Finite Group Databasebeta

← #13168525

Subgroups — #13168525

Order 1728.

1100 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723688C211yesmaximal, characteristic, complemented
2#11723434C211yesmaximal, characteristic, complemented
3#11723433C211yesmaximal, characteristic, complemented
4#11723391C211yesmaximal, characteristic, complemented
5C3×#63886C211yesmaximal, characteristic
6C3×#63884C211yesmaximal, characteristic, complemented
7C3×#63840C211yesmaximal, characteristic, complemented
8#11723019C211yesmaximal, characteristic, complemented
9#11723002C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722994C211yesmaximal, characteristic, complemented
12#11722971C211yesmaximal, characteristic, complemented
13#11722969C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595203—31nomaximal
17#10594494—31nomaximal
18#10594458—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#626C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32C32×Dic3⋊C4C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88814C2211yescharacteristic
36#88807C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64145—31no—
55#64107—31no—
56#64096—31no—
57C3×#939—31no—
58C3×#935—31no—
59C3×#895—31no—
60C3×#894—31no—
61C3×#888—31no—
62C3×#888—31no—
63Dic3×#67—31no—
64#63969—31no—
65#63964—31no—
66#63964—31no—
67#63959—31no—
68#63959—31no—
69#63956—31no—
70#63955—31no—
71#63907—31no—
72#63904—31no—
73#63898—31no—
74#63896—31no—
75#63893—31no—
76#63888—31no—
77#63887—31no—
78#63887—31no—
79#63886D311yescharacteristic
80#63884—31no—
81#63884D311yescharacteristic, complemented
82#63877—31no—
83#63863—31no—
84#63863—31no—
85#63863—31no—
86#63863—61no—
87#63862—31no—
88#63862—31no—
89#63862—31no—
90#63862—61no—
91#63860—31no—
92#63858—31no—
93#63857—31no—
94#63856—31no—
95#63855—31no—
96#63854—31no—
97#63852—31no—
98#63840D311yescharacteristic, complemented
99#63838—31no—
100#63838—31no—
101#63838—61no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C3×#634—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×D12—41no—
119#6294—41no—
120#6293—22no—
121C3×#627—41no—
122C3×#626—22no—
123C3×#626—41no—
124C3×D3×Dic3—22no—
125C3×D3×Dic3—41no—
126#5733—91no—
127#5662—91no—
128#5603—91no—
129C2×C32×D4—31no—
130C2×#634—31no—
131C2×#634C2×D311yescharacteristic
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C22×C3×Dic3—31no—
135C22×C3×Dic3—31no—
136C2×C3×D12—21no—
137C2×C3×D12—31no—
138C2×C3×D12—31no—
139C2×C3×D12C2×D311yescharacteristic
140C2×C3×D12C2×D311yescharacteristic
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×C3×Dic6—31no—
144C2×C3×Dic6—31no—
145C2×C3×Dic6—31no—
146C2×C3×Dic6—31no—
147C2×C3×Dic6—61no—
148C2×#627—31no—
149C2×#627—31no—
150C2×#627—61no—
151C2×#627C2×D311yescharacteristic
152C2×#626C2×D311yescharacteristic
153C2×#626C2×D311yescharacteristic
154C2×#624—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3C2×D311yescharacteristic
158C2×D3×Dic3C2×D311yescharacteristic
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161#3757—31no—
162#3757—31no—
163#3757—31no—
164#3757—31no—
165#3752—31no—
166#3752—31no—
167#3752C2×D311yescharacteristic
168C4⋊(C3⋊Dic3)—31no—
169#3750—31no—
170#3750—31no—
171#3750C2×D311yescharacteristic
172C4×C3⋊Dic3—31no—
173C4×C3⋊Dic3—31no—
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—31no—
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—61no—
178C4×C3⋊Dic3—61no—
179C4×C3⋊Dic3—61no—
180C4×C3⋊Dic3—121no—
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—61no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×Dic3⋊C4—21no—
