Finite Group Databasebeta

← #13168255

Subgroups — #13168255

Order 1728.

1162 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊#6296C211yesmaximal, characteristic, complemented
2C4×#6293C211yesmaximal, characteristic, complemented
3#11723499C211yesmaximal, characteristic
4#11723450C211yesmaximal, characteristic, complemented
5C3×#63898C211yesmaximal, characteristic
6C3×Dic3×D12C211yesmaximal, characteristic
7C3×#63869C211yesmaximal, characteristic, complemented
8#11722981C212yesmaximal, complemented
9#11722978C212yesmaximal, complemented
10#11722975C212yesmaximal, complemented
11D3×Dic3⋊Dic3C212yesmaximal, complemented
12#10595272—31nomaximal
13#10594452—31nomaximal
14#10593941—31nomaximal
15C2×C32×D12C2211yescharacteristic
16C2×#6296C2212yes—
17C2×#6293C2211yescharacteristic
18C2×D3×C3⋊Dic3C2212yes—
19C2×C3×D3×Dic3C2212yes—
20C2×C3×D3×Dic3C2212yes—
21C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×C4×C3⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4×Dic3C2211yescharacteristic
27#88815C2212yes—
28#88807C2211yescharacteristic
29#88807C2212yes—
30#88806C2211yescharacteristic
31Dic3⋊(C3⋊Dic3)C2211yescharacteristic
32Dic3⋊(C3⋊Dic3)C2212yes—
33(C2×D3)⋊(C3⋊Dic3)C2212yes—
34C3×#3724C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38D4×C3⋊Dic3—31no—
39#64099—31no—
40C4×#634—31no—
41C3×D4×Dic3—31no—
42C3×D4×Dic3—31no—
43C3×#893—31no—
44C3×#890—31no—
45C3×C4×D12—31no—
46C3×#870—31no—
47#63982—32no—
48C2×Dic3⋊Dic3—32no—
49#63964—32no—
50#63964—32no—
51#63919—31no—
52#63918—31no—
53#63918—31no—
54C4×#627—31no—
55C4×#627—31no—
56C4×#627—61no—
57#63899—32no—
58#63898—31no—
59#63898—31no—
60#63898—61no—
61#63898D311yescharacteristic
62#63896—32no—
63#63893—32no—
64#63893—32no—
65Dic3×D12D311yescharacteristic
66D3×C4⋊Dic3—32no—
67D3×Dic3⋊C4—32no—
68#63872—31no—
69#63872—31no—
70#63872—61no—
71#63869D311yescharacteristic, complemented
72#63851—32no—
73#63851—32no—
74C22×C32×D3C2312yes—
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85C32×D12Q814yescomplemented
86#6296—42no—
87#6293—22no—
88D3×C3⋊Dic3—42no—
89C3×D3×Dic3—24no—
90C3×D3×Dic3—42no—
91#5690—91no—
92#5543—91no—
93#5539—91no—
94C2×C32×D4—31no—
95C22×C3⋊Dic3—32no—
96C2×#634—31no—
97C22×C3×Dic3—32no—
98C22×C3×Dic3—32no—
99C2×C3×D12—21no—
100C2×C3×D12C2×D311yescharacteristic
101C2×C3×D12C2×D311yescharacteristic
102C2×C3×C4×D3—32no—
103C2×C3×C4×D3—32no—
104C2×#627—31no—
105C2×#627—31no—
106C2×#627—32no—
107C2×#627—32no—
108C2×#627—32no—
109C2×#627—61no—
110C2×D3×Dic3—32no—
111C2×D3×Dic3—32no—
112C2×D3×Dic3—62no—
113C2×D3×Dic3C2×D312yes—
114C2×D3×Dic3C2×D312yes—
115C32×C4⋊C4—31no—
116C32×C42—31no—
117#3757—32no—
118C4⋊(C3⋊Dic3)—31no—
119C4⋊(C3⋊Dic3)—32no—
120C4⋊(C3⋊Dic3)C2×D311yescharacteristic
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic
122#3750—31no—
123#3750—31no—
124#3750—32no—
125C4×C3⋊Dic3—31no—
126C4×C3⋊Dic3—31no—
