—91no—
287#898—91no—
288#898—91no—
289#898—91no—
290#898—91no—
291#898—91no—
292#898—181no—
293#898—181no—
294#897—91no—
295#897—91no—
296#896—91no—
297#892—91no—
298#892—91no—
299#892—91no—
300#892—91no—
301#888—31no—
302#887—31no—
303#887—91no—
304#885—91no—
305#885—91no—
306#67⋊C4—91no—
307#879—91no—
308#878—91no—
309#877—91no—
310#875—91no—
311#875—91no—
312C4×D12—91no—
313C4×D12—91no—
314C4×D12—181no—
315#872—91no—
316#869—31no—
317C4×Dic6—31no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C4×Dic6—91no—
321C22×C3⋊D3—31no—
322C22×C3⋊D3—31no—
323C22×C3⋊D3—31no—
324C22×C3⋊D3—61no—
325C22×C3⋊D3—61no—
326C22×C3⋊D3—61no—
327C22×C3⋊D3—121no—
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—61no—
332C2×C32×C4—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—41no—
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—121no—
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C4⋊(C3⋊D3)—62no—
358C4×C3⋊D3—62no—
359C4×C3⋊D3—62no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C3×Dic6—62no—
394C3×Dic6—62no—
395C3×Dic6—62no—
396C3×Dic6—62no—
397C3×Dic6—62no—
398C3×Dic6—62no—
399#627—22no—
400#627—22no—
401#627—22no—
402#626—64no—
403#626—62no—
404#626—62no—
405#624—62no—
406#624—62no—
407#624—122no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—122no—
411#556—271noSylow
412C2×C33C2×#4111yescharacteristic
413C2×C33C2×#4111yescharacteristic
414C2×C332−1+411yescharacteristic
415C3⋊(C3⋊D3)—41no—
416C3×C3⋊D3—41no—
417C2×C3×Q8—91no—
418C2×C3×Q8—91no—
419C2×C3×Q8—91no—
420C2×#67—91no—
421C22×Dic3—91no—
422C2×D12—91no—
423C2×D12—91no—
424C2×D12—181no—
425C2×C4×D3—91no—
426C2×C4×D3—91no—
427C2×C4×D3—91no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×C4×D3—181no—
431C2×C4×D3—181no—
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—31no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—61no—
443C3×C4⋊C4—61no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C22⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C42—31no—
454C3×C42—31no—
455C3×C42—61no—
456C3×C42—91no—
457C3×C42—91no—
458C3×C42—91no—
459#217—91no—
460#217—91no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—61no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—181no—
488(C2×D3)⋊C4—181no—
489(C2×D3)⋊C4—181no—
490(C2×D3)⋊C4—181no—
491(C2×D3)⋊C4—181no—
492(C2×D3)⋊C4—181no—
493(C2×D3)⋊C4—181no—
494(C2×D3)⋊C4—361no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—31no—
499C4⋊Dic3—31no—
500C4⋊Dic3—31no—
501C4⋊Dic3—61no—
502C4⋊Dic3—91no—
503C4⋊Dic3—91no—
504C4⋊Dic3—91no—
505C4⋊Dic3—91no—
506C4⋊Dic3—91no—
507C4⋊Dic3—91no—
508C4⋊Dic3—181no—
509C4⋊Dic3—181no—
510C4⋊Dic3D3211yescharacteristic
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—31no—
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—31no—
517Dic3⋊C4—61no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—181no—
525Dic3⋊C4D3211yescharacteristic
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—91no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—181no—
542C4×Dic3—181no—
543C4×Dic3D3211yescharacteristic
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—41no—
548C22×C32C23×D311yescharacteristic
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3—61no—
555C2×C3⋊D3—62no—
556C2×C3⋊D3—61no—
557C2×C3⋊D3—61no—
558C2×C3⋊D3—61no—
559C2×C3⋊D3—61no—
560C2×C3⋊D3—61no—
561C2×C3⋊D3—61no—
562C2×C3⋊D3—61no—
563C2×C3⋊D3—61no—
564C2×C3⋊D3—121no—
565C2×C3⋊D3—121no—
566C2×C3⋊D3—122no—
567C2×C3⋊D3—121no—
568C2×C3⋊D3—121no—
569C2×C3⋊D3—121no—
570C2×C3⋊D3—121no—
571C2×C3⋊D3—121no—
572C2×C3⋊D3—121no—
573C2×C3⋊D3—241no—
574C2×C3⋊D3—241no—
575C2×C3×D3—62no—
576C2×C3×D3—61no—
577C2×C3×D3—61no—
578C2×C3×D3—61no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—121no—
