Finite Group Databasebeta

← #13169377

Subgroups — #13169377

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic, complemented
2#11723424C211yesmaximal, characteristic, complemented
3#11723404C211yesmaximal, characteristic, complemented
4Dic3×#634C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic
7C3×#63857C211yesmaximal, characteristic, complemented
8#11723025C212yesmaximal, complemented
9#11723019C212yesmaximal, complemented
10#11723001C212yesmaximal
11#11722941C212yesmaximal, complemented
12#10594841—31nomaximal
13#10594557—31nomaximal
14#10593863—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C3×#627C2212yes—
19C2×C3×#626C2211yescharacteristic
20C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C32×C4×Dic3C2211yescharacteristic
24#88815C2212yes—
25#88814C2212yes—
26#88807C2212yes—
27#88803C2212yes—
28(C2×D3)⋊(C3⋊Dic3)C2212yes—
29Dic3×C3⋊Dic3C2212yes—
30Dic3×C3⋊Dic3C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2211yescharacteristic
35C3×#3722C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2212yes—
38#64135—31no—
39#64101—31no—
40C4×#634—31no—
41C3×C4×#67—31no—
42C3×#924—31no—
43C3×#897—31no—
44C3×#888—31no—
45C3×C4×D12—31no—
46C3×#869—31no—
47#63959—32no—
48#63956—32no—
49#63918D311yescharacteristic, complemented
50#63907—32no—
51C4×#626D311yescharacteristic
52#63871—31no—
53#63863—32no—
54#63862—32no—
55#63862—32no—
56#63858—32no—
57#63858—32no—
58#63857—31no—
59#63857D311yescharacteristic, complemented
60#63856—31no—
61#63848—32no—
62#63843—32no—
63#63843—32no—
64Dic3×Dic6—31no—
65Dic3×Dic6—31no—
66Dic3×Dic6—61no—
67#63841—31no—
68#63841—31no—
69#63841—31no—
70#63841—31no—
71#63841—61no—
72#63841—61no—
73#63838—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78C2×C3×C3⋊Dic3C2312yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C3×C4×C3⋊D3—22no—
82C3×#634—22no—
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3—22no—
88C3×#627—24no—
89C3×#626—22no—
90#5732—91no—
91#5641—91no—
92#5542—91no—
93C22×C32×C4—31no—
94C2×C4×C3⋊D3C2×D311yescharacteristic
95C2×#634C2×D311yescharacteristic
96C2×C3×#67—31no—
97C2×C3×D12—31no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—61no—
102C2×C3×C4×D3C2×D311yescharacteristic
103C2×C3×C4×D3C2×D311yescharacteristic
104C2×C3×Dic6—31no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—32no—
107C2×C3×Dic6—32no—
108C2×C3×Dic6—61no—
109C2×#627C2×D312yes—
110C2×#626C2×D311yescharacteristic
111C32×C4⋊C4—31no—
112C32×C42—31no—
113#3757—32no—
114#3752—32no—
115C4⋊(C3⋊Dic3)—31no—
116C4⋊(C3⋊Dic3)—31no—
117C4⋊(C3⋊Dic3)—31no—
118C4⋊(C3⋊Dic3)—61no—
119C4⋊(C3⋊Dic3)—61no—
120C4⋊(C3⋊Dic3)—61no—
121C4⋊(C3⋊Dic3)—121no—
122C4⋊(C3⋊Dic3)C2×D311yescharacteristic
123#3750—32no—
124C4×C3⋊Dic3—32no—
125C4×C3⋊Dic3—32no—
126C4×C3⋊Dic3—32no—
127C3×#217—32no—
128C3×#217—31no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—61no—
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—31no—
145C3×C4×Dic3—21no—
146C3×C4×Dic3C2×D311yescharacteristic
147C3×C4×Dic3C2×D311yescharacteristic
148#3724—32no—
149Dic3⋊Dic3—32no—
150Dic3⋊Dic3—32no—
151Dic3⋊Dic3—32no—
152Dic3⋊Dic3—32no—
153Dic3⋊Dic3—62no—
154Dic3⋊Dic3C2×D311yescharacteristic
155Dic3⋊Dic3C2×D312yes—
156Dic3⋊Dic3C2×D312yes—
157#3722—32no—
158#3722C2×D311yescharacteristic
159(C2×D3)⋊Dic3—32no—
160(C2×D3)⋊Dic3—32no—
161(C2×D3)⋊Dic3—32no—
162(C2×D3)⋊Dic3—32no—
163(C2×D3)⋊Dic3—32no—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—62no—
166(C2×D3)⋊Dic3—62no—
167(C2×D3)⋊Dic3C2×D312yes—
168(C2×D3)⋊Dic3C2×D311yescharacteristic
169Dic32—32no—
170Dic32—32no—