195C3×Dic3⋊C4—21no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—61no—
201C3×Dic3⋊C4C2×D311yescharacteristic
202C3×Dic3⋊C4C2×D311yescharacteristic
203C3×Dic3⋊C4C2×D311yescharacteristic
204C3×Dic3⋊C4C2×D311yescharacteristic
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—61no—
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—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3C2×D311yescharacteristic
223Dic3⋊Dic3C2×D311yescharacteristic
224#3722—31no—
225(C2×D3)⋊Dic3—31no—
226(C2×D3)⋊Dic3—31no—
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)⋊Dic3—61no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3C2×D311yescharacteristic
246(C2×D3)⋊Dic3C2×D311yescharacteristic
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—61no—
254Dic32—61no—
255Dic32C2×D311yescharacteristic
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—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—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—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×C4⋊Q8—91no—
279C3×#123—91no—
280C3×#121—91no—
281#947—91no—
282#947—91no—
283#946—91no—
284#946—91no—
285#939—31no—
286#936—91no—
287#936—91no—
288#936—91no—
289#936—91no—
290#936—181no—
291#935—31no—
292#935—91no—
293D4×Dic3—91no—
294C4×#67—91no—
295#926—91no—
296#924—91no—
297#924—91no—
298#898—91no—
299#898—91no—
300#898—91no—
301#898—181no—
302#897—91no—
303#896—91no—
304#895—31no—
305#894—31no—
306#894—91no—
307#893—91no—
308#888—31no—
309#888—31no—
310#887—91no—
311#887—91no—
312#887—91no—
313#887—181no—
314#885—91no—
315#885—91no—
316#883—91no—
317#879—91no—
318#879—91no—
319#879—91no—
320#878—91no—
321#878—91no—
322#878—91no—
323#877—91no—
324#875—91no—
325#872—91no—
326C23×C32—31no—
327C23×C32—31no—
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—21no—
330C22×C3×D3—21no—
331C22×C3×D3—31no—
332C22×C3×D3—31no—
333C22×C3×D3—61no—
334C22×C3×D3C22×D311yescharacteristic
335C22×C3×D3C22×D311yescharacteristic
336C22×C3×D3C22×D311yescharacteristic
337C22×C3×D3C22×D311yescharacteristic
338C32×D4—121no—
339C2×C32×C4—21no—
340C2×C32×C4—21no—
341C2×C32×C4—21no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—41no—
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—121no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369#634—41no—
370#634—62no—
371C3×#67—62no—
372C3×#67—121no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—62no—
393C2×C3×Dic3—121no—
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C3×D12—41no—
403C3×D12—41no—
404C3×D12—42no—
405C3×D12—62no—
406C3×D12—121no—
407C3×C4×D3—62no—
408C3×C4×D3—121no—
409C3×Dic6—121no—
410C3×Dic6—121no—
411C3×Dic6—121no—
412C3×Dic6—121no—
413C3×Dic6—122no—
414#627—41no—
415#627—64no—
416#627—62no—
417#627—62no—
418#626—22no—
419#626—41no—
420#624—121no—
421D3×Dic3—22no—
422D3×Dic3—41no—
423D3×Dic3—121no—
424D3×Dic3—121no—
425#542—271noSylow
426C2×C33C2×#4111yescharacteristic
427C2×C33H(5,𝔽2)11yescharacteristic
428C2×C332−1+411yescharacteristic
429C3×C3⋊D3—41no—
430C32×D3—41no—
431C32×D3—41no—
432C2×C3×Q8—91no—
433C2×C3×Q8—91no—
434C2×C3×D4—31no—
435C2×C3×D4—31no—
436C2×C3×D4—61no—
437C2×C3×D4—91no—
438C2×C3×D4—91no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C2×#67—31no—
442C2×#67—31no—
443C22×Dic3—31no—
444C22×Dic3—31no—
445C22×Dic3—91no—
446C2×D12—31no—
447C2×D12—31no—
448C2×D12D3211yescharacteristic
449C2×C4×D3—31no—
450C2×C4×D3—31no—
451C2×C4×D3—91no—
452C2×C4×D3—91no—
453C2×Dic6—31no—