583C2×C3×D3—121no—
584C32×C4—21no—
585C32×C4—21no—
586C32×C4—21no—
587C32×C4—32no—
588C32×C4—32no—
589C32×C4—41no—
590C32×C4—41no—
591C32×C4—41no—
592C32×C4—61no—
593C32×C4—61no—
594C32×C4—61no—
595C32×C4—61no—
596C32×C4—81no—
597C3⋊Dic3—21no—
598C3⋊Dic3—21no—
599C3⋊Dic3—21no—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—61no—
603C3⋊Dic3—61no—
604C3⋊Dic3—61no—
605C3⋊Dic3—121no—
606C3⋊Dic3—121no—
607C3⋊Dic3—121no—
608C3⋊Dic3—241no—
609C3×Dic3—21no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—22no—
618C3×Dic3—22no—
619C3×Dic3—41no—
620C3×Dic3—41no—
621C3×Dic3—41no—
622C3×Dic3—41no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—121no—
634C3×Dic3—121no—
635C3×Dic3—121no—
636C3×Dic3—121no—
637C3×Dic3—121no—
638C3×Dic3#23512yes—
639C3×Dic3#23712yes—
640C3×Dic3#23912yes—
641C3×Dic3#23912yes—
642C4⋊Q8—91no—
643#126—91no—
644#126—271no—
645#126—271no—
646#126—271no—
647#124—271no—
648#124—271no—
649C22⋊Q8—271no—
650C22⋊Q8—271no—
651C4×Q8—91no—
652C4×Q8—271no—
653C4×Q8—271no—
654C4×D4—271no—
655#117—271no—
656#117—271no—
657C33#55611yescharacteristic, complemented, Sylow
658C23×C3—91no—
659C22×D3—31no—
660C22×D3—31no—
661C22×D3—61no—
662C22×D3—91no—
663C22×D3—91no—
664C22×D3—91no—
665C22×D3—181no—
666C22×D3—181no—
667C22×D3—181no—
668C22×D3—361no—
669C3×Q8—182no—
670C3×Q8—182no—
671C3×Q8—182no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—31no—
684C2×C3×C4—31no—
685C2×C3×C4—31no—
686C2×C3×C4—31no—
687C2×C3×C4—41no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—91no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—91no—
698C2×C3×C4—91no—
699C2×C3×C4C2×D3211yescharacteristic
700C2×C3×C4C2×D3211yescharacteristic
701C2×C3×C4C2×D3211yescharacteristic
702#67—182no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—91no—
719C2×Dic3—91no—
720C2×Dic3—91no—
721C2×Dic3—181no—
722C2×Dic3—181no—
723C2×Dic3—181no—
724C2×Dic3—182no—
725C2×Dic3—361no—
726C2×Dic3C2×D3211yescharacteristic
727C2×Dic3C2×D3211yescharacteristic
728C2×Dic3C2×D3211yescharacteristic
729C2×Dic3C2×D3211yescharacteristic
730C2×Dic3C2×D3211yescharacteristic
731C2×Dic3C2×D3211yescharacteristic
732D12—182no—
733D12—182no—
734D12—184no—
735C4×D3—182no—
736C4×D3—182no—
737C4×D3—182no—
738C4×D3—182no—
739C4×D3—182no—
740C4×D3—362no—
741C4×D3—362no—
742Dic6—62no—
743Dic6—62no—
744Dic6—62no—
745Dic6—62no—
746Dic6—62no—
747Dic6—62no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32C2×#23511yescharacteristic
761C2×C32C2×#23711yescharacteristic
762C2×C32C2×#23911yescharacteristic
763C2×C32C2×#23911yescharacteristic
764C2×C32#100711yescharacteristic
765C2×C32D3×#4111yescharacteristic
766C2×C32D3×#4111yescharacteristic
767C2×C32#101011yescharacteristic
768C2×C32#101011yescharacteristic
769C3⋊D3—41no—
770C3⋊D3—121no—
771C3⋊D3—122no—
772C3⋊D3—121no—
773C3⋊D3—121no—
774C3⋊D3—241no—
775C3⋊D3—241no—
776C3⋊D3—242no—
777C3×D3—122no—
778C3×D3—121no—
779C3×D3—121no—
780C2×Q8—91no—
781C2×Q8—91no—
782C2×Q8—91no—
783C2×D4—271no—
784C22×C4—271no—
785C22×C4—271no—
786C4⋊C4—31no—
787C4⋊C4—31no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4—91no—
792C4⋊C4—91no—
793C4⋊C4—91no—
794C4⋊C4—271no—
795C4⋊C4—271no—
796C4⋊C4—271no—
797C4⋊C4—271no—
798C22⋊C4—91no—
799C22⋊C4—91no—
800C22⋊C4—91no—
801C22⋊C4—271no—
802C22⋊C4—271no—
803C22⋊C4—271no—
804C22⋊C4—271no—
805C22⋊C4—271no—
806C22⋊C4—271no—
807C22⋊C4—271no—
808C42—31no—
809C42—91no—
810C42—91no—
811C42—91no—
812C42—271no—
813C42—271no—
814C42—271no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—41no—
819C22×C3—181no—
820C22×C3—181no—
821C22×C3—181no—
822C22×C3C22×D3211yescharacteristic
823C22×C3C22×D3211yescharacteristic
824C22×C3C22×D3211yescharacteristic
