Finite Group Databasebeta

← #13168673

Subgroups — #13168673

Order 1728.

980 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723665C211yesmaximal, characteristic, complemented
2#11723491C211yesmaximal, characteristic
3#11723447C211yesmaximal, characteristic, complemented
4#11723400C211yesmaximal, characteristic, complemented
5C3×#63862C211yesmaximal, characteristic
6C3×#63858C211yesmaximal, characteristic
7C3×#63847C211yesmaximal, characteristic, complemented
8#11723036C211yesmaximal, characteristic, complemented
9#11723026C211yesmaximal, characteristic
10#11723022C211yesmaximal, characteristic
11#11723017C211yesmaximal, characteristic, complemented
12#11723012C211yesmaximal, characteristic, complemented
13#11722981C211yesmaximal, characteristic
14#11722943C211yesmaximal, characteristic, complemented
15#11722916C211yesmaximal, characteristic
16#10594459—31nomaximal
17#10594459—31nomaximal
18#10594031—31nomaximal
19C2×#6296C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
23C3×#3750C2211yescharacteristic
24C3×#3750C2211yescharacteristic
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C32×(C2×D3)⋊C4C2211yescharacteristic
27C32×C4⋊Dic3C2211yescharacteristic
28C32×Dic3⋊C4C2211yescharacteristic
29#88815C2211yescharacteristic
30#88813C2211yescharacteristic
31#88813C2211yescharacteristic
32#88807C2211yescharacteristic
33#88806C2211yescharacteristic
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
41Dic3×C3⋊Dic3C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64099—31no—
55#64099—31no—
56#64087—31no—
57C3×#898—31no—
58C3×#898—31no—
59C3×#889—31no—
60C3×#889—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63982—31no—
64#63957—31no—
65#63956—31no—
66#63956—31no—
67#63918—31no—
68#63918—31no—
69#63893—31no—
70#63893—31no—
71#63893—31no—
72#63893—31no—
73#63893—61no—
74#63877—31no—
75#63877—31no—
76#63869—31no—
77#63869—31no—
78#63869—31no—
79#63869—61no—
80#63867—31no—
81#63862—31no—
82#63862D311yescharacteristic
83#63861—31no—
84#63861—31no—
85#63858—31no—
86#63858D311yescharacteristic
87#63847—31no—
88#63847D311yescharacteristic, complemented
89#63846—31no—
90#63846—31no—
91#63845—31no—
92#63845—31no—
93#63845—31no—
94#63845—61no—
95#63844—31no—
96#63840—31no—
97#63838—31no—
98#63838—31no—
99#63837—31no—
100#63837—31no—
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
117#6296—22no—
118#6293—22no—
119D3×C3⋊Dic3—22no—
120#5701—91no—
121#5701—91no—
122#5698—91no—
123C22×C3⋊Dic3—31no—
124C2×#634—31no—
125C2×#627—31no—
126C2×#627—31no—
127C2×#627—31no—
128C2×#627—31no—
129C2×#627—31no—
130C2×#627—61no—
131C2×D3×Dic3—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—61no—
134C32×C4⋊C4—31no—
135C32×C4⋊C4—31no—
136C32×C22⋊C4—31no—
137#3757—31no—
138C4⋊(C3⋊Dic3)—31no—
139C4⋊(C3⋊Dic3)—31no—
140C4⋊(C3⋊Dic3)—31no—
141C4⋊(C3⋊Dic3)—31no—
142C4⋊(C3⋊Dic3)—31no—
143C4⋊(C3⋊Dic3)—31no—
144C4⋊(C3⋊Dic3)—31no—
145C4⋊(C3⋊Dic3)—61no—
146C4⋊(C3⋊Dic3)—61no—
147C4⋊(C3⋊Dic3)—61no—
148C4⋊(C3⋊Dic3)—121no—
149#3750—31no—
150#3750—31no—
151#3750—31no—
152#3750—31no—
153#3750C2×D311yescharacteristic
154#3750C2×D311yescharacteristic
155C4×C3⋊Dic3—31no—