171Dic32—32no—
172Dic32—32no—
173Dic32—32no—
174Dic32—32no—
175Dic32—62no—
176Dic32—62no—
177Dic32—62no—
178C22×C33C2411yescharacteristic
179C2×C3×C3⋊D3—21no—
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—21no—
182C2×C32×D3—21no—
183C2×C32×D3—21no—
184C2×C32×D3—21no—
185C33×C4#4112yes—
186C3⋊(C3⋊Dic3)—22no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—22no—
190C32×Dic3—21no—
191C32×Dic3—22no—
192C32×Dic3—21no—
193C32×Dic3#4112yes—
194C3×C4⋊Q8—91no—
195C3×C22⋊Q8—91no—
196C3×C4×D4—91no—
197#947—92no—
198#946—91no—
199Q8×Dic3—92no—
200Q8×Dic3—91no—
201#936—92no—
202C4×#67—31no—
203#926—91no—
204#926—91no—
205#926—91no—
206#926—181no—
207#924—31no—
208#924—91no—
209#898—92no—
210#898—92no—
211#898—92no—
212#897—31no—
213#897—91no—
214#892—91no—
215#892—91no—
216#892—91no—
217#892—181no—
218#888—31no—
219#887—92no—
220#887—92no—
221#885—92no—
222#879—92no—
223#879—92no—
224#879—92no—
225C4×D12—31no—
226#869—31no—
227C4×Dic6—91no—
228C4×Dic6—91no—
229C4×Dic6—181no—
230C23×C32—31no—
231C22×C3⋊D3C22×D311yescharacteristic
232C22×C3×D3—21no—
233C22×C3×D3—31no—
234C22×C3×D3—31no—
235C22×C3×D3—61no—
236C22×C3×D3C22×D311yescharacteristic
237C22×C3×D3C22×D311yescharacteristic
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—31no—
242C2×C32×C4—31no—
243C2×C32×C4—32no—
244C2×C32×C4—31no—
245C2×C32×C4—41no—
246C2×C32×C4—62no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C3⋊Dic3—32no—
251C2×C3⋊Dic3—32no—
252C2×C3⋊Dic3—32no—
253C2×C3⋊Dic3—62no—
254C2×C3⋊Dic3—62no—
255C2×C3⋊Dic3—62no—
256C2×C3⋊Dic3—122no—
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D312yes—
259C2×C3⋊Dic3C22×D311yescharacteristic
260C4×C3⋊D3—22no—
261#634—22no—
262C3×#67—62no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—22no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D312yes—
279C2×C3×Dic3C22×D312yes—
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C3×D12—62no—
285C3×C4×D3—24no—
286C3×C4×D3—22no—
287C3×C4×D3—22no—
288C3×C4×D3—64no—
289C3×C4×D3—62no—
290C3×C4×D3—62no—
291C3×Dic6—64no—
292C3×Dic6—64no—
293C3×Dic6—62no—
294C3×Dic6—62no—
295C3×Dic6—64no—
296#627—24no—
297#626—22no—
298#556—271noSylow
299C2×C33C2×#4111yescharacteristic
300C2×C33C2×#4111yescharacteristic
301C2×C332−1+411yescharacteristic
302C3×C3⋊D3—41no—
303C32×D3—41no—
304C2×C3×Q8—92no—
305C2×C3×Q8—91no—
306C2×C3×D4—91no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4—91no—
311C2×#67—31no—
312C2×D12—31no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—61no—
316C2×C4×D3D3211yescharacteristic
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—32no—
320C2×Dic6—32no—
321C2×Dic6—61no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—91no—
326C3×C4⋊C4—92no—
327C3×C4⋊C4—92no—
328C3×C4⋊C4—91no—
329C3×C22⋊C4—91no—
330C3×C22⋊C4—91no—
331C3×C22⋊C4—92no—
332C3×C42—31no—
333C3×C42—31no—
334C3×C42—61no—
335#217—31no—
336#217—32no—
337#217—92no—
338#217—92no—
339#217—92no—
340#217—92no—
341#217—182no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4—31no—
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—92no—
347(C2×D3)⋊C4—92no—
348(C2×D3)⋊C4—92no—
349(C2×D3)⋊C4—92no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—182no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—32no—
355C4⋊Dic3—31no—
356C4⋊Dic3—32no—
357C4⋊Dic3—61no—
358C4⋊Dic3—92no—
359C4⋊Dic3—91no—
360C4⋊Dic3—91no—
361C4⋊Dic3—91no—
362C4⋊Dic3—92no—
363C4⋊Dic3—181no—
364C4⋊Dic3—181no—
365C4⋊Dic3—181no—
366C4⋊Dic3—361no—
367C4⋊Dic3D3211yescharacteristic
368Dic3⋊C4—32no—
369Dic3⋊C4—32no—