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6—61no—
458C2×Dic6—91no—
459C2×Dic6—91no—
460C2×Dic6—91no—
461C2×Dic6—181no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4—31no—
464C3×C4⋊C4—31no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—61no—
467C3×C4⋊C4—61no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4—91no—
470C3×C4⋊C4—91no—
471C3×C22⋊C4—91no—
472C3×C22⋊C4—91no—
473C3×C22⋊C4—91no—
474C3×C22⋊C4—91no—
475C3×C22⋊C4—91no—
476C3×C42—91no—
477#217—31no—
478#217—31no—
479#217—31no—
480#217—31no—
481#217—91no—
482#217—91no—
483#217—91no—
484#217—91no—
485#217—91no—
486#217—91no—
487#217—91no—
488#217—91no—
489#217—91no—
490#217—91no—
491#217—91no—
492#217—181no—
493#217—181no—
494#217—181no—
495#217—181no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—61no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—181no—
514(C2×D3)⋊C4—181no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—91no—
518C4⋊Dic3—91no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—181no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—61no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530Dic3⋊C4—91no—
531Dic3⋊C4—91no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—181no—
539Dic3⋊C4—181no—
540Dic3⋊C4D3211yescharacteristic
541Dic3⋊C4D3211yescharacteristic
542C4×Dic3—31no—
543C4×Dic3—31no—
544C4×Dic3—91no—
545C4×Dic3—91no—
546C4×Dic3—91no—
547C4×Dic3—91no—
548C4×Dic3—91no—
549C4×Dic3—91no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C4×Dic3—91no—
553C4×Dic3—181no—
554C4×Dic3—181no—
555C4×Dic3—181no—
556C4×Dic3—181no—
557C4×Dic3—181no—
558C4×Dic3—361no—
559C22×C32—21no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—41no—
563C22×C32—61no—
564C22×C32—61no—
565C22×C32—61no—
566C22×C32—61no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32C23×D311yescharacteristic
570C22×C32C23×D311yescharacteristic
571C22×C32C23×D311yescharacteristic
572C2×C3⋊D3—21no—
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—21no—
583C2×C3×D3—21no—
584C2×C3×D3—21no—
585C2×C3×D3—21no—
586C2×C3×D3—21no—
587C2×C3×D3—41no—
588C2×C3×D3—41no—
589C2×C3×D3—41no—
590C2×C3×D3—41no—
591C2×C3×D3—41no—
592C2×C3×D3—41no—
593C2×C3×D3—61no—
594C2×C3×D3—61no—
595C2×C3×D3—61no—
596C2×C3×D3—61no—
597C2×C3×D3—61no—
598C2×C3×D3—61no—
599C2×C3×D3—121no—
600C2×C3×D3—121no—
601C2×C3×D3—121no—
602C32×C4—21no—
603C32×C4—22no—
604C32×C4—21no—
605C32×C4—21no—
606C32×C4—32no—
607C32×C4—41no—
608C32×C4—41no—
609C32×C4—42no—
610C32×C4—61no—
611C32×C4—61no—
612C32×C4—61no—
613C3⋊Dic3—21no—
614C3⋊Dic3—21no—
615C3⋊Dic3—21no—
616C3⋊Dic3—21no—
617C3⋊Dic3—21no—
618C3⋊Dic3—61no—
619C3⋊Dic3—61no—
620C3⋊Dic3—62no—
621C3⋊Dic3—62no—
622C3⋊Dic3—61no—
623C3⋊Dic3—61no—
624C3⋊Dic3—61no—
625C3⋊Dic3—61no—
626C3⋊Dic3—121no—
627C3⋊Dic3—121no—
628C3⋊Dic3—121no—
629C3⋊Dic3—121no—
630C3⋊Dic3—122no—
631C3⋊Dic3—122no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—22no—
639C3×Dic3—41no—
640C3×Dic3—41no—
641C3×Dic3—41no—
642C3×Dic3—62no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—121no—
654C3×Dic3—121no—
655C3×Dic3—121no—
656C3×Dic3—121no—
657C3×Dic3#23712yes—
658C3×Dic3#23912yes—
659C4⋊Q8—91no—
660#126—271no—
661#126—271no—
662#124—271no—
663#124—271no—
664#124—271no—
665#123—91no—
666#123—271no—
667C22⋊Q8—271no—
668C22⋊Q8—271no—
669C22⋊Q8—271no—
670#121—91no—
671C4×Q8—271no—
672C4×D4—271no—
673#117—271no—
674C33#54211yescharacteristic, complemented, Sylow
675C23×C3—31no—
676C23×C3—31no—
677C23×C3—31no—
678C23×C3—31no—
679C23×C3—61no—
680C23×C3—61no—
681C23×C3—91no—
682C22×D3—31no—
