Finite Group Databasebeta

← #13178135

Subgroups — #13178135

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
1C3×#64085C211yesmaximal, characteristic
2C3×#64079C211yesmaximal, characteristic, complemented
3C3×C4×#634C211yesmaximal, characteristic, complemented
4#11723692C211yesmaximal, characteristic
5#11723688C211yesmaximal, characteristic
6#11723683C211yesmaximal, characteristic
7#11723679C211yesmaximal, characteristic, complemented
8#11723676C211yesmaximal, characteristic
9#11723675C211yesmaximal, characteristic
10#11723675C211yesmaximal, characteristic
11#11723669C211yesmaximal, characteristic, complemented
12#11723669C211yesmaximal, characteristic, complemented
13#11723669C211yesmaximal, characteristic, complemented
14#11723666C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10593945—31nomaximal
17#10593928—31nomaximal
18#10593849—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×#6296C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C33×C42C2211yescharacteristic
23C3×#3752C2211yescharacteristic
24C3×#3752C2211yescharacteristic
25C3×#3752C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×C4×C3⋊Dic3C2211yescharacteristic
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#88814C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64085D311yescharacteristic
55#64079D311yescharacteristic, complemented
56C4×#634D311yescharacteristic, complemented
57C3×#876—31no—
58C3×#876—31no—
59C3×#876—61no—
60C3×#870—31no—
61C3×#870—31no—
62C3×#870—61no—
63C3×C4×Dic6—31no—
64C3×C4×Dic6—31no—
65C3×C4×Dic6—61no—
66#63899—31no—
67#63896—31no—
68#63895—31no—
69#63893—31no—
70#63888—31no—
71#63887—31no—
72#63878—31no—
73#63877—31no—
74#63870—31no—
75#63868—31no—
76#63867—31no—
77#63867—31no—
78#63862—31no—
79#63861—31no—
80#63861—31no—
81#63859—31no—
82#63858—31no—
83#63858—31no—
84#63848—31no—
85#63848—31no—
86#63847—31no—
87#63847—31no—
88#63847—31no—
89#63846—31no—
90#63846—31no—
91#63846—31no—
92#63845—31no—
93#63845—31no—
94#63845—31no—
95#63840—31no—
96#63839—31no—
97#63839—31no—
98#63838—31no—
99#63837—31no—
100#63837—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
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×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×#634—22no—
118#6296—22no—
119#6294—22no—
120#5701—91no—
121#5696—91no—
122#5583—91no—
123C2×#634C2×D311yescharacteristic
124C2×C3×Dic6—31no—
125C2×C3×Dic6—31no—
126C2×C3×Dic6—61no—
127C2×#627—31no—
128C2×#627—31no—
129C2×#627—31no—
130C2×#624—31no—
131C2×D3×Dic3—31no—
132C2×D3×Dic3—31no—
133C32×C42—21no—
134C32×C42—21no—
135C32×C42—21no—
136C32×C42—41no—
137C32×C42C2×D311yescharacteristic
138C32×C42C2×D311yescharacteristic
139C32×C42C2×D311yescharacteristic
140#3752C2×D311yescharacteristic
141#3752C2×D311yescharacteristic
142#3752C2×D311yescharacteristic
143C4⋊(C3⋊Dic3)C2×D311yescharacteristic
144C4⋊(C3⋊Dic3)C2×D311yescharacteristic
145C4⋊(C3⋊Dic3)C2×D311yescharacteristic
146#3750C2×D311yescharacteristic
147#3750C2×D311yescharacteristic
148#3750C2×D311yescharacteristic
149#3750C2×D311yescharacteristic
150#3750C2×D311yescharacteristic
151#3750C2×D311yescharacteristic
152#3750C2×D311yescharacteristic
153#3750C2×D311yescharacteristic
154#3750C2×D311yescharacteristic
155C4×C3⋊Dic3C2×D311yescharacteristic
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×(C2×D3)⋊C4—61no—
165C3×(C2×D3)⋊C4—61no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—31no—
172C3×C4⋊Dic3—61no—
173C3×C4⋊Dic3—61no—
174C3×C4⋊Dic3—61no—
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—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
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⋊C4—61no—
195C3×Dic3⋊C4—61no—
196C3×Dic3⋊C4—61no—
197C3×Dic3⋊C4—61no—
