Finite Group Databasebeta

← #13169373

Subgroups — #13169373

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723667C211yesmaximal, characteristic, complemented
2#11723431C211yesmaximal, characteristic, complemented
3#11723426C211yesmaximal, characteristic, complemented
4#11723399C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic
7C3×#63841C211yesmaximal, characteristic, complemented
8#11723026C212yesmaximal, complemented
9#11723024C212yesmaximal, complemented
10#11723001C212yesmaximal
11#11722940C212yesmaximal, complemented
12#10594840—31nomaximal
13#10594556—31nomaximal
14#10593863—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C3×#627C2212yes—
19C2×C3×#626C2211yescharacteristic
20C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C32×C4⋊Dic3C2211yescharacteristic
23C32×C4×Dic3C2211yescharacteristic
24#88814C2212yes—
25#88813C2212yes—
26#88807C2212yes—
27#88806C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29#88803C2212yes—
30(C2×D3)⋊(C3⋊Dic3)C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2211yescharacteristic
34C3×#3722C2211yescharacteristic
35C3×(C2×D3)⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×Dic32C2212yes—
38#64133—31no—
39#64106—31no—
40C4×#634—31no—
41C3×C4×#67—31no—
42C3×#926—31no—
43C3×#892—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#63868—32no—
53#63863—32no—
54#63861—32no—
55#63859—32no—
56#63858—32no—
57#63858—32no—
58#63857—31no—
59#63857—31no—
60#63857—31no—
61#63857—31no—
62#63857—61no—
63#63857—61no—
64#63849—31no—
65#63844—31no—
66#63844—31no—
67#63844—61no—
68#63843—32no—
69Dic3×Dic6—32no—
70#63841—31no—
71#63841—31no—
72#63841D311yescharacteristic, complemented
73#63837—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78#6308—22no—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4×C3⋊D3—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#5542—91no—
92#5533—91no—
93C22×C32×C4—31no—
94C2×C4×C3⋊D3C2×D311yescharacteristic
95C2×#634—31no—
96C2×#634—31no—
97C2×#634—31no—
98C2×#634—61no—
99C2×#634—61no—
100C2×#634—61no—
101C2×#634—121no—
102C2×C3×#67—31no—
103C2×C3×D12—31no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—61no—
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×Dic6—32no—
111C2×C3×Dic6—32no—
112C2×#627C2×D312yes—
113C2×#626C2×D311yescharacteristic
114C32×C4⋊C4—31no—
115C32×C42—31no—
116#3757—32no—
117#3752—32no—
118C4⋊(C3⋊Dic3)—32no—
119C4⋊(C3⋊Dic3)C2×D311yescharacteristic
120C4⋊(C3⋊Dic3)C2×D311yescharacteristic
121#3750—32no—
122#3750—32no—
123C4×C3⋊Dic3—32no—
124C3×#217—32no—
125C3×#217—31no—
126C3×(C2×D3)⋊C4—32no—
127C3×(C2×D3)⋊C4—31no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—61no—
138C3×C4⋊Dic3—61no—
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×Dic3⋊C4—32no—
142C3×Dic3⋊C4—31no—
143C3×C4×Dic3—21no—
144C3×C4×Dic3—32no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3C2×D311yescharacteristic
147C3×C4×Dic3C2×D311yescharacteristic
148#3724—32no—
149#3724—32no—
150#3724—62no—
151Dic3⋊Dic3—32no—
152Dic3⋊Dic3—32no—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—62no—
156Dic3⋊Dic3—62no—
157Dic3⋊Dic3C2×D311yescharacteristic
158Dic3⋊Dic3C2×D312yes—
159#3722—32no—
160#3722C2×D311yescharacteristic
161(C2×D3)⋊Dic3—32no—
162(C2×D3)⋊Dic3—32no—