156C4×C3⋊Dic3C2×D311yescharacteristic
157C3×#217—31no—
158C3×#217—31no—
159C3×#217—31no—
160C3×#217—31no—
161C3×(C2×D3)⋊C4—21no—
162C3×(C2×D3)⋊C4—31no—
163C3×(C2×D3)⋊C4—31no—
164C3×(C2×D3)⋊C4—31no—
165C3×(C2×D3)⋊C4—31no—
166C3×(C2×D3)⋊C4C2×D311yescharacteristic
167C3×(C2×D3)⋊C4C2×D311yescharacteristic
168C3×C4⋊Dic3—21no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—31no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3C2×D311yescharacteristic
174C3×C4⋊Dic3C2×D311yescharacteristic
175C3×Dic3⋊C4—21no—
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—61no—
189C3×Dic3⋊C4—61no—
190C3×Dic3⋊C4C2×D311yescharacteristic
191C3×Dic3⋊C4C2×D311yescharacteristic
192C3×C4×Dic3—31no—
193C3×C4×Dic3—31no—
194C3×C4×Dic3—31no—
195C3×C4×Dic3—31no—
196C3×C4×Dic3—31no—
197C3×C4×Dic3—31no—
198C3×C4×Dic3—61no—
199#3724—31no—
200#3724—31no—
201#3724—31no—
202#3724—31no—
203#3724—31no—
204#3724—31no—
205#3724—31no—
206#3724—61no—
207#3724—61no—
208#3724—61no—
209#3724C2×D311yescharacteristic
210#3724C2×D311yescharacteristic
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—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—61no—
235(C2×D3)⋊Dic3C2×D311yescharacteristic
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—31no—
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#4112yes—
263C32×Dic3—21no—
264C32×Dic3—21no—
265C32×Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C3×#126—91no—
269C3×#126—91no—
270C3×#125—91no—
271#898—31no—
272#898—31no—
273#898—91no—
274#898—91no—
275#897—91no—
276#897—91no—
277#890—91no—
278#890—91no—
279#890—91no—
280#890—91no—
281#890—91no—
282#890—91no—
283#890—181no—
284#890—181no—
285#889—31no—
286#889—31no—
287#889—91no—
288#889—91no—
289#889—91no—
290#889—91no—
291#888—91no—
292#888—91no—
293#887—91no—
294#887—91no—
295#887—91no—
296#887—91no—
297#879—31no—
298#879—31no—
299#879—91no—
300#879—91no—
301#879—91no—
302#879—91no—
303#878—91no—
304#878—91no—
305#878—91no—
306#878—91no—
307#878—181no—
308#877—91no—
309#877—91no—
310#872—91no—
311#870—91no—
312#870—91no—
313#869—91no—
314C4×Dic6—91no—
315C4×Dic6—91no—
316C23×C32—31no—
317C22×C3×D3—21no—
318C22×C3×D3C22×D311yescharacteristic
319C22×C3×D3C22×D311yescharacteristic
320C2×C32×C4—21no—
321C2×C32×C4—21no—
322C2×C32×C4—21no—
323C2×C32×C4—31no—
324C2×C32×C4—31no—
325C2×C32×C4—31no—
326C2×C32×C4—31no—
327C2×C32×C4—31no—
328C2×C32×C4—41no—
329C2×C32×C4C22×D311yescharacteristic
330C2×C32×C4C22×D311yescharacteristic
331C2×C32×C4C22×D311yescharacteristic
332C2×C3⋊Dic3—31no—
333C2×C3⋊Dic3—31no—
334C2×C3⋊Dic3—31no—
335C2×C3⋊Dic3—31no—
336C2×C3⋊Dic3—31no—
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—61no—
339C2×C3⋊Dic3—61no—
340C2×C3⋊Dic3—61no—
341C2×C3⋊Dic3—61no—
342C2×C3⋊Dic3—61no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—62no—
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
353#634—62no—
354C2×C3×Dic3—21no—
355C2×C3×Dic3—21no—
356C2×C3×Dic3—21no—
357C2×C3×Dic3—21no—
358C2×C3×Dic3—21no—
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—61no—
372C2×C3×Dic3—61no—
373C2×C3×Dic3—61no—
374C2×C3×Dic3—61no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—61no—