370Dic3⋊C4—31no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—182no—
376C4×Dic3—92no—
377C4×Dic3—92no—
378C4×Dic3—92no—
379C4×Dic3—92no—
380C4×Dic3—92no—
381C4×Dic3—92no—
382C4×Dic3—92no—
383C4×Dic3—92no—
384C4×Dic3—92no—
385C4×Dic3—182no—
386C4×Dic3—182no—
387C4×Dic3—182no—
388C4×Dic3D3211yescharacteristic
389C22×C32—21no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—41no—
393C22×C32—61no—
394C22×C32—61no—
395C22×C32—61no—
396C22×C32C23×D311yescharacteristic
397C22×C32C23×D311yescharacteristic
398C22×C32C23×D311yescharacteristic
399C2×C3⋊D3—21no—
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3×D3—22no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—62no—
412C2×C3×D3—61no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—121no—
419C2×C3×D3—121no—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—22no—
423C32×C4—32no—
424C32×C4—42no—
425C32×C4—61no—
426C32×C4—62no—
427C32×C4—61no—
428C32×C4#23712yes—
429C32×C4#23712yes—
430C32×C4#23912yes—
431C3⋊Dic3—22no—
432C3⋊Dic3—21no—
433C3⋊Dic3—22no—
434C3⋊Dic3—62no—
435C3⋊Dic3—62no—
436C3⋊Dic3—62no—
437C3⋊Dic3—122no—
438C3⋊Dic3—122no—
439C3⋊Dic3—122no—
440C3⋊Dic3—242no—
441C3×Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—22no—
447C3×Dic3—21no—
448C3×Dic3—22no—
449C3×Dic3—41no—
450C3×Dic3—42no—
451C3×Dic3—64no—
452C3×Dic3—62no—
453C3×Dic3—62no—
454C3×Dic3—62no—
455C3×Dic3—61no—
456C3×Dic3—62no—
457C3×Dic3—61no—
458C3×Dic3—62no—
459C3×Dic3—122no—
460C3×Dic3#23512yes—
461C3×Dic3#23712yes—
462C4⋊Q8—91no—
463#126—272no—
464#126—272no—
465#124—272no—
466C22⋊Q8—91no—
467C22⋊Q8—271no—
468C4×Q8—271no—
469C4×Q8—272no—
470C4×D4—91no—
471#117—271no—
472#117—271no—
473C33#55611yescharacteristic, complemented, Sylow
474C23×C3—31no—
475C23×C3—31no—
476C23×C3—61no—
477C23×C3—91no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—61no—
481C22×D3C2×D3211yescharacteristic
482C3×Q8—184no—
483C3×Q8—182no—
484C3×D4—182no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—62no—
500C2×C3×C4—61no—
501C2×C3×C4—64no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—91no—
505C2×C3×C4—92no—
506C2×C3×C4—92no—
507C2×C3×C4—182no—
508C2×C3×C4C2×D3211yescharacteristic
509C2×C3×C4C2×D3211yescharacteristic
510C2×C3×C4C2×D3211yescharacteristic
511#67—62no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—61no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—92no—
522C2×Dic3—92no—
523C2×Dic3—92no—
524C2×Dic3—182no—
525C2×Dic3—182no—
526C2×Dic3—182no—
527C2×Dic3—362no—
528C2×Dic3C2×D3211yescharacteristic
529C2×Dic3C2×D3212yes—
530C2×Dic3C2×D3211yescharacteristic
531C2×Dic3C2×D3211yescharacteristic
532D12—62no—
533C4×D3—22no—
534C4×D3—64no—
535C4×D3—62no—
536C4×D3—62no—
537Dic6—64no—
538Dic6—64no—
539Dic6—62no—
540Dic6—62no—
541Dic6—64no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—21no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—41no—
552C2×C32—41no—
553C2×C32—41no—
554C2×C32—121no—
555C2×C32C2×#23511yescharacteristic
556C2×C32C2×#23711yescharacteristic
557C2×C32C2×#23711yescharacteristic
558C2×C32C2×#23711yescharacteristic
559C2×C32C2×#23911yescharacteristic
560C2×C32#100711yescharacteristic
561C2×C32#100711yescharacteristic
562C2×C32D3×#4111yescharacteristic
563C2×C32#101011yescharacteristic
564C3⋊D3—41no—
565C3×D3—42no—
566C3×D3—41no—
567C3×D3—41no—
568C3×D3—122no—
569C3×D3—121no—
570C3×D3—121no—
571C2×Q8—92no—
572C2×Q8—91no—
573C2×D4—91no—
574C22×C4—31no—
575C22×C4—91no—
576C4⋊C4—31no—
577C4⋊C4—91no—
578C4⋊C4—92no—
579C4⋊C4—92no—
580C4⋊C4—91no—
581C4⋊C4—272no—
582C4⋊C4—272no—
583C4⋊C4—271no—
584C22⋊C4—91no—
585C22⋊C4—91no—
