Finite Group Databasebeta

← #13168478

Subgroups — #13168478

Order 1728.

984 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723448C211yesmaximal, characteristic, complemented
3#11723432C211yesmaximal, characteristic
4#11723397C211yesmaximal, characteristic, complemented
5C3×#63887C211yesmaximal, characteristic
6C3×#63861C211yesmaximal, characteristic
7C3×#63839C211yesmaximal, characteristic, complemented
8#11723026C211yesmaximal, characteristic
9#11723022C211yesmaximal, characteristic
10#11723015C211yesmaximal, characteristic, complemented
11#11723011C211yesmaximal, characteristic, complemented
12#11723011C211yesmaximal, characteristic, complemented
13#11722969C211yesmaximal, characteristic
14#11722940C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic
16#10595349—31nomaximal
17#10594446—31nomaximal
18#10594027—31nomaximal
19C2×C32×Dic6C2211yescharacteristic
20C2×C3×#627C2211yescharacteristic
21C2×C3×D3×Dic3C2211yescharacteristic
22C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×#3750C2211yescharacteristic
25C3×#3750C2211yescharacteristic
26C32×(C2×D3)⋊C4C2211yescharacteristic
27C32×Dic3⋊C4C2211yescharacteristic
28#88815C2211yescharacteristic
29#88815C2211yescharacteristic
30#88815C2211yescharacteristic
31#88813C2211yescharacteristic
32#88807C2211yescharacteristic
33#88807C2211yescharacteristic
34#88806C2211yescharacteristic
35#88806C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54Q8×C3⋊Dic3—31no—
55#64098—31no—
56#64088—31no—
57C3×#946—31no—
58C3×#944—31no—
59C3×#898—31no—
60C3×#888—31no—
61C3×#879—31no—
62C3×#878—31no—
63#63964—31no—
64#63956—31no—
65#63956—31no—
66#63955—31no—
67#63887—31no—
68#63887D311yescharacteristic
69#63877—31no—
70#63870—31no—
71#63870—31no—
72#63870—31no—
73#63870—61no—
74#63869—31no—
75#63869—31no—
76#63867—31no—
77#63867—31no—
78#63862—31no—
79#63862—31no—
80#63862—31no—
81#63862—61no—
82#63861—31no—
83#63861—31no—
84#63861D311yescharacteristic
85#63858—31no—
86#63856—31no—
87#63855—31no—
88#63847—31no—
89#63846—31no—
90#63846—31no—
91#63846—31no—
92#63845—31no—
93#63845—31no—
94#63845—31no—
95#63843—31no—
96#63843—31no—
97#63843—31no—
98#63843—61no—
99Dic3×Dic6—31no—
100#63839D311yescharacteristic, complemented
101#63837—31no—
102C22×C32×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×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×Dic6—22no—
118C3×#627—22no—
119C3×D3×Dic3—22no—
120#5731—91no—
121#5701—91no—
122#5625—91no—
123C2×C32×Q8—31no—
124C22×C3×Dic3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×Dic6—21no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6C2×D311yescharacteristic
130C2×C3×Dic6C2×D311yescharacteristic
131C2×#627C2×D311yescharacteristic
132C2×D3×Dic3C2×D311yescharacteristic
133C32×C4⋊C4—31no—
134C32×C22⋊C4—31no—
135#3757—31no—
136#3757—31no—
137C4⋊(C3⋊Dic3)—31no—
138C4⋊(C3⋊Dic3)—31no—
139C4⋊(C3⋊Dic3)—31no—
140C4⋊(C3⋊Dic3)—31no—
141C4⋊(C3⋊Dic3)C2×D311yescharacteristic
142#3750—31no—
143#3750—31no—
144#3750—31no—
145#3750—31no—
146#3750C2×D311yescharacteristic
147#3750C2×D311yescharacteristic
148C4×C3⋊Dic3—31no—
149C4×C3⋊Dic3—31no—