198C3×Dic3⋊C4—61no—
199C3×Dic3⋊C4—61no—
200C3×Dic3⋊C4—61no—
201C3×Dic3⋊C4—61no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206C3×C4×Dic3—61no—
207C3×C4×Dic3—61no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—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—
232#3722—31no—
233#3722—31no—
234#3722—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—31no—
240(C2×D3)⋊Dic3—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250C22×C33C2411yescharacteristic
251C2×C3×C3⋊D3—21no—
252C2×C3×C3⋊D3—21no—
253C2×C3×C3⋊D3—21no—
254C33×C4—21no—
255C33×C4—21no—
256C33×C4—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—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3#4112yes—
268C3×#126—91no—
269C3×#125—91no—
270C3×C4×Q8—91no—
271#946—91no—
272#944—91no—
273#898—91no—
274#898—91no—
275#898—91no—
276#898—91no—
277#898—91no—
278#897—91no—
279#896—91no—
280#896—91no—
281#892—91no—
282#890—91no—
283#890—91no—
284#890—91no—
285#889—91no—
286#889—91no—
287#889—91no—
288#889—91no—
289#889—91no—
290#889—91no—
291#889—91no—
292#889—91no—
293#888—91no—
294#888—91no—
295#887—91no—
296#887—91no—
297#879—91no—
298#879—91no—
299#879—91no—
300#878—91no—
301#878—91no—
302#877—91no—
303#876—31no—
304#876—31no—
305#876—61no—
306#876—91no—
307#872—91no—
308#870—31no—
309#870—31no—
310#870—61no—
311#870—91no—
312C4×Dic6—31no—
313C4×Dic6—31no—
314C4×Dic6—61no—
315C4×Dic6—91no—
316C22×C3⋊D3C22×D311yescharacteristic
317C22×C3×D3—31no—
318C22×C3×D3—31no—
319C22×C3×D3—61no—
320C2×C32×C4—21no—
321C2×C32×C4—21no—
322C2×C32×C4—21no—
323C2×C32×C4—21no—
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—41no—
330C2×C32×C4—41no—
331C2×C32×C4—41no—
332C2×C32×C4C22×D311yescharacteristic
333C2×C32×C4C22×D311yescharacteristic
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C32×C4C22×D311yescharacteristic
337C2×C32×C4C22×D311yescharacteristic
338C2×C32×C4C22×D311yescharacteristic
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C3⋊Dic3C22×D311yescharacteristic
342C2×C3⋊Dic3C22×D311yescharacteristic
343C2×C3⋊Dic3C22×D311yescharacteristic
344C2×C3⋊Dic3C22×D311yescharacteristic
345C2×C3⋊Dic3C22×D311yescharacteristic
346C2×C3⋊Dic3C22×D311yescharacteristic
347C2×C3⋊Dic3C22×D311yescharacteristic
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350C2×C3⋊Dic3C22×D311yescharacteristic
351C2×C3⋊Dic3C22×D311yescharacteristic
352#634—22no—
353C2×C3×Dic3—31no—
354C2×C3×Dic3—31no—
355C2×C3×Dic3—31no—
356C2×C3×Dic3—31no—
357C2×C3×Dic3—31no—
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—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C3×Dic6—62no—
387C3×Dic6—62no—
388C3×Dic6—64no—
389#627—62no—
390#627—62no—
391#627—62no—
392#624—62no—
393D3×Dic3—62no—
394D3×Dic3—62no—
395#541—271noSylow
396C2×C33C2×#4111yescharacteristic
397C2×C332−1+411yescharacteristic
398C2×C332−1+411yescharacteristic
399C3×C3⋊D3—41no—
400C2×C3×Q8—91no—
401C22×Dic3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×Dic6—31no—
405C2×Dic6—31no—
406C2×Dic6—61no—
407C2×Dic6—91no—
408C2×Dic6—91no—
409C2×Dic6—91no—
410C3×C4⋊C4—91no—
411C3×C4⋊C4—91no—
412C3×C4⋊C4—91no—
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×C4⋊C4—91no—
422C3×C22⋊C4—91no—
423C3×C22⋊C4—91no—
424C3×C22⋊C4—91no—
425C3×C42—21no—
426C3×C42—21no—
427C3×C42—21no—
428C3×C42—41no—
429C3×C42—91no—
430C3×C42—91no—
431C3×C42D3211yescharacteristic
432C3×C42D3211yescharacteristic
433C3×C42D3211yescharacteristic
434#217—91no—
435#217—91no—
436#217—91no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—31no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—91no—
449(C2×D3)⋊C4—91no—
450(C2×D3)⋊C4—91no—
451(C2×D3)⋊C4—91no—
452C4⋊Dic3—31no—
453C4⋊Dic3—31no—
454C4⋊Dic3—31no—
455C4⋊Dic3—31no—
456C4⋊Dic3—31no—