825C2×D3—62no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—182no—
835C2×D3—181no—
836C2×D3—181no—
837C2×D3—181no—
838C2×D3—181no—
839C2×D3—181no—
840C2×D3—181no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—181no—
844C2×D3—361no—
845C2×D3—361no—
846C2×D3—361no—
847C2×D3—361no—
848C2×D3—361no—
849C2×D3—361no—
850C2×D3—361no—
851C2×D3—361no—
852C2×D3—362no—
853C2×D3—721no—
854C2×D3—721no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—32no—
859C3×C4—32no—
860C3×C4—32no—
861C3×C4—32no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—62no—
866C3×C4—62no—
867C3×C4—61no—
868C3×C4—61no—
869C3×C4—61no—
870C3×C4—61no—
871C3×C4—61no—
872C3×C4—61no—
873C3×C4—61no—
874C3×C4—61no—
875C3×C4—81no—
876C3×C4—121no—
877C3×C4—121no—
878C3×C4—121no—
879C3×C4—121no—
880C3×C4—181no—
881C3×C4—181no—
882C3×C4—181no—
883C3×C4—181no—
884C3×C4—181no—
885Dic3—21no—
886Dic3—21no—
887Dic3—21no—
888Dic3—21no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—121no—
900Dic3—121no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—181no—
905Dic3—181no—
906Dic3—181no—
907Dic3—361no—
908Dic3—361no—
909Dic3—361no—
910Dic3—721no—
911Dic3#379612yes—
912Dic3#379912yes—
913C32—21no—
914C32—21no—
915C32—21no—
916C32—41no—
917C32#558411yescharacteristic, complemented
918C32#570211yescharacteristic, complemented
919C32#573211yescharacteristic, complemented
920C23—91no—
921C23—271no—
922Q8—182no—
923Q8—182no—
924Q8—182no—
925D4—542no—
926C2×C4—31no—
927C2×C4—31no—
928C2×C4—31no—
929C2×C4—31no—
930C2×C4—31no—
931C2×C4—31no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—91no—
936C2×C4—91no—
937C2×C4—271no—
938C2×C4—542no—
939C2×C4—542no—
940C2×C4D3311yescharacteristic
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—41no—
951C2×C3—41no—
952C2×C3—41no—
953C2×C3—361no—
954C2×C3C2×#379611yescharacteristic
955C2×C3#6429711yescharacteristic
956C2×C3#6429711yescharacteristic
957C2×C3C2×#379911yescharacteristic
958C2×C3D3×#23511yescharacteristic
959C2×C3#6430911yescharacteristic
960C2×C3D3×#23711yescharacteristic
961C2×C3D3×#23911yescharacteristic
962C2×C3D3×#23911yescharacteristic
963D3—122no—
964D3—121no—
965D3—121no—
966D3—362no—
967D3—361no—
968D3—361no—
969D3—361no—
970D3—721no—
971D3—721no—
972D3—722no—
973C22—181no—
974C22—181no—
975C22—181no—
976C22—541no—
977C22—541no—
978C22—541no—
979C22C2×D3311yescharacteristic
980C4—21no—
981C4—32no—
982C4—32no—
983C4—61no—
984C4—61no—
985C4—61no—
986C4—61no—
987C4—181no—
988C4—181no—
989C4—181no—
990C4—181no—
991C4—181no—
992C4—541no—
993C3—21no—
994C3—21no—
995C3—21no—
996C3—41no—
997C3#1059386511yescharacteristic, complemented
998C3#1059442111yescharacteristic, complemented
999C3#1059445011yescharacteristic, complemented
1000C2—361no—
1001C2—1081no—
1002C2D3×#379611yescharacteristic
1003C2D3×#379911yescharacteristic
1004C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6292C22
hypercenterC2×C4D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723675C2semidirect
3. #11723411C2semidirect
4. #11723403C2semidirect
5. C3×#63918C2semidirect
6. C3×#63848C2semidirect
7. C3×#63837C2semidirect
10. #11722974C2semidirect
11. #11722973C2semidirect
12. #11722940C2semidirect
13. Dic3×#627C2semidirect
14. #11722921C2semidirect
15. #11722920C2semidirect
63. #63918D3semidirect
93. #63848D3semidirect
99. #63837D3semidirect
657. C33#556semidirect
917. C32#5584semidirect
918. C32#5702semidirect
919. C32#5732semidirect
997. C3#10593865semidirect
998. C3#10594421semidirect
999. C3#10594450semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117234712
#117234112
#117234032
C3×#639182
C3×#638482
C3×#638372
#117230032
#117229742
#117229732
#117229402
Dic3×#6272
#117229212
#117229202
#105944503
#105944213
#105938653