127C4×C3⋊Dic3—31no—
128C4×C3⋊Dic3—61no—
129C4×C3⋊Dic3—61no—
130C4×C3⋊Dic3—61no—
131C4×C3⋊Dic3—121no—
132C4×C3⋊Dic3C2×D311yescharacteristic
133C3×#217—32no—
134C3×#217—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—32no—
143C3×C4⋊Dic3—61no—
144C3×C4⋊Dic3—61no—
145C3×C4⋊Dic3C2×D311yescharacteristic
146C3×C4⋊Dic3C2×D311yescharacteristic
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4—32no—
150C3×C4×Dic3—21no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—61no—
154C3×C4×Dic3C2×D311yescharacteristic
155C3×C4×Dic3C2×D311yescharacteristic
156#3724—32no—
157#3724—31no—
158#3724—31no—
159#3724—61no—
160#3724C2×D312yes—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—62no—
172Dic3⋊Dic3—61no—
173Dic3⋊Dic3—62no—
174Dic3⋊Dic3—61no—
175Dic3⋊Dic3C2×D312yes—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—62no—
179(C2×D3)⋊Dic3C2×D312yes—
180(C2×D3)⋊Dic3C2×D312yes—
181C22×C33C2411yescharacteristic
182C2×C32×D3—22no—
183C2×C32×D3—22no—
184C2×C32×D3C2×Q814yes—
185C33×C4C2×Q812yes—
186C3⋊(C3⋊Dic3)—21no—
187C3⋊(C3⋊Dic3)—21no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3#4112yes—
192C32×Dic3—21no—
193C32×Dic3—22no—
194C32×Dic3—21no—
195C3×#125—91no—
196C3×C4×D4—91no—
197C3×C4×D4—91no—
198D4×Dic3—31no—
199D4×Dic3—31no—
200D4×Dic3—91no—
201D4×Dic3—91no—
202D4×Dic3—181no—
203C2×C4⋊Dic3—92no—
204#924—92no—
205#924—92no—
206C2×Dic3⋊C4—92no—
207#897—92no—
208#896—92no—
209#896—92no—
210#893—31no—
211#893—91no—
212D3×C4⋊C4—92no—
213#890—31no—
214#890—91no—
215#890—91no—
216#890—91no—
217#890—181no—
218#888—91no—
219#888—91no—
220#878—92no—
221#878—92no—
222#878—92no—
223#878—92no—
224C4×D12—31no—
225#870—31no—
226#869—91no—
227C4×Dic6—91no—
228C4×Dic6—91no—
229C4×Dic6—91no—
230C4×Dic6—181no—
231C23×C32—32no—
232C22×C3×D3—22no—
233C22×C3×D3C22×D312yes—
234C22×C3×D3C22×D312yes—
235C32×D4—34no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—31no—
240C2×C32×C4—31no—
241C2×C32×C4—32no—
242C2×C32×C4—41no—
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C3⋊Dic3—31no—
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—31no—
249C2×C3⋊Dic3—31no—
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—31no—
252C2×C3⋊Dic3—61no—
253C2×C3⋊Dic3—61no—
254C2×C3⋊Dic3—61no—
255C2×C3⋊Dic3—61no—
256C2×C3⋊Dic3—61no—
257C2×C3⋊Dic3—61no—
258C2×C3⋊Dic3—121no—
259C2×C3⋊Dic3—121no—
260C2×C3⋊Dic3—122no—
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D312yes—
264C2×C3⋊Dic3C22×D311yescharacteristic
265#634—62no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—62no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—64no—
282C2×C3×Dic3—122no—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C3×D12—24no—
290C3×D12Dic614yescomplemented
291C3×D12Dic614yescomplemented
292C3×C4×D3—64no—
293C3×C4×D3—122no—
294#627—62no—
295#627—62no—
296#627—64no—
297#627—122no—
298#627—122no—
299#627—122no—