163(C2×D3)⋊Dic3—32no—
164(C2×D3)⋊Dic3—32no—
165(C2×D3)⋊Dic3—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—62no—
168(C2×D3)⋊Dic3—62no—
169(C2×D3)⋊Dic3C2×D312yes—
170(C2×D3)⋊Dic3C2×D311yescharacteristic
171Dic32—32no—
172Dic32—32no—
173Dic32—32no—
174Dic32—32no—
175Dic32—32no—
176Dic32—62no—
177Dic32C2×D312yes—
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—22no—
191C32×Dic3—21no—
192C32×Dic3—21no—
193C32×Dic3#4112yes—
194C3×C4⋊Q8—91no—
195C3×C4×D4—91no—
196C3×#117—91no—
197#947—92no—
198Q8×Dic3—92no—
199#936—92no—
200C4×#67—31no—
201#926—31no—
202#926—91no—
203#924—91no—
204#924—91no—
205#924—91no—
206#924—181no—
207#898—92no—
208#898—92no—
209#897—91no—
210#897—91no—
211#897—91no—
212#897—181no—
213#892—31no—
214#892—91no—
215#892—91no—
216#888—31no—
217#887—92no—
218#887—91no—
219#885—92no—
220#879—92no—
221#879—92no—
222#879—92no—
223#876—92no—
224C4×D12—31no—
225#869—31no—
226C4×Dic6—92no—
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×D311yescharacteristic
258C2×C3⋊Dic3C22×D312yes—
259C2×C3⋊Dic3C22×D312yes—
260C4×C3⋊D3—22no—
261#634—62no—
262#634—64no—
263#634—62no—
264#634—62no—
265#634—122no—
266#634—122no—
267#634—124no—
268C3×#67—62no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C3×D12—62no—
291C3×C4×D3—22no—
292C3×C4×D3—22no—
293C3×C4×D3—42no—
294C3×C4×D3—62no—
295C3×C4×D3—62no—
296C3×C4×D3—122no—
297C3×Dic6—64no—
298C3×Dic6—64no—
299#627—24no—
300#626—22no—
301#556—271noSylow
302C2×C33C2×#4111yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C2×C332−1+411yescharacteristic
305C3×C3⋊D3—41no—
306C32×D3—41no—
307C2×C3×Q8—92no—
308C2×C3×D4—91no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—91no—
313C2×#67—31no—
314C2×D12—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—61no—
318C2×C4×D3D3211yescharacteristic
319C2×Dic6—32no—
320C2×Dic6—32no—
321C2×Dic6—91no—
322C2×Dic6—91no—
323C2×Dic6—91no—
324C2×Dic6—181no—
325C2×Dic6—181no—
326C2×Dic6—181no—
327C2×Dic6—361no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—92no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C22⋊C4—91no—
337C3×C22⋊C4—92no—
338C3×C42—31no—
339C3×C42—31no—
340C3×C42—61no—
341C3×C42—92no—
342#217—31no—
343#217—32no—
344#217—92no—
345#217—92no—
346#217—92no—
347#217—92no—
348#217—182no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—32no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—92no—
355(C2×D3)⋊C4—92no—
356(C2×D3)⋊C4—92no—
357(C2×D3)⋊C4—92no—
358(C2×D3)⋊C4—182no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—32no—
364C4⋊Dic3—31no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—92no—
368C4⋊Dic3—92no—
369C4⋊Dic3—92no—
370C4⋊Dic3—182no—
371C4⋊Dic3D3211yescharacteristic
372Dic3⋊C4—31no—
373Dic3⋊C4—32no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—182no—
381Dic3⋊C4—182no—
382C4×Dic3—32no—
383C4×Dic3—32no—
384C4×Dic3—92no—
385C4×Dic3—92no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—92no—
389C4×Dic3—92no—
390C4×Dic3—182no—
391C4×Dic3D3211yescharacteristic
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—41no—
396C22×C32—61no—
397C22×C32—61no—
398C22×C32—61no—
399C22×C32C23×D311yescharacteristic
400C22×C32C23×D311yescharacteristic
401C22×C32C23×D311yescharacteristic