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
387#627—62no—
388#627—62no—
389#627—62no—
390#627—62no—
391#627—62no—
392#627—122no—
393D3×Dic3—62no—
394D3×Dic3—62no—
395D3×Dic3—122no—
396#541—271noSylow
397C2×C33C2×#4111yescharacteristic
398C2×C332−1+411yescharacteristic
399C2×C332−1+411yescharacteristic
400C32×D3—41no—
401C22×Dic3—91no—
402C22×Dic3—91no—
403C22×Dic3—181no—
404C2×C4×D3—91no—
405C2×Dic6—91no—
406C2×Dic6—91no—
407C2×Dic6—91no—
408C2×Dic6—91no—
409C2×Dic6—91no—
410C2×Dic6—91no—
411C2×Dic6—181no—
412C3×C4⋊C4—31no—
413C3×C4⋊C4—31no—
414C3×C4⋊C4—31no—
415C3×C4⋊C4—31no—
416C3×C4⋊C4—61no—
417C3×C4⋊C4—61no—
418C3×C4⋊C4—91no—
419C3×C4⋊C4—91no—
420C3×C4⋊C4—91no—
421C3×C4⋊C4—91no—
422C3×C4⋊C4—91no—
423C3×C4⋊C4—91no—
424C3×C4⋊C4—91no—
425C3×C4⋊C4—91no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—31no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—91no—
432C3×C22⋊C4—91no—
433C3×C42—91no—
434C3×C42—91no—
435C3×C42—91no—
436#217—31no—
437#217—31no—
438#217—31no—
439#217—31no—
440#217—91no—
441#217—91no—
442#217—181no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—31no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4D3211yescharacteristic
449C4⋊Dic3—31no—
450C4⋊Dic3—31no—
451C4⋊Dic3—31no—
452C4⋊Dic3—31no—
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—91no—
464C4⋊Dic3—91no—
465C4⋊Dic3—91no—
466C4⋊Dic3—181no—
467C4⋊Dic3—181no—
468C4⋊Dic3—181no—
469C4⋊Dic3—181no—
470C4⋊Dic3—181no—
471C4⋊Dic3—181no—
472C4⋊Dic3—181no—
473C4⋊Dic3—361no—
474C4⋊Dic3D3211yescharacteristic
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—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—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—91no—
503Dic3⋊C4—91no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—181no—
507Dic3⋊C4—181no—
508Dic3⋊C4—181no—
509Dic3⋊C4—181no—
510Dic3⋊C4D3211yescharacteristic
511C4×Dic3—31no—
512C4×Dic3—31no—
513C4×Dic3—31no—
514C4×Dic3—31no—
515C4×Dic3—31no—
516C4×Dic3—31no—
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—
527C4×Dic3—181no—
528C22×C32—21no—
529C22×C32—21no—
530C22×C32—21no—
531C22×C32—41no—
532C22×C32—61no—
533C22×C32—61no—
534C22×C32—61no—
535C22×C32C23×D311yescharacteristic
536C22×C32C23×D311yescharacteristic
537C22×C32C23×D311yescharacteristic
538C2×C3×D3—22no—
539C2×C3×D3—21no—
540C2×C3×D3—21no—
541C2×C3×D3—21no—
542C2×C3×D3—21no—
543C2×C3×D3—21no—
544C2×C3×D3—21no—
545C2×C3×D3—41no—
546C2×C3×D3—41no—
547C32×C4—21no—
548C32×C4—22no—
549C32×C4—21no—
550C32×C4—21no—
551C32×C4—41no—
552C32×C4—41no—
553C32×C4—42no—
554C32×C4—61no—
555C32×C4—61no—
556C32×C4—61no—
557C32×C4—61no—
558C32×C4—61no—
559C3⋊Dic3—21no—
560C3⋊Dic3—21no—
561C3⋊Dic3—21no—
562C3⋊Dic3—21no—
563C3⋊Dic3—21no—
564C3⋊Dic3—61no—
565C3⋊Dic3—61no—
566C3⋊Dic3—61no—
567C3⋊Dic3—61no—
568C3⋊Dic3—61no—
569C3⋊Dic3—61no—
570C3⋊Dic3—121no—
571C3⋊Dic3—121no—
572C3⋊Dic3—121no—
573C3⋊Dic3—121no—
574C3⋊Dic3—121no—
575C3⋊Dic3—121no—
576C3⋊Dic3—241no—
577C3⋊Dic3—241no—
578C3⋊Dic3#23912yes—
579C3×Dic3—22no—
580C3×Dic3—21no—
581C3×Dic3—21no—
582C3×Dic3—21no—
583C3×Dic3—21no—
584C3×Dic3—21no—
585C3×Dic3—21no—
586C3×Dic3—21no—
587C3×Dic3—21no—
588C3×Dic3—21no—