457C4⋊Dic3—31no—
458C4⋊Dic3—61no—
459C4⋊Dic3—61no—
460C4⋊Dic3—61no—
461C4⋊Dic3—91no—
462C4⋊Dic3—91no—
463C4⋊Dic3—91no—
464C4⋊Dic3—91no—
465C4⋊Dic3—91no—
466C4⋊Dic3—91no—
467C4⋊Dic3—91no—
468C4⋊Dic3—91no—
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—31no—
479Dic3⋊C4—31no—
480Dic3⋊C4—31no—
481Dic3⋊C4—31no—
482Dic3⋊C4—31no—
483Dic3⋊C4—31no—
484Dic3⋊C4—31no—
485Dic3⋊C4—31no—
486Dic3⋊C4—31no—
487Dic3⋊C4—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—91no—
503Dic3⋊C4—91no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512C4×Dic3—31no—
513C4×Dic3—31no—
514C4×Dic3—31no—
515C4×Dic3—31no—
516C4×Dic3—61no—
517C4×Dic3—61no—
518C4×Dic3—91no—
519C4×Dic3—91no—
520C4×Dic3—91no—
521C4×Dic3—91no—
522C4×Dic3—91no—
523C4×Dic3—91no—
524C4×Dic3—91no—
525C4×Dic3—91no—
526C4×Dic3—91no—
527C22×C32—21no—
528C22×C32—21no—
529C22×C32—21no—
530C22×C32—41no—
531C22×C32C23×D311yescharacteristic
532C22×C32C23×D311yescharacteristic
533C22×C32C23×D311yescharacteristic
534C2×C3⋊D3—21no—
535C2×C3⋊D3—21no—
536C2×C3⋊D3—21no—
537C2×C3×D3—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—61no—
542C2×C3×D3—61no—
543C2×C3×D3—121no—
544C2×C3×D3—121no—
545C2×C3×D3—121no—
546C32×C4—21no—
547C32×C4—21no—
548C32×C4—21no—
549C32×C4—22no—
550C32×C4—22no—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—41no—
559C32×C4—41no—
560C32×C4—41no—
561C32×C4—41no—
562C32×C4—41no—
563C32×C4—41no—
564C32×C4—42no—
565C32×C4—42no—
566C32×C4—42no—
567C3⋊Dic3—21no—
568C3⋊Dic3—21no—
569C3⋊Dic3—21no—
570C3⋊Dic3—21no—
571C3⋊Dic3—21no—
572C3⋊Dic3—21no—
573C3⋊Dic3—21no—
574C3⋊Dic3—21no—
575C3⋊Dic3—21no—
576C3⋊Dic3—21no—
577C3⋊Dic3#23512yes—
578C3×Dic3—32no—
579C3×Dic3—32no—
580C3×Dic3—62no—
581C3×Dic3—62no—
582C3×Dic3—61no—
583C3×Dic3—61no—
584C3×Dic3—61no—
585C3×Dic3—61no—
586C3×Dic3—61no—
587C3×Dic3—61no—
588C3×Dic3—61no—
589C3×Dic3—61no—
590C3×Dic3—61no—
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—121no—
603C3×Dic3—121no—
604C3×Dic3—121no—
605C3×Dic3—121no—
606C3×Dic3—121no—
607C3×Dic3—121no—
608C3×Dic3—121no—
609C3×Dic3—121no—
610C3×Dic3—121no—
611C4⋊Q8—271no—
612#126—91no—
613#126—271no—
614#126—271no—
615#126—271no—
616#125—91no—
617#125—271no—
618#125—271no—
619#125—271no—
620#125—271no—
621C22⋊Q8—271no—
622C22⋊Q8—271no—
623C4×Q8—91no—
624C4×Q8—271no—
625#117—271no—
626C33#54111yescharacteristic, complemented, Sylow
627C23×C3—91no—
628C22×D3—31no—
629C22×D3—31no—
630C22×D3—61no—
631C3×Q8—182no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—91no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—91no—
648C2×C3×C4—91no—
649C2×C3×C4—91no—
650C2×C3×C4—91no—
651C2×C3×C4—91no—
652C2×C3×C4—91no—
653C2×C3×C4—91no—
654C2×C3×C4—91no—
655C2×C3×C4C2×D3211yescharacteristic
656C2×C3×C4C2×D3211yescharacteristic
657C2×C3×C4C2×D3211yescharacteristic
658C2×C3×C4C2×D3211yescharacteristic
659C2×C3×C4C2×D3211yescharacteristic
660C2×C3×C4C2×D3211yescharacteristic
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—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—182no—
698C4×D3—182no—
699C4×D3—182no—
700Dic6—62no—
701Dic6—62no—
702Dic6—64no—
703Dic6—182no—
704Dic6—182no—
705Dic6—182no—
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×C32C2×#23511yescharacteristic
719C2×C32#100711yescharacteristic
720C2×C32#100711yescharacteristic
721C2×C32D3×#4111yescharacteristic
722C2×C32D3×#4111yescharacteristic
723C2×C32#101011yescharacteristic
724C2×C32#101011yescharacteristic
725C2×C32#101011yescharacteristic
726C2×C32#101011yescharacteristic
727C3⋊D3—41no—
728C3×D3—121no—
729C3×D3—121no—
730C3×D3—241no—
731C2×Q8—91no—
732C2×Q8—271no—
733C22×C4—271no—
734C4⋊C4—91no—
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—91no—
744C4⋊C4—91no—
745C4⋊C4—91no—