683C22×D3—31no—
684C22×D3—61no—
685C22×D3C2×D3211yescharacteristic
686C22×D3C2×D3211yescharacteristic
687C3×Q8—361no—
688C3×Q8—361no—
689C3×D4—121no—
690C3×D4—121no—
691C3×D4—122no—
692C3×D4—182no—
693C3×D4—361no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—41no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—91no—
711C2×C3×C4—91no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—91no—
715C2×C3×C4—182no—
716C2×C3×C4—361no—
717C2×C3×C4C2×D3211yescharacteristic
718C2×C3×C4C2×D3211yescharacteristic
719C2×C3×C4C2×D3211yescharacteristic
720#67—62no—
721#67—121no—
722C2×Dic3—31no—
723C2×Dic3—31no—
724C2×Dic3—31no—
725C2×Dic3—31no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—61no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—61no—
736C2×Dic3—61no—
737C2×Dic3—62no—
738C2×Dic3—91no—
739C2×Dic3—91no—
740C2×Dic3—91no—
741C2×Dic3—91no—
742C2×Dic3—91no—
743C2×Dic3—91no—
744C2×Dic3—121no—
745C2×Dic3—181no—
746C2×Dic3—181no—
747C2×Dic3—181no—
748C2×Dic3—181no—
749C2×Dic3—181no—
750C2×Dic3—181no—
751C2×Dic3—361no—
752C2×Dic3—361no—
753C2×Dic3—361no—
754C2×Dic3C2×D3211yescharacteristic
755C2×Dic3C2×D3211yescharacteristic
756C2×Dic3C2×D3211yescharacteristic
757C2×Dic3C2×D3211yescharacteristic
758D12—41no—
759D12—62no—
760D12—121no—
761C4×D3—62no—
762C4×D3—121no—
763C4×D3—361no—
764C4×D3—361no—
765Dic6—121no—
766Dic6—121no—
767Dic6—121no—
768Dic6—121no—
769Dic6—122no—
770Dic6—182no—
771Dic6—182no—
772Dic6—184no—
773Dic6—182no—
774C2×C32—21no—
775C2×C32—21no—
776C2×C32—21no—
777C2×C32—21no—
778C2×C32—21no—
779C2×C32—21no—
780C2×C32—21no—
781C2×C32—21no—
782C2×C32—21no—
783C2×C32—41no—
784C2×C32—41no—
785C2×C32—41no—
786C2×C32—121no—
787C2×C32—121no—
788C2×C32C2×#23711yescharacteristic
789C2×C32#100411yescharacteristic
790C2×C32#100411yescharacteristic
791C2×C32#100411yescharacteristic
792C2×C32C2×#23911yescharacteristic
793C2×C32#100711yescharacteristic
794C2×C32D3×#4111yescharacteristic
795C2×C32#101011yescharacteristic
796C2×C32#101011yescharacteristic
797C3⋊D3—41no—
798C3×D3—41no—
799C3×D3—41no—
800C3×D3—41no—
801C3×D3—41no—
802C3×D3—81no—
803C3×D3—81no—
804C3×D3—121no—
805C3×D3—121no—
806C3×D3—241no—
807C2×Q8—91no—
808C2×Q8—91no—
809C2×Q8—271no—
810C2×D4—31no—
811C2×D4—91no—
812C2×D4—91no—
813C22×C4—91no—
814C22×C4—91no—
815C22×C4—271no—
816C4⋊C4—31no—
817C4⋊C4—31no—
818C4⋊C4—91no—
819C4⋊C4—91no—
820C4⋊C4—91no—
821C4⋊C4—271no—
822C4⋊C4—271no—
823C4⋊C4—271no—
824C4⋊C4—271no—
825C4⋊C4—271no—
826C22⋊C4—91no—
827C22⋊C4—91no—
828C22⋊C4—91no—
829C22⋊C4—91no—
830C22⋊C4—91no—
831C22⋊C4—271no—
832C22⋊C4—271no—
833C22⋊C4—271no—
834C22⋊C4—271no—
835C22⋊C4—271no—
836C22⋊C4—271no—
837C22⋊C4—271no—
838C42—91no—
839C42—271no—
840C42—271no—
841C42—271no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—41no—
846C22×C3—61no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—61no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—61no—
857C22×C3—61no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—181no—
865C22×C3—181no—
866C22×C3—181no—
867C22×C3C22×D3211yescharacteristic
868C22×C3C22×D3211yescharacteristic
869C22×C3C22×D3211yescharacteristic
870C2×D3—21no—
871C2×D3—21no—
872C2×D3—21no—
873C2×D3—21no—
874C2×D3—21no—
875C2×D3—21no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—61no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C3×C4—22no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—32no—
890C3×C4—32no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—42no—
894C3×C4—62no—
895C3×C4—61no—
