Finite Group Databasebeta

← #13178214

Subgroups — #13178214

Order 1728.

1102 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64092C211yesmaximal, characteristic
2C3×#64088C211yesmaximal, characteristic, complemented
3C3×#64087C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic
5#11723724C211yesmaximal, characteristic
6#11723716C211yesmaximal, characteristic, complemented
7#11723715C211yesmaximal, characteristic, complemented
8#11723688C211yesmaximal, characteristic, complemented
9#11723683C211yesmaximal, characteristic, complemented
10#11723682C211yesmaximal, characteristic, complemented
11#11723669C211yesmaximal, characteristic, complemented
12#11723669C211yesmaximal, characteristic, complemented
13#11723669C211yesmaximal, characteristic, complemented
14#11723668C211yesmaximal, characteristic, complemented
15#11723667C211yesmaximal, characteristic, complemented
16#10594118—31nomaximal
17#10594116—31nomaximal
18#10594026—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×#634C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C33×C22⋊C4C2211yescharacteristic
26C3×#3757C2211yescharacteristic
27C3×#3757C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×C4×C3⋊Dic3C2211yescharacteristic
40#88815C2211yescharacteristic
41#88815C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88813C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64092D311yescharacteristic
55#64088D311yescharacteristic, complemented
56#64087D311yescharacteristic, complemented
57C3×#883—31no—
58C3×#883—31no—
59C3×#883—61no—
60C3×#879—31no—
61C3×#879—31no—
62C3×#879—61no—
63C3×#878—31no—
64C3×#878—31no—
65C3×#878—61no—
66#63975—31no—
67#67⋊Dic3—31no—
68Dic3×#67—31no—
69#63969—31no—
70#63969—31no—
71#63957—31no—
72#63956—31no—
73#63956—31no—
74#63956—31no—
75#63955—31no—
76#63955—31no—
77#63952—31no—
78#63896—31no—
79#63888—31no—
80#63887—31no—
81#63883—31no—
82#63878—31no—
83#63877—31no—
84D3×Dic3⋊C4—31no—
85D3×Dic3⋊C4—31no—
86#63849—31no—
87#63847—31no—
88#63847—31no—
89#63847—31no—
90#63846—31no—
91#63846—31no—
92#63846—31no—
93#63845—31no—
94#63845—31no—
95#63845—31no—
96#63844—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63841—31no—
100#63841—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C3×#638—22no—
107C2×C3×C3⋊Dic3—22no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C3×C4×C3⋊D3—22no—
120C3×#634—22no—
121#6294—22no—
122#6294—22no—
123#5708—91no—
124#5650—91no—
125#5639—91no—
126C2×#638C2×D311yescharacteristic
127C22×C3⋊Dic3C2×D311yescharacteristic
128C2×C4×C3⋊D3C2×D311yescharacteristic
129C2×#634C2×D311yescharacteristic
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—61no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3—31no—
135C22×C3×Dic3—61no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—61no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—61no—
142C2×#624—31no—
143C2×#624—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C32×C22⋊C4—21no—
149C32×C22⋊C4—21no—
150C32×C22⋊C4—21no—
151C32×C22⋊C4—41no—
152C32×C22⋊C4C2×D311yescharacteristic
153C32×C22⋊C4C2×D311yescharacteristic
154C32×C22⋊C4C2×D311yescharacteristic
155#3757C2×D311yescharacteristic
156#3757C2×D311yescharacteristic
157#3757C2×D311yescharacteristic
158#3757C2×D311yescharacteristic
159#3752C2×D311yescharacteristic
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic
161C4⋊(C3⋊Dic3)C2×D311yescharacteristic
162C4⋊(C3⋊Dic3)C2×D311yescharacteristic
163#3750C2×D311yescharacteristic
164#3750C2×D311yescharacteristic
165#3750C2×D311yescharacteristic
166#3750C2×D311yescharacteristic
167#3750C2×D311yescharacteristic
168C4×C3⋊Dic3C2×D311yescharacteristic
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—31no—
177C3×#217—61no—
178C3×#217—61no—
179C3×#217—61no—
180C3×#217—61no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—61no—
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—61no—
191C3×C4⋊Dic3—61no—
192C3×C4⋊Dic3—61no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—61no—