150C4×C3⋊Dic3—31no—
151C4×C3⋊Dic3—31no—
152C4×C3⋊Dic3—31no—
153C4×C3⋊Dic3—61no—
154C4×C3⋊Dic3—61no—
155C4×C3⋊Dic3—61no—
156C4×C3⋊Dic3—121no—
157C3×#217—31no—
158C3×#217—31no—
159C3×#217—31no—
160C3×(C2×D3)⋊C4—21no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—31no—
163C3×(C2×D3)⋊C4—31no—
164C3×(C2×D3)⋊C4C2×D311yescharacteristic
165C3×(C2×D3)⋊C4C2×D311yescharacteristic
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—61no—
172C3×Dic3⋊C4—21no—
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—31no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—61no—
185C3×Dic3⋊C4—61no—
186C3×Dic3⋊C4C2×D311yescharacteristic
187C3×Dic3⋊C4C2×D311yescharacteristic
188C3×C4×Dic3—31no—
189C3×C4×Dic3—31no—
190C3×C4×Dic3—31no—
191C3×C4×Dic3—31no—
192#3724—31no—
193#3724—31no—
194#3724—31no—
195#3724—31no—
196#3724—31no—
197#3724—31no—
198#3724—31no—
199#3724—61no—
200#3724—61no—
201#3724C2×D311yescharacteristic
202#3724C2×D311yescharacteristic
203Dic3⋊Dic3—31no—
204Dic3⋊Dic3—31no—
205Dic3⋊Dic3—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—31no—
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⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—61no—
235(C2×D3)⋊Dic3—61no—
236(C2×D3)⋊Dic3C2×D311yescharacteristic
237(C2×D3)⋊Dic3C2×D311yescharacteristic
238(C2×D3)⋊Dic3C2×D311yescharacteristic
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—61no—
247Dic32—61no—
248Dic32C2×D311yescharacteristic
249Dic32C2×D311yescharacteristic
250C22×C33C2411yescharacteristic
251C2×C32×D3—21no—
252C2×C32×D3—21no—
253C2×C32×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—
262C3×C3⋊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×C22⋊Q8—91no—
271#946—31no—
272#946—91no—
273Q8×Dic3—91no—
274Q8×Dic3—91no—
275Q8×Dic3—91no—
276Q8×Dic3—181no—
277#944—31no—
278#926—91no—
279#924—91no—
280#898—31no—
281#898—91no—
282#898—91no—
283#898—91no—
284#890—91no—
285#890—91no—
286#890—91no—
287#890—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—91no—
297#889—181no—
298#888—31no—
299#887—91no—
300#887—91no—
301#879—31no—
302#879—91no—
303#879—91no—
304#879—91no—
305#879—91no—
306#879—91no—
307#879—91no—
308#879—181no—
309#878—31no—
310#878—91no—
311#877—91no—
312#872—91no—
313#870—91no—
314#870—91no—
315C4×Dic6—91no—
316C23×C32—31no—
317C22×C3×D3—21no—
318C22×C3×D3C22×D311yescharacteristic
319C22×C3×D3C22×D311yescharacteristic
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—41no—
330C2×C32×C4C22×D311yescharacteristic
331C2×C32×C4C22×D311yescharacteristic
332C2×C32×C4C22×D311yescharacteristic
333C2×C3⋊Dic3—31no—
334C2×C3⋊Dic3—31no—
335C2×C3⋊Dic3—31no—
336C2×C3⋊Dic3—31no—
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—61no—
340C2×C3⋊Dic3—61no—
341C2×C3⋊Dic3—61no—
342C2×C3⋊Dic3—61no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—121no—
346C2×C3⋊Dic3—121no—
347C2×C3⋊Dic3C22×D311yescharacteristic
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350C2×C3⋊Dic3C22×D311yescharacteristic
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3×Dic3—21no—
354C2×C3×Dic3—21no—
355C2×C3×Dic3—21no—
356C2×C3×Dic3—21no—