589C3×Dic3—21no—
590C3×Dic3—32no—
591C3×Dic3—32no—
592C3×Dic3—41no—
593C3×Dic3—41no—
594C3×Dic3—41no—
595C3×Dic3—41no—
596C3×Dic3—62no—
597C3×Dic3—61no—
598C3×Dic3—61no—
599C3×Dic3—61no—
600C3×Dic3—61no—
601C3×Dic3—61no—
602C3×Dic3—61no—
603C3×Dic3—61no—
604C3×Dic3—61no—
605C3×Dic3—61no—
606C3×Dic3—61no—
607C3×Dic3—121no—
608C3×Dic3—121no—
609C3×Dic3—121no—
610C3×Dic3—121no—
611C3×Dic3—121no—
612C4⋊Q8—271no—
613#126—91no—
614#126—91no—
615#126—271no—
616#126—271no—
617#125—91no—
618#125—271no—
619#125—271no—
620#125—271no—
621#125—271no—
622C22⋊Q8—271no—
623C22⋊Q8—271no—
624C4×Q8—271no—
625C4×Q8—271no—
626#117—271no—
627C33#54111yescharacteristic, complemented, Sylow
628C23×C3—31no—
629C23×C3—31no—
630C23×C3—61no—
631C22×D3C2×D3211yescharacteristic
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
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—41no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—91no—
652C2×C3×C4—91no—
653C2×C3×C4—91no—
654C2×C3×C4—91no—
655C2×C3×C4—91no—
656C2×C3×C4—91no—
657C2×C3×C4C2×D3211yescharacteristic
658C2×C3×C4C2×D3211yescharacteristic
659C2×C3×C4C2×D3211yescharacteristic
660C2×Dic3—31no—
661C2×Dic3—31no—
662C2×Dic3—31no—
663C2×Dic3—31no—
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—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—91no—
679C2×Dic3—91no—
680C2×Dic3—91no—
681C2×Dic3—91no—
682C2×Dic3—91no—
683C2×Dic3—91no—
684C2×Dic3—181no—
685C2×Dic3—181no—
686C2×Dic3—181no—
687C2×Dic3—181no—
688C2×Dic3—181no—
689C2×Dic3—181no—
690C2×Dic3—182no—
691C2×Dic3—182no—
692C2×Dic3—361no—
693C2×Dic3—361no—
694C2×Dic3—362no—
695C2×Dic3C2×D3211yescharacteristic
696C2×Dic3C2×D3211yescharacteristic
697C2×Dic3C2×D3211yescharacteristic
698C2×Dic3C2×D3211yescharacteristic
699C2×Dic3C2×D3211yescharacteristic
700C4×D3—182no—
701Dic6—182no—
702Dic6—182no—
703Dic6—182no—
704Dic6—182no—
705Dic6—182no—
706Dic6—182no—
707Dic6—362no—
708C2×C32—21no—
709C2×C32—21no—
710C2×C32—21no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—21no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—41no—
718C2×C32—41no—
719C2×C32—41no—
720C2×C32—121no—
721C2×C32C2×#23911yescharacteristic
722C2×C32D3×#4111yescharacteristic
723C2×C32D3×#4111yescharacteristic
724C2×C32#101011yescharacteristic
725C2×C32#101011yescharacteristic
726C2×C32#101011yescharacteristic
727C2×C32#101011yescharacteristic
728C2×C32#101011yescharacteristic
729C2×C32#101011yescharacteristic
730C3×D3—42no—
731C3×D3—41no—
732C3×D3—41no—
733C2×Q8—271no—
734C2×Q8—271no—
735C22×C4—271no—
736C4⋊C4—31no—
737C4⋊C4—31no—
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—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C22⋊C4—31no—
757C22⋊C4—91no—
758C22⋊C4—91no—
759C22⋊C4—91no—
760C22⋊C4—91no—
761C22⋊C4—271no—
762C42—91no—
763C42—91no—
764C42—91no—
765C42—271no—
766C42—271no—
767C42—271no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—41no—
772C22×C3—62no—
773C22×C3—61no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3—61no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3C22×D3211yescharacteristic
782C22×C3C22×D3211yescharacteristic
783C22×C3C22×D3211yescharacteristic