586C22⋊C4—92no—
587C22⋊C4—272no—
588C22⋊C4—272no—
589C22⋊C4—272no—
590C42—31no—
591C42—272no—
592C42—272no—
593C42—272no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—41no—
598C22×C3—62no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—121no—
606C22×C3—121no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3C22×D3211yescharacteristic
611C22×C3C22×D3211yescharacteristic
612C22×C3C22×D3211yescharacteristic
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—62no—
617C2×D3—61no—
618C2×D3—61no—
619C2×D3—61no—
620C2×D3—61no—
621C2×D3—61no—
622C2×D3—61no—
623C2×D3—121no—
624C2×D3—121no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—22no—
628C3×C4—32no—
629C3×C4—32no—
630C3×C4—42no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—62no—
638C3×C4—61no—
639C3×C4—122no—
640C3×C4—121no—
641C3×C4—181no—
642C3×C4—182no—
643C3×C4—182no—
644C3×C4#379612yes—
645C3×C4#379612yes—
646C3×C4#380512yes—
647Dic3—21no—
648Dic3—22no—
649Dic3—21no—
650Dic3—64no—
651Dic3—62no—
652Dic3—62no—
653Dic3—62no—
654Dic3—61no—
655Dic3—62no—
656Dic3—62no—
657Dic3—61no—
658Dic3—122no—
659Dic3—182no—
660Dic3—182no—
661Dic3—182no—
662Dic3—362no—
663Dic3—362no—
664Dic3—362no—
665Dic3—722no—
666Dic3#379512yes—
667C32—21no—
668C32—21no—
669C32—21no—
670C32—41no—
671C32#554211yescharacteristic, complemented
672C32#564111yescharacteristic, complemented
673C32#573211yescharacteristic, complemented
674C23—31no—
675C23—91no—
676Q8—184no—
677Q8—182no—
678D4—182no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—32no—
683C2×C4—62no—
684C2×C4—91no—
685C2×C4—92no—
686C2×C4—92no—
687C2×C4—182no—
688C2×C4—272no—
689C2×C4D3311yescharacteristic
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—41no—
700C2×C3—41no—
701C2×C3—41no—
702C2×C3—122no—
703C2×C3—121no—
704C2×C3—121no—
705C2×C3—361no—
706C2×C3C2×#379511yescharacteristic
707C2×C3C2×#379611yescharacteristic
708C2×C3C2×#379611yescharacteristic
709C2×C3#6429711yescharacteristic
710C2×C3#6429711yescharacteristic
711C2×C3D3×#23511yescharacteristic
712C2×C3D3×#23711yescharacteristic
713C2×C3#6431611yescharacteristic
714C2×C3C2×#380511yescharacteristic
715D3—41no—
716D3—122no—
717D3—121no—
718D3—121no—
719C22—61no—
720C22—61no—
721C22—61no—
722C22—181no—
723C22—181no—
724C22—181no—
725C22C2×D3311yescharacteristic
726C4—32no—
727C4—62no—
728C4—61no—
729C4—61no—
730C4—182no—
731C4—181no—
732C4—182no—
733C4—542no—
734C4#8896412yes—
735C3—21no—
736C3—21no—
737C3—21no—
738C3—41no—
739C3#1059386311yescharacteristic, complemented
740C3#1059455711yescharacteristic, complemented
741C3#1059484111yescharacteristic, complemented
742C2—121no—
743C2—361no—
744C2D3×#379511yescharacteristic
745C2#1172439511yescharacteristic
746C2C2×#8896411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#626C22
hypercenterC2×C4D33
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723674C2semidirect
2. #11723424C2semidirect
3. #11723404C2semidirect
4. Dic3×#634C2semidirect
5. C3×#63918C2semidirect
7. C3×#63857C2semidirect
8. #11723025C2semidirect
9. #11723019C2semidirect
11. #11722941C2semidirect
49. #63918D3semidirect
59. #63857D3semidirect
473. C33#556semidirect
671. C32#5542semidirect
672. C32#5641semidirect
673. C32#5732semidirect
739. C3#10593863semidirect
740. C3#10594557semidirect
741. C3#10594841semidirect

Maximal subgroups

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

subgroupindex
#117236742
#117234242
#117234042
Dic3×#6342
C3×#639182
C3×C4×#6262
C3×#638572
#117230252
#117230192
#117230012
#117229412
#105948413
#105945573
#105938633