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—91no—
755C22⋊C4—91no—
756C22⋊C4—91no—
757C22⋊C4—271no—
758C22⋊C4—271no—
759C22⋊C4—271no—
760C42—91no—
761C42—91no—
762C42—271no—
763C42—271no—
764C42—271no—
765C42#111311yescharacteristic
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—41no—
770C22×C3—181no—
771C22×C3—181no—
772C22×C3—181no—
773C22×C3C22×D3211yescharacteristic
774C22×C3C22×D3211yescharacteristic
775C22×C3C22×D3211yescharacteristic
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—61no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C3×C4—22no—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—41no—
802C3×C4—41no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—42no—
806C3×C4—92no—
807C3×C4—181no—
808C3×C4—181no—
809C3×C4—181no—
810C3×C4—181no—
811C3×C4—181no—
812C3×C4—181no—
813C3×C4—181no—
814C3×C4—181no—
815C3×C4—181no—
816C3×C4—181no—
817Dic3—32no—
818Dic3—32no—
819Dic3—62no—
820Dic3—62no—
821Dic3—61no—
822Dic3—61no—
823Dic3—61no—
824Dic3—61no—
825Dic3—61no—
826Dic3—61no—
827Dic3—61no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—61no—
833Dic3—61no—
834Dic3—61no—
835Dic3—61no—
836Dic3—61no—
837Dic3—61no—
838Dic3—61no—
839Dic3—61no—
840Dic3—61no—
841Dic3—121no—
842Dic3—121no—
843Dic3—121no—
844Dic3—121no—
845Dic3—121no—
846Dic3—121no—
847Dic3—121no—
848Dic3—121no—
849Dic3—121no—
850C32—21no—
851C32—21no—
852C32—21no—
853C32—41no—
854C32#558311yescharacteristic, complemented
855C32#569611yescharacteristic, complemented
856C32#570111yescharacteristic, complemented
857C23—91no—
858Q8—182no—
859Q8—542no—
860C2×C4—91no—
861C2×C4—91no—
862C2×C4—91no—
863C2×C4—91no—
864C2×C4—91no—
865C2×C4—91no—
866C2×C4—91no—
867C2×C4—91no—
868C2×C4—91no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—542no—
872C2×C4C2×#111311yescharacteristic
873C2×C4C2×#111311yescharacteristic
874C2×C4C2×#111311yescharacteristic
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—361no—
888C2×C3#6429711yescharacteristic
889C2×C3#6429711yescharacteristic
890C2×C3#6429711yescharacteristic
891C2×C3#6429711yescharacteristic
892C2×C3#6429811yescharacteristic
893C2×C3#6429811yescharacteristic
894C2×C3D3×#23511yescharacteristic
895C2×C3D3×#23511yescharacteristic
896C2×C3#6430611yescharacteristic
897D3—121no—
898D3—121no—
899D3—241no—
900C22—181no—
901C22—181no—
902C22—181no—
903C22C22×#111311yescharacteristic
904C4—21no—
905C4—21no—
906C4—21no—
907C4—92no—
908C4—181no—
909C4—181no—
910C4—181no—
911C4—181no—
912C4—181no—
913C4—181no—
914C4—181no—
915C4—181no—
916C4—181no—
917C4—181no—
918C3—21no—
919C3—21no—
920C3—21no—
921C3—41no—
922C3#1059384911yescharacteristic, complemented
923C3#1059392811yescharacteristic, complemented
924C3#1059394511yescharacteristic, complemented
925C2—361no—
926C2#1172461411yescharacteristic
927C2#1172461411yescharacteristic
928C2#1172461811yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C42C22
prime radicalC22×C3×C3⋊D3C23
hypercenterC42#1113
hypocenterC33#541
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C3×#64079C2semidirect
3. C3×C4×#634C2semidirect
7. #11723679C2semidirect
11. #11723669C2semidirect
12. #11723669C2semidirect
13. #11723669C2semidirect
14. #11723666C2semidirect
15. #11723665C2semidirect
55. #64079D3semidirect
56. C4×#634D3semidirect
626. C33#541semidirect
854. C32#5583semidirect
855. C32#5696semidirect
856. C32#5701semidirect
922. C3#10593849semidirect
923. C3#10593928semidirect
924. C3#10593945semidirect

Maximal subgroups

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

subgroupindex
C3×#640852
C3×#640792
C3×C4×#6342
#117236922
#117236882
#117236832
#117236792
#117236762
#117236752
#117236692
#117236662
#117236652
#105939453
#105939283
#105938493