204C3×Dic3⋊C4—61no—
205C3×Dic3⋊C4—61no—
206C3×Dic3⋊C4—61no—
207C3×Dic3⋊C4—61no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—61no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235#3722—31no—
236#3722—31no—
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—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253C22×C33—21no—
254C22×C33—21no—
255C22×C33—21no—
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3#4112yes—
260C33×C4—21no—
261C33×C4—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3#4112yes—
273C3×#126—91no—
274C3×#123—91no—
275C3×C22⋊Q8—91no—
276#946—91no—
277Q8×Dic3—91no—
278#935—91no—
279D4×Dic3—91no—
280C4×#67—91no—
281#926—91no—
282#926—91no—
283C2×Dic3⋊C4—91no—
284#896—91no—
285#892—91no—
286#892—91no—
287#892—91no—
288D3×C4⋊C4—91no—
289D3×C4⋊C4—91no—
290#890—91no—
291#890—91no—
292#890—91no—
293#889—91no—
294#889—91no—
295#889—91no—
296#889—91no—
297#889—91no—
298#889—91no—
299#887—91no—
300#883—31no—
301#883—31no—
302#883—61no—
303#883—91no—
304#883—91no—
305#67⋊C4—91no—
306#879—31no—
307#879—31no—
308#879—61no—
309#879—91no—
310#879—91no—
311#879—91no—
312#878—31no—
313#878—31no—
314#878—61no—
315#878—91no—
316#877—91no—
317#877—91no—
318#877—91no—
319#872—91no—
320C4×Dic6—91no—
321C23×C32—21no—
322C23×C32—21no—
323C23×C32—21no—
324C23×C32—41no—
325C23×C32C22×D311yescharacteristic
326C23×C32C22×D311yescharacteristic
327C23×C32C22×D311yescharacteristic
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—21no—
336C2×C32×C4—21no—
337C2×C32×C4—21no—
338C2×C32×C4—41no—
339C2×C32×C4—41no—
340C2×C32×C4C22×D311yescharacteristic
341C2×C32×C4C22×D311yescharacteristic
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345C2×C32×C4C22×D311yescharacteristic
346#638—22no—
347C2×C3⋊Dic3—22no—
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350C2×C3⋊Dic3C22×D311yescharacteristic
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C4×C3⋊D3—22no—
360#634—22no—
361C3×#67—62no—
362C3×#67—62no—
363C3×#67—122no—
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—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
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—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—62no—
398C2×C3×Dic3—62no—
399C2×C3×Dic3—122no—
400C3×C4×D3—62no—
401C3×C4×D3—62no—
402C3×C4×D3—122no—
403C3×Dic6—62no—
404C3×Dic6—62no—
405C3×Dic6—122no—
406#624—62no—
407#624—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411D3×Dic3—62no—
412#552—271noSylow
413C2×C33—41no—
414C2×C33C2×#4111yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C332−1+411yescharacteristic
417C3×C3⋊D3—22no—
418C2×C3×Q8—91no—
419C2×C3×D4—91no—
420C22×C3×C4—91no—
421C22×C3×C4—91no—
422C2×#67—31no—
423C2×#67—31no—
424C2×#67—61no—
425C22×Dic3—31no—
426C22×Dic3—31no—
427C22×Dic3—61no—
428C22×Dic3—91no—
429C22×Dic3—91no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—61no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×Dic6—31no—
438C2×Dic6—31no—
439C2×Dic6—61no—
440C3×C4⋊C4—91no—
441C3×C4⋊C4—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C22⋊C4—21no—
449C3×C22⋊C4—21no—
450C3×C22⋊C4—21no—
451C3×C22⋊C4—41no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4D3211yescharacteristic
458C3×C22⋊C4D3211yescharacteristic
459C3×C22⋊C4D3211yescharacteristic
460C3×C42—91no—
461#217—31no—
462#217—31no—
463#217—31no—
464#217—31no—
465#217—31no—
466#217—31no—
467#217—31no—
468#217—31no—
469#217—61no—
470#217—61no—
471#217—61no—
472#217—61no—
473#217—91no—
474#217—91no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4—31no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482C4⋊Dic3—31no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—61no—
489C4⋊Dic3—61no—
490C4⋊Dic3—61no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497C4⋊Dic3—91no—
498C4⋊Dic3—91no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—61no—
510Dic3⋊C4—61no—
511Dic3⋊C4—61no—
512Dic3⋊C4—61no—