896C3×C4—61no—
897C3×C4—61no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—61no—
901C3×C4—121no—
902C3×C4—121no—
903C3×C4—121no—
904C3×C4—181no—
905C3×C4—181no—
906C3×C4—181no—
907C3×C4—181no—
908C3×C4—181no—
909Dic3—21no—
910Dic3—21no—
911Dic3—21no—
912Dic3—62no—
913Dic3—61no—
914Dic3—61no—
915Dic3—61no—
916Dic3—61no—
917Dic3—61no—
918Dic3—61no—
919Dic3—61no—
920Dic3—61no—
921Dic3—61no—
922Dic3—61no—
923Dic3—121no—
924Dic3—121no—
925Dic3—121no—
926Dic3—121no—
927Dic3—182no—
928Dic3—182no—
929Dic3—181no—
930Dic3—181no—
931Dic3—181no—
932Dic3—181no—
933Dic3—181no—
934Dic3—181no—
935Dic3—361no—
936Dic3—361no—
937Dic3—361no—
938Dic3—361no—
939Dic3—362no—
940Dic3—362no—
941Dic3#379612yes—
942C32—21no—
943C32—21no—
944C32—21no—
945C32—41no—
946C32#560311yescharacteristic, complemented
947C32#566211yescharacteristic, complemented
948C32#573311yescharacteristic, complemented
949C23—31no—
950C23—31no—
951C23—91no—
952Q8—361no—
953Q8—361no—
954Q8—542no—
955D4—121no—
956D4—182no—
957D4—361no—
958C2×C4—31no—
959C2×C4—31no—
960C2×C4—31no—
961C2×C4—31no—
962C2×C4—91no—
963C2×C4—91no—
964C2×C4—91no—
965C2×C4—91no—
966C2×C4—91no—
967C2×C4—182no—
968C2×C4—271no—
969C2×C4—271no—
970C2×C4—361no—
971C2×C4—1081no—
972C2×C4D3311yescharacteristic
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—41no—
983C2×C3—41no—
984C2×C3—41no—
985C2×C3—121no—
986C2×C3—121no—
987C2×C3—121no—
988C2×C3—121no—
989C2×C3—241no—
990C2×C3—241no—
991C2×C3—361no—
992C2×C3C2×#379611yescharacteristic
993C2×C3#6429711yescharacteristic
994C2×C3#6430911yescharacteristic
995C2×C3D3×#23711yescharacteristic
996C2×C3#6431311yescharacteristic
997C2×C3#6431311yescharacteristic
998C2×C3#6431511yescharacteristic
999C2×C3D3×#23911yescharacteristic
1000C2×C3#6433011yescharacteristic
1001D3—41no—
1002D3—41no—
1003D3—121no—
1004D3—121no—
1005D3—241no—
1006C22—61no—
1007C22—61no—
1008C22—61no—
1009C22—61no—
1010C22—61no—
1011C22—61no—
1012C22—181no—
1013C22—181no—
1014C22—181no—
1015C22C2×D3311yescharacteristic
1016C4—21no—
1017C4—32no—
1018C4—61no—
1019C4—61no—
1020C4—61no—
1021C4—181no—
1022C4—181no—
1023C4—181no—
1024C4—181no—
1025C4—181no—
1026C4—541no—
1027C4—541no—
1028C3—21no—
1029C3—21no—
1030C3—21no—
1031C3—41no—
1032C3#1059445811yescharacteristic, complemented
1033C3#1059449411yescharacteristic, complemented
1034C3#1059520311yescharacteristic, complemented
1035C2—121no—
1036C2—121no—
1037C2—361no—
1038C2D3×#379611yescharacteristic
1039C2#1172439311yescharacteristic
1040C2#1172441511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC3×#63886C2
hypercenterC2×C4D33
hypocenterC33#542
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723688C2semidirect
2. #11723434C2semidirect
3. #11723433C2semidirect
4. #11723391C2semidirect
6. C3×#63884C2semidirect
7. C3×#63840C2semidirect
8. #11723019C2semidirect
9. #11723002C2semidirect
10. #11723001C2semidirect
11. #11722994C2semidirect
12. #11722971C2semidirect
13. #11722969C2semidirect
14. #11722927C2semidirect
15. #11722913C2semidirect
81. #63884D3semidirect
98. #63840D3semidirect
674. C33#542semidirect
946. C32#5603semidirect
947. C32#5662semidirect
948. C32#5733semidirect
1032. C3#10594458semidirect
1033. C3#10594494semidirect
1034. C3#10595203semidirect

Maximal subgroups

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

subgroupindex
#117236882
#117234342
#117234332
#117233912
C3×#638862
C3×#638842
C3×#638402
#117230192
#117230022
#117230012
#117229942
#117229712
#117229692
#117229272
#117229132
#105952033
#105944943
#105944583