357C2×C3×Dic3—21no—
358C2×C3×Dic3—31no—
359C2×C3×Dic3—31no—
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×Dic3—61no—
376C2×C3×Dic3—62no—
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×C4×D3—62no—
388C3×Dic6—24no—
389C3×Dic6—22no—
390C3×Dic6—22no—
391C3×Dic6—62no—
392C3×Dic6—62no—
393#627—22no—
394D3×Dic3—22no—
395#541—271noSylow
396C2×C33C2×#4111yescharacteristic
397C2×C332−1+411yescharacteristic
398C2×C332−1+411yescharacteristic
399C32×D3—41no—
400C2×C3×Q8—31no—
401C2×C3×Q8—31no—
402C2×C3×Q8—61no—
403C2×C3×Q8—91no—
404C22×C3×C4—91no—
405C22×Dic3—31no—
406C2×C4×D3—31no—
407C2×Dic6—31no—
408C2×Dic6—31no—
409C2×Dic6D3211yescharacteristic
410C3×C4⋊C4—31no—
411C3×C4⋊C4—31no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4—91no—
414C3×C4⋊C4—91no—
415C3×C4⋊C4—91no—
416C3×C4⋊C4—91no—
417C3×C4⋊C4—91no—
418C3×C4⋊C4—91no—
419C3×C4⋊C4—91no—
420C3×C4⋊C4—91no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4—91no—
426C3×C22⋊C4—91no—
427C3×C42—91no—
428C3×C42—91no—
429#217—31no—
430#217—31no—
431#217—31no—
432#217—91no—
433#217—91no—
434#217—91no—
435#217—91no—
436#217—181no—
437#217—181no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4D3211yescharacteristic
444C4⋊Dic3—31no—
445C4⋊Dic3—31no—
446C4⋊Dic3—31no—
447C4⋊Dic3—31no—
448C4⋊Dic3—31no—
449C4⋊Dic3—61no—
450C4⋊Dic3—91no—
451C4⋊Dic3—91no—
452C4⋊Dic3—91no—
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—181no—
464C4⋊Dic3—181no—
465C4⋊Dic3—181no—
466C4⋊Dic3—181no—
467Dic3⋊C4—31no—
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—31no—
477Dic3⋊C4—31no—
478Dic3⋊C4—61no—
479Dic3⋊C4—61no—
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—181no—
501Dic3⋊C4—181no—
502Dic3⋊C4—181no—
503Dic3⋊C4—181no—
504Dic3⋊C4D3211yescharacteristic
505C4×Dic3—31no—
506C4×Dic3—31no—
507C4×Dic3—31no—
508C4×Dic3—31no—
509C4×Dic3—91no—
510C4×Dic3—91no—
511C4×Dic3—91no—
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—91no—
521C4×Dic3—181no—
522C4×Dic3—181no—
523C4×Dic3—181no—
524C4×Dic3—181no—
525C4×Dic3—181no—
526C4×Dic3—361no—
527C22×C32—21no—
528C22×C32—21no—
529C22×C32—21no—
530C22×C32—41no—
531C22×C32—61no—
532C22×C32—61no—
533C22×C32—61no—
534C22×C32C23×D311yescharacteristic
535C22×C32C23×D311yescharacteristic
536C22×C32C23×D311yescharacteristic
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—41no—
544C2×C3×D3—41no—
545C2×C3×D3—41no—
546C32×C4—21no—
547C32×C4—22no—
548C32×C4—21no—
549C32×C4—21no—
550C32×C4—32no—
551C32×C4—41no—
552C32×C4—41no—
553C32×C4—42no—
554C32×C4—61no—
555C32×C4—61no—
556C32×C4—61no—
557C32×C4—61no—
558C3⋊Dic3—21no—
559C3⋊Dic3—21no—
560C3⋊Dic3—21no—
561C3⋊Dic3—21no—
562C3⋊Dic3—21no—
563C3⋊Dic3—21no—
564C3⋊Dic3—61no—
565C3⋊Dic3—61no—
566C3⋊Dic3—62no—
567C3⋊Dic3—62no—
568C3⋊Dic3—61no—
569C3⋊Dic3—61no—
570C3⋊Dic3—61no—
571C3⋊Dic3—61no—
572C3⋊Dic3—121no—
573C3⋊Dic3—121no—
574C3⋊Dic3—121no—
575C3⋊Dic3—121no—
576C3⋊Dic3—122no—
577C3⋊Dic3—122no—
578C3×Dic3—22no—
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—22no—
588C3×Dic3—41no—
589C3×Dic3—41no—
590C3×Dic3—41no—
591C3×Dic3—61no—
592C3×Dic3—61no—
593C3×Dic3—61no—