513Dic3⋊C4—61no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—61no—
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—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C22×C32—21no—
546C22×C32—22no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—21no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32—21no—
557C22×C32—21no—
558C22×C32—41no—
559C22×C32—41no—
560C22×C32—41no—
561C22×C32—42no—
562C22×C32—41no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—41no—
568C22×C32—81no—
569C22×C32—81no—
570C22×C32C23×D311yescharacteristic
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
575C2×C3⋊D3#23712yes—
576C2×C3×D3—32no—
577C2×C3×D3—32no—
578C2×C3×D3—62no—
579C2×C3×D3—61no—
580C2×C3×D3—61no—
581C2×C3×D3—61no—
582C2×C3×D3—61no—
583C2×C3×D3—121no—
584C2×C3×D3—121no—
585C32×C4—21no—
586C32×C4—21no—
587C32×C4—21no—
588C32×C4—21no—
589C32×C4—21no—
590C32×C4—21no—
591C32×C4—41no—
592C32×C4—41no—
593C32×C4—41no—
594C32×C4—41no—
595C32×C4—41no—
596C32×C4—41no—
597C32×C4—81no—
598C32×C4—81no—
599C3⋊Dic3—21no—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3⋊Dic3—21no—
605C3⋊Dic3—21no—
606C3⋊Dic3—21no—
607C3⋊Dic3—21no—
608C3⋊Dic3—21no—
609C3⋊Dic3#23712yes—
610C3×Dic3—32no—
611C3×Dic3—32no—
612C3×Dic3—62no—
613C3×Dic3—61no—
614C3×Dic3—61no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
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—121no—
639C3×Dic3—121no—
640C3×Dic3—121no—
641C3×Dic3—121no—
642C3×Dic3—121no—
643#126—91no—
644#126—271no—
645#125—271no—
646#125—271no—
647#125—271no—
648#123—91no—
649#123—271no—
650C22⋊Q8—91no—
651C22⋊Q8—271no—
652C4×Q8—271no—
653C4×D4—271no—
654#117—271no—
655#117—271no—
656#117—271no—
657C2×C4⋊C4—271no—
658C33#55211yescharacteristic, complemented, Sylow
659C23×C3—21no—
660C23×C3—21no—
661C23×C3—21no—
662C23×C3—41no—
663C23×C3—91no—
664C23×C3C2×D3211yescharacteristic
665C23×C3C2×D3211yescharacteristic
666C23×C3C2×D3211yescharacteristic
667C22×D3—31no—
668C22×D3—31no—
669C22×D3—61no—
670C3×Q8—182no—
671C3×D4—182no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—91no—
681C2×C3×C4—91no—
682C2×C3×C4—91no—
683C2×C3×C4—91no—
684C2×C3×C4—91no—
685C2×C3×C4—91no—
686C2×C3×C4—91no—
687C2×C3×C4—91no—
688C2×C3×C4—91no—
689C2×C3×C4—91no—
690C2×C3×C4—91no—
691C2×C3×C4—182no—
692C2×C3×C4—182no—
693C2×C3×C4C2×D3211yescharacteristic
694C2×C3×C4C2×D3211yescharacteristic
695C2×C3×C4C2×D3211yescharacteristic
696C2×C3×C4C2×D3211yescharacteristic
697C2×C3×C4C2×D3211yescharacteristic
698C2×C3×C4C2×D3211yescharacteristic
699#67—62no—
700#67—62no—
701#67—122no—
702C2×Dic3—31no—
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—31no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—31no—
718C2×Dic3—31no—
719C2×Dic3—31no—
720C2×Dic3—31no—
721C2×Dic3—31no—
722C2×Dic3—31no—
723C2×Dic3—31no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—61no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—62no—
736C2×Dic3—62no—
737C2×Dic3—122no—
738C2×Dic3—182no—
739C2×Dic3—182no—
740C4×D3—62no—
741C4×D3—62no—
742C4×D3—122no—
743C4×D3—182no—
744C4×D3—182no—
745C4×D3—182no—
746C4×D3—182no—
747Dic6—62no—
748Dic6—62no—
749Dic6—122no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—41no—
762C2×C32—41no—
763C2×C32—42no—
764C2×C32—41no—
765C2×C32—41no—
766C2×C32—81no—
767C2×C32—81no—
768C2×C32—82no—
769C2×C32C2×#23711yescharacteristic
770C2×C32C2×#23711yescharacteristic
771C2×C32#100711yescharacteristic
772C2×C32D3×#4111yescharacteristic
773C2×C32D3×#4111yescharacteristic
774C2×C32D3×#4111yescharacteristic
775C2×C32D3×#4111yescharacteristic
776C2×C32#101011yescharacteristic
777C2×C32#101011yescharacteristic
778C3⋊D3—22no—
779C3×D3—62no—
780C3×D3—62no—
781C3×D3—122no—
782C2×Q8—91no—
783C2×D4—91no—
784C22×C4—91no—
785C22×C4—91no—
786C22×C4—271no—
787C22×C4—271no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4—91no—
792C4⋊C4—91no—
793C4⋊C4—91no—
794C4⋊C4—91no—
795C4⋊C4—91no—
796C4⋊C4—271no—
797C4⋊C4—271no—
798C4⋊C4—271no—
799C4⋊C4—271no—
800C4⋊C4—271no—