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3×D3—22no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—62no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—121no—
422C2×C3×D3—121no—
423C32×C4—22no—
424C32×C4—22no—
425C32×C4—22no—
426C32×C4—32no—
427C32×C4—42no—
428C32×C4—62no—
429C32×C4—61no—
430C32×C4—61no—
431C32×C4#23512yes—
432C32×C4#23712yes—
433C32×C4#23912yes—
434C3⋊Dic3—22no—
435C3⋊Dic3—21no—
436C3⋊Dic3—22no—
437C3⋊Dic3—62no—
438C3⋊Dic3—64no—
439C3⋊Dic3—62no—
440C3⋊Dic3—62no—
441C3⋊Dic3—122no—
442C3⋊Dic3—122no—
443C3⋊Dic3—124no—
444C3×Dic3—21no—
445C3×Dic3—22no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—22no—
449C3×Dic3—21no—
450C3×Dic3—22no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—42no—
454C3×Dic3—62no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3—62no—
460C3×Dic3—121no—
461C3×Dic3—122no—
462C3×Dic3—122no—
463C3×Dic3#23512yes—
464C3×Dic3#23712yes—
465C4⋊Q8—91no—
466#126—272no—
467#126—272no—
468#124—272no—
469C22⋊Q8—271no—
470C22⋊Q8—271no—
471C4×Q8—271no—
472C4×Q8—272no—
473C4×D4—91no—
474#117—91no—
475#117—271no—
476C33#55611yescharacteristic, complemented, Sylow
477C23×C3—31no—
478C23×C3—31no—
479C23×C3—61no—
480C23×C3—91no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C22×D3C2×D3211yescharacteristic
485C3×Q8—184no—
486C3×D4—182no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—32no—
494C2×C3×C4—31no—
495C2×C3×C4—32no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—91no—
506C2×C3×C4—92no—
507C2×C3×C4—92no—
508C2×C3×C4—122no—
509C2×C3×C4—182no—
510C2×C3×C4C2×D3211yescharacteristic
511C2×C3×C4C2×D3211yescharacteristic
512C2×C3×C4C2×D3211yescharacteristic
513#67—62no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—61no—
523C2×Dic3—92no—
524C2×Dic3—92no—
525C2×Dic3—92no—
526C2×Dic3—182no—
527C2×Dic3—182no—
528C2×Dic3—182no—
529C2×Dic3—362no—
530C2×Dic3C2×D3211yescharacteristic
531C2×Dic3C2×D3212yes—
532C2×Dic3C2×D3211yescharacteristic
533C2×Dic3C2×D3211yescharacteristic
534D12—62no—
535C4×D3—22no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—122no—
539Dic6—64no—
540Dic6—64no—
541Dic6—184no—
542Dic6—182no—
543Dic6—182no—
544Dic6—182no—
545Dic6—362no—
546Dic6—362no—
547Dic6—364no—
548C2×C32—21no—
549C2×C32—21no—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—41no—
558C2×C32—41no—
559C2×C32—41no—
560C2×C32—121no—
561C2×C32C2×#23511yescharacteristic
562C2×C32C2×#23511yescharacteristic
563C2×C32C2×#23711yescharacteristic
564C2×C32C2×#23711yescharacteristic
565C2×C32C2×#23911yescharacteristic
566C2×C32#100711yescharacteristic
567C2×C32D3×#4111yescharacteristic
568C2×C32#101011yescharacteristic
569C2×C32#101011yescharacteristic
570C3⋊D3—41no—
571C3×D3—42no—
572C3×D3—41no—
573C3×D3—41no—
574C3×D3—122no—
575C3×D3—121no—
576C3×D3—121no—
577C2×Q8—92no—
578C2×Q8—271no—
579C2×D4—91no—
580C22×C4—31no—
581C22×C4—91no—
582C4⋊C4—31no—
583C4⋊C4—91no—
584C4⋊C4—92no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—272no—
588C4⋊C4—272no—
589C4⋊C4—272no—
590C22⋊C4—91no—
591C22⋊C4—92no—
592C22⋊C4—91no—
593C22⋊C4—272no—
594C22⋊C4—272no—
595C22⋊C4—272no—
596C42—31no—
597C42—92no—
598C42—272no—
599C42—272no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—41no—