594C3×Dic3—61no—
595C3×Dic3—61no—
596C3×Dic3—61no—
597C3×Dic3—61no—
598C3×Dic3—61no—
599C3×Dic3—61no—
600C3×Dic3—61no—
601C3×Dic3—61no—
602C3×Dic3—61no—
603C3×Dic3—121no—
604C3×Dic3—121no—
605C3×Dic3—121no—
606C3×Dic3—121no—
607C3×Dic3—121no—
608C3×Dic3—121no—
609C3×Dic3#23712yes—
610C3×Dic3#23712yes—
611C4⋊Q8—91no—
612#126—91no—
613#126—271no—
614#126—271no—
615#126—271no—
616#125—271no—
617#125—271no—
618#125—271no—
619#125—271no—
620#125—271no—
621C22⋊Q8—91no—
622C22⋊Q8—271no—
623C4×Q8—271no—
624C4×Q8—271no—
625#117—271no—
626C33#54111yescharacteristic, complemented, Sylow
627C23×C3—31no—
628C23×C3—31no—
629C23×C3—61no—
630C22×D3C2×D3211yescharacteristic
631C3×Q8—62no—
632C3×Q8—62no—
633C3×Q8—64no—
634C3×Q8—182no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—31no—
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—41no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—91no—
655C2×C3×C4—91no—
656C2×C3×C4—91no—
657C2×C3×C4—91no—
658C2×C3×C4—91no—
659C2×C3×C4—91no—
660C2×C3×C4—182no—
661C2×C3×C4C2×D3211yescharacteristic
662C2×C3×C4C2×D3211yescharacteristic
663C2×C3×C4C2×D3211yescharacteristic
664C2×Dic3—31no—
665C2×Dic3—31no—
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—61no—
682C2×Dic3—62no—
683C2×Dic3—91no—
684C2×Dic3—91no—
685C2×Dic3—91no—
686C2×Dic3—91no—
687C2×Dic3—91no—
688C2×Dic3—91no—
689C2×Dic3—181no—
690C2×Dic3—181no—
691C2×Dic3—181no—
692C2×Dic3—181no—
693C2×Dic3—181no—
694C2×Dic3—181no—
695C2×Dic3—361no—
696C2×Dic3—361no—
697C2×Dic3C2×D3211yescharacteristic
698C2×Dic3C2×D3211yescharacteristic
699C2×Dic3C2×D3211yescharacteristic
700C2×Dic3C2×D3211yescharacteristic
701C2×Dic3C2×D3211yescharacteristic
702C4×D3—62no—
703Dic6—22no—
704Dic6—62no—
705Dic6—62no—
706C2×C32—21no—
707C2×C32—21no—
708C2×C32—21no—
709C2×C32—21no—
710C2×C32—21no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—21no—
714C2×C32—21no—
715C2×C32—41no—
716C2×C32—41no—
717C2×C32—41no—
718C2×C32—121no—
719C2×C32C2×#23711yescharacteristic
720C2×C32C2×#23711yescharacteristic
721C2×C32#100711yescharacteristic
722C2×C32#100711yescharacteristic
723C2×C32#100711yescharacteristic
724C2×C32D3×#4111yescharacteristic
725C2×C32#101011yescharacteristic
726C2×C32#101011yescharacteristic
727C2×C32#101011yescharacteristic
728C3×D3—41no—
729C3×D3—41no—
730C3×D3—81no—
731C2×Q8—31no—
732C2×Q8—91no—
733C22×C4—91no—
734C4⋊C4—31no—
735C4⋊C4—91no—
736C4⋊C4—91no—
737C4⋊C4—91no—
738C4⋊C4—91no—
739C4⋊C4—91no—
740C4⋊C4—91no—
741C4⋊C4—91no—
742C4⋊C4—91no—
743C4⋊C4—271no—
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—
754C22⋊C4—31no—
755C22⋊C4—91no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4—271no—
759C22⋊C4—271no—
760C42—91no—
761C42—91no—
762C42—271no—
763C42—271no—
764C42—271no—
765C42—271no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—41no—
770C22×C3—61no—
771C22×C3—61no—
772C22×C3—61no—
773C22×C3—61no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3C22×D3211yescharacteristic
780C22×C3C22×D3211yescharacteristic
781C22×C3C22×D3211yescharacteristic
782C2×D3—21no—
783C2×D3—21no—
784C2×D3—21no—