801C4⋊C4—271no—
802C4⋊C4—271no—
803C4⋊C4—271no—
804C22⋊C4—91no—
805C22⋊C4—91no—
806C22⋊C4—91no—
807C22⋊C4—91no—
808C22⋊C4—91no—
809C22⋊C4—271no—
810C22⋊C4—271no—
811C22⋊C4#111311yescharacteristic
812C42—91no—
813C42—271no—
814C42—271no—
815C42—271no—
816C42—271no—
817C22×C3—22no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—42no—
839C22×C3—41no—
840C22×C3—81no—
841C22×C3—81no—
842C22×C3—92no—
843C22×C3—181no—
844C22×C3—181no—
845C22×C3C22×D3211yescharacteristic
846C22×C3C22×D3211yescharacteristic
847C22×C3C22×D3211yescharacteristic
848C2×D3—32no—
849C2×D3—32no—
850C2×D3—62no—
851C2×D3—61no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—121no—
856C2×D3—121no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—41no—
868C3×C4—41no—
869C3×C4—81no—
870C3×C4—81no—
871C3×C4—92no—
872C3×C4—181no—
873C3×C4—181no—
874C3×C4—181no—
875C3×C4—181no—
876C3×C4—181no—
877C3×C4—181no—
878C3×C4—181no—
879C3×C4—181no—
880C3×C4—181no—
881C3×C4—181no—
882Dic3—32no—
883Dic3—32no—
884Dic3—62no—
885Dic3—61no—
886Dic3—61no—
887Dic3—61no—
888Dic3—61no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—61no—
900Dic3—61no—
901Dic3—61no—
902Dic3—61no—
903Dic3—61no—
904Dic3—61no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—121no—
910Dic3—121no—
911Dic3—121no—
912Dic3—121no—
913Dic3—121no—
914Dic3—121no—
915C32—21no—
916C32—21no—
917C32—21no—
918C32—41no—
919C32#563911yescharacteristic, complemented
920C32#565011yescharacteristic, complemented
921C32#570811yescharacteristic, complemented
922C23—91no—
923C23C2×#111311yescharacteristic
924Q8—182no—
925D4—182no—
926C2×C4—91no—
927C2×C4—91no—
928C2×C4—91no—
929C2×C4—91no—
930C2×C4—91no—
931C2×C4—91no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—91no—
936C2×C4—91no—
937C2×C4—182no—
938C2×C4—182no—
939C2×C4—542no—
940C2×C4—542no—
941C2×C4C2×#111311yescharacteristic
942C2×C4C2×#111311yescharacteristic
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—42no—
953C2×C3—41no—
954C2×C3—41no—
955C2×C3—41no—
956C2×C3—41no—
957C2×C3—41no—
958C2×C3—41no—
959C2×C3—81no—
960C2×C3—81no—
961C2×C3—82no—
962C2×C3—182no—
963C2×C3#6429711yescharacteristic
964C2×C3#6429711yescharacteristic
965C2×C3#6429811yescharacteristic
966C2×C3D3×#23711yescharacteristic
967C2×C3D3×#23711yescharacteristic
968C2×C3D3×#23711yescharacteristic
969C2×C3D3×#23711yescharacteristic
970C2×C3#6431211yescharacteristic
971C2×C3#6431211yescharacteristic
972D3—62no—
973D3—62no—
974D3—122no—
975C22—21no—
976C22—21no—
977C22—21no—
978C22—92no—
979C22—181no—
980C22—181no—
981C22C22×#111311yescharacteristic
982C4—21no—
983C4—21no—
984C4—92no—
985C4—181no—
986C4—181no—
987C4—181no—
988C4—181no—
989C4—181no—
990C4—181no—
991C4—181no—
992C4—181no—
993C4—181no—
994C4—181no—
995C3—21no—
996C3—21no—
997C3—21no—
998C3—41no—
999C3#1059402611yescharacteristic, complemented
1000C3#1059411611yescharacteristic, complemented
1001C3#1059411811yescharacteristic, complemented
1002C2—41no—
1003C2—182no—
1004C2#1172461411yescharacteristic
1005C2#1172462211yescharacteristic
1006C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×C3×#638C22
hypercenterC22⋊C4#1113
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64088C2semidirect
3. C3×#64087C2semidirect
6. #11723716C2semidirect
7. #11723715C2semidirect
8. #11723688C2semidirect
9. #11723683C2semidirect
10. #11723682C2semidirect
11. #11723669C2semidirect
12. #11723669C2semidirect
13. #11723669C2semidirect
14. #11723668C2semidirect
15. #11723667C2semidirect
55. #64088D3semidirect
56. #64087D3semidirect
658. C33#552semidirect
919. C32#5639semidirect
920. C32#5650semidirect
921. C32#5708semidirect
999. C3#10594026semidirect
1000. C3#10594116semidirect
1001. C3#10594118semidirect

Maximal subgroups

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

subgroupindex
C3×#640922
C3×#640882
C3×#640872
#117237262
#117237242
#117237162
#117237152
#117236882
#117236832
#117236822
#117236692
#117236682
#117236672
#105941183
#105941163
#105940263