784C2×D3—21no—
785C2×D3—21no—
786C2×D3—21no—
787C3×C4—22no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—42no—
794C3×C4—62no—
795C3×C4—61no—
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—61no—
805C3×C4—92no—
806C3×C4—121no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4—181no—
811C3×C4—181no—
812C3×C4—181no—
813C3×C4—181no—
814C3×C4—181no—
815Dic3—21no—
816Dic3—21no—
817Dic3—21no—
818Dic3—21no—
819Dic3—21no—
820Dic3—32no—
821Dic3—32no—
822Dic3—62no—
823Dic3—61no—
824Dic3—61no—
825Dic3—61no—
826Dic3—61no—
827Dic3—61no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—61no—
832Dic3—61no—
833Dic3—121no—
834Dic3—121no—
835Dic3—121no—
836Dic3—121no—
837Dic3—121no—
838Dic3—181no—
839Dic3—181no—
840Dic3—181no—
841Dic3—181no—
842Dic3—181no—
843Dic3—181no—
844Dic3—361no—
845Dic3—361no—
846Dic3—361no—
847Dic3—361no—
848Dic3—361no—
849Dic3—361no—
850Dic3—721no—
851Dic3—721no—
852C32—21no—
853C32—21no—
854C32—21no—
855C32—41no—
856C32#569811yescharacteristic, complemented
857C32#570111yescharacteristic, complemented
858C32#570111yescharacteristic, complemented
859C23—31no—
860Q8—542no—
861Q8—542no—
862C2×C4—31no—
863C2×C4—31no—
864C2×C4—31no—
865C2×C4—31no—
866C2×C4—31no—
867C2×C4—91no—
868C2×C4—91no—
869C2×C4—91no—
870C2×C4—91no—
871C2×C4—91no—
872C2×C4—91no—
873C2×C4—271no—
874C2×C4—271no—
875C2×C4—542no—
876C2×C4D3311yescharacteristic
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—41no—
887C2×C3—41no—
888C2×C3—41no—
889C2×C3—122no—
890C2×C3—121no—
891C2×C3—121no—
892C2×C3#6429811yescharacteristic
893C2×C3#6429811yescharacteristic
894C2×C3#6429811yescharacteristic
895C2×C3#6430911yescharacteristic
896C2×C3#6430911yescharacteristic
897C2×C3#6430911yescharacteristic
898C2×C3#6431211yescharacteristic
899C2×C3D3×#23911yescharacteristic
900C2×C3D3×#23911yescharacteristic
901D3—41no—
902C22—61no—
903C22—61no—
904C22—61no—
905C22C2×D3311yescharacteristic
906C4—21no—
907C4—61no—
908C4—61no—
909C4—61no—
910C4—61no—
911C4—61no—
912C4—92no—
913C4—181no—
914C4—181no—
915C4—181no—
916C4—181no—
917C4—181no—
918C4—541no—
919C4—541no—
920C3—21no—
921C3—21no—
922C3—21no—
923C3—41no—
924C3#1059403111yescharacteristic, complemented
925C3#1059445911yescharacteristic, complemented
926C3#1059445911yescharacteristic, complemented
927C2—121no—
928C2#1172437711yescharacteristic
929C2#1172439211yescharacteristic
930C2#1172442711yescharacteristic
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. #11723665C2semidirect
3. #11723447C2semidirect
4. #11723400C2semidirect
7. C3×#63847C2semidirect
8. #11723036C2semidirect
11. #11723017C2semidirect
12. #11723012C2semidirect
14. #11722943C2semidirect
88. #63847D3semidirect
627. C33#541semidirect
856. C32#5698semidirect
857. C32#5701semidirect
858. C32#5701semidirect
924. C3#10594031semidirect
925. C3#10594459semidirect
926. C3#10594459semidirect

Maximal subgroups

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

subgroupindex
#117236652
#117234912
#117234472
#117234002
C3×#638622
C3×#638582
C3×#638472
#117230362
#117230262
#117230222
#117230172
#117230122
#117229812
#117229432
#117229162
#105944593
#105940313