604C22×C3—62no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—61no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3—181no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3C22×D3211yescharacteristic
617C22×C3C22×D3211yescharacteristic
618C22×C3C22×D3211yescharacteristic
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—62no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—121no—
630C2×D3—121no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—32no—
635C3×C4—32no—
636C3×C4—42no—
637C3×C4—62no—
638C3×C4—62no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—62no—
643C3×C4—61no—
644C3×C4—121no—
645C3×C4—122no—
646C3×C4—121no—
647C3×C4—182no—
648C3×C4—181no—
649C3×C4—182no—
650C3×C4#379612yes—
651C3×C4#379912yes—
652C3×C4#380412yes—
653Dic3—21no—
654Dic3—22no—
655Dic3—21no—
656Dic3—62no—
657Dic3—61no—
658Dic3—62no—
659Dic3—62no—
660Dic3—62no—
661Dic3—61no—
662Dic3—121no—
663Dic3—122no—
664Dic3—122no—
665Dic3—184no—
666Dic3—182no—
667Dic3—182no—
668Dic3—182no—
669Dic3—362no—
670Dic3—362no—
671Dic3—364no—
672Dic3#379512yes—
673C32—21no—
674C32—21no—
675C32—21no—
676C32—41no—
677C32#553311yescharacteristic, complemented
678C32#554211yescharacteristic, complemented
679C32#573211yescharacteristic, complemented
680C23—31no—
681C23—91no—
682Q8—184no—
683Q8—542no—
684D4—182no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—32no—
689C2×C4—62no—
690C2×C4—92no—
691C2×C4—91no—
692C2×C4—92no—
693C2×C4—182no—
694C2×C4—272no—
695C2×C4D3311yescharacteristic
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—122no—
709C2×C3—121no—
710C2×C3—121no—
711C2×C3—361no—
712C2×C3C2×#379511yescharacteristic
713C2×C3C2×#379611yescharacteristic
714C2×C3#6429711yescharacteristic
715C2×C3#6429811yescharacteristic
716C2×C3C2×#379911yescharacteristic
717C2×C3D3×#23511yescharacteristic
718C2×C3D3×#23711yescharacteristic
719C2×C3#6431511yescharacteristic
720C2×C3C2×#380411yescharacteristic
721D3—41no—
722D3—122no—
723D3—121no—
724D3—121no—
725C22—61no—
726C22—61no—
727C22—61no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22C2×D3311yescharacteristic
732C4—32no—
733C4—62no—
734C4—61no—
735C4—61no—
736C4—182no—
737C4—182no—
738C4—181no—
739C4—542no—
740C4#8896212yes—
741C3—21no—
742C3—21no—
743C3—21no—
744C3—41no—
745C3#1059386311yescharacteristic, complemented
746C3#1059455611yescharacteristic, complemented
747C3#1059484011yescharacteristic, complemented
748C2—121no—
749C2—361no—
750C2D3×#379511yescharacteristic
751C2#1172439611yescharacteristic
752C2C2×#8896211yescharacteristic
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. #11723667C2semidirect
2. #11723431C2semidirect
3. #11723426C2semidirect
4. #11723399C2semidirect
5. C3×#63918C2semidirect
7. C3×#63841C2semidirect
8. #11723026C2semidirect
9. #11723024C2semidirect
11. #11722940C2semidirect
49. #63918D3semidirect
72. #63841D3semidirect
476. C33#556semidirect
677. C32#5533semidirect
678. C32#5542semidirect
679. C32#5732semidirect
745. C3#10593863semidirect
746. C3#10594556semidirect
747. C3#10594840semidirect

Maximal subgroups

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

subgroupindex
#117236672
#117234312
#117234262
#117233992
C3×#639182
C3×C4×#6262
C3×#638412
#117230262
#117230242
#117230012
#117229402
#105948403
#105945563
#105938633