785C3×C4—22no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—32no—
790C3×C4—32no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—42no—
794C3×C4—62no—
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—121no—
805C3×C4—121no—
806C3×C4—121no—
807C3×C4—181no—
808C3×C4—181no—
809C3×C4—181no—
810C3×C4—181no—
811C3×C4—181no—
812C3×C4—181no—
813Dic3—21no—
814Dic3—21no—
815Dic3—21no—
816Dic3—21no—
817Dic3—61no—
818Dic3—61no—
819Dic3—61no—
820Dic3—61no—
821Dic3—61no—
822Dic3—61no—
823Dic3—61no—
824Dic3—61no—
825Dic3—61no—
826Dic3—61no—
827Dic3—61no—
828Dic3—61no—
829Dic3—121no—
830Dic3—121no—
831Dic3—121no—
832Dic3—121no—
833Dic3—121no—
834Dic3—121no—
835Dic3—182no—
836Dic3—182no—
837Dic3—181no—
838Dic3—181no—
839Dic3—181no—
840Dic3—181no—
841Dic3—181no—
842Dic3—181no—
843Dic3—361no—
844Dic3—361no—
845Dic3—361no—
846Dic3—361no—
847Dic3—362no—
848Dic3—362no—
849Dic3#380512yes—
850C32—21no—
851C32—21no—
852C32—21no—
853C32—41no—
854C32#562511yescharacteristic, complemented
855C32#570111yescharacteristic, complemented
856C32#573111yescharacteristic, complemented
857C23—31no—
858Q8—62no—
859Q8—182no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—31no—
863C2×C4—31no—
864C2×C4—31no—
865C2×C4—91no—
866C2×C4—91no—
867C2×C4—91no—
868C2×C4—91no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—182no—
872C2×C4—271no—
873C2×C4—271no—
874C2×C4D3311yescharacteristic
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—41no—
885C2×C3—41no—
886C2×C3—41no—
887C2×C3—121no—
888C2×C3—121no—
889C2×C3—241no—
890C2×C3#6429711yescharacteristic
891C2×C3#6429711yescharacteristic
892C2×C3#6430911yescharacteristic
893C2×C3D3×#23711yescharacteristic
894C2×C3D3×#23711yescharacteristic
895C2×C3#6431511yescharacteristic
896C2×C3#6431511yescharacteristic
897C2×C3#6431611yescharacteristic
898C2×C3C2×#380511yescharacteristic
899D3—41no—
900C22—61no—
901C22—61no—
902C22—61no—
903C22C2×D3311yescharacteristic
904C4—21no—
905C4—32no—
906C4—61no—
907C4—61no—
908C4—61no—
909C4—61no—
910C4—181no—
911C4—181no—
912C4—181no—
913C4—181no—
914C4—181no—
915C4—181no—
916C4—541no—
917C4—541no—
918C3—21no—
919C3—21no—
920C3—21no—
921C3—41no—
922C3#1059402711yescharacteristic, complemented
923C3#1059444611yescharacteristic, complemented
924C3#1059534911yescharacteristic, complemented
925C2—121no—
926C2#1172439311yescharacteristic
927C2#1172439711yescharacteristic
928C2D3×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×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
1. #11723669C2semidirect
2. #11723448C2semidirect
4. #11723397C2semidirect
7. C3×#63839C2semidirect
10. #11723015C2semidirect
11. #11723011C2semidirect
12. #11723011C2semidirect
14. #11722940C2semidirect
100. #63839D3semidirect
626. C33#541semidirect
854. C32#5625semidirect
855. C32#5701semidirect
856. C32#5731semidirect
922. C3#10594027semidirect
923. C3#10594446semidirect
924. C3#10595349semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117234482
#117234322
#117233972
C3×#638872
C3×#638612
C3×#638392
#117230262
#117230222
#117230152
#117230112
#117229692
#117229402
#117229132
#105953493
#105944463
#105940273