300D3×Dic3—24no—
301D3×Dic3—42no—
302D3×Dic3—122no—
303D3×Dic3—122no—
304D3×Dic3—124no—
305#554—271noSylow
306C2×C33C22×Q811yescharacteristic
307C2×C33C2×#4111yescharacteristic
308C2×C33H(5,𝔽2)11yescharacteristic
309C32×D3—24no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—61no—
313C22×C3×C4—92no—
314C22×C3×C4—92no—
315C22×Dic3—32no—
316C22×Dic3—32no—
317C22×Dic3—92no—
318C22×Dic3—92no—
319C22×Dic3—182no—
320C2×D12D3211yescharacteristic
321C2×C4×D3—32no—
322C2×C4×D3—32no—
323C2×C4×D3—92no—
324C2×Dic6—91no—
325C2×Dic6—91no—
326C2×Dic6—91no—
327C2×Dic6—92no—
328C2×Dic6—92no—
329C2×Dic6—92no—
330C2×Dic6—181no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—92no—
335C3×C4⋊C4—92no—
336C3×C4⋊C4—91no—
337C3×C4⋊C4—91no—
338C3×C22⋊C4—92no—
339C3×C22⋊C4—92no—
340C3×C42—31no—
341C3×C42—31no—
342C3×C42—61no—
343C3×C42—91no—
344#217—32no—
345#217—32no—
346#217—92no—
347#217—92no—
348#217—182no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—32no—
351(C2×D3)⋊C4—92no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—32no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—92no—
360C4⋊Dic3—91no—
361C4⋊Dic3—91no—
362C4⋊Dic3—92no—
363C4⋊Dic3—92no—
364C4⋊Dic3—91no—
365C4⋊Dic3—92no—
366C4⋊Dic3—181no—
367C4⋊Dic3—182no—
368C4⋊Dic3D3211yescharacteristic
369Dic3⋊C4—32no—
370Dic3⋊C4—32no—
371Dic3⋊C4—32no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—91no—
378Dic3⋊C4—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—92no—
383Dic3⋊C4—181no—
384Dic3⋊C4—181no—
385Dic3⋊C4—182no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—181no—
393C4×Dic3—181no—
394C4×Dic3—181no—
395C4×Dic3—361no—
396C4×Dic3D3211yescharacteristic
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—34no—
401C22×C32—41no—
402C22×C32—62no—
403C22×C32—62no—
404C22×C32C23×D311yescharacteristic
405C22×C32C23×D311yescharacteristic
406C22×C32C23×D311yescharacteristic
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—24no—
412C2×C3×D3—42no—
413C2×C3×D3—42no—
414C2×C3×D3C2×Dic614yes—
415C2×C3×D3C2×Dic614yes—
416C32×C4—22no—
417C32×C4—22no—
418C32×C4—22no—
419C32×C4—42no—
420C32×C4—61no—
421C32×C4—62no—
422C32×C4—61no—
423C32×C4C2×Dic612yes—
424C32×C4C2×Dic612yes—
425C32×C4D3×Q812yes—
426C3⋊Dic3—22no—
427C3⋊Dic3—21no—
428C3⋊Dic3—22no—
429C3⋊Dic3—61no—
430C3⋊Dic3—61no—
431C3⋊Dic3—62no—
432C3⋊Dic3—62no—
433C3⋊Dic3—61no—
434C3⋊Dic3—61no—
435C3⋊Dic3—61no—
436C3⋊Dic3—61no—
437C3⋊Dic3—121no—
438C3⋊Dic3—121no—
439C3⋊Dic3—121no—
440C3⋊Dic3—121no—
441C3⋊Dic3—122no—
442C3⋊Dic3—122no—
443C3⋊Dic3#23712yes—
444C3×Dic3—22no—
445C3×Dic3—22no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—21no—
449C3×Dic3—22no—
450C3×Dic3—21no—
451C3×Dic3—32no—
452C3×Dic3—32no—
453C3×Dic3—41no—
454C3×Dic3—42no—
455C3×Dic3—62no—
456C3×Dic3—62no—
457C3×Dic3—61no—
458C3×Dic3—62no—
459C3×Dic3—61no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—122no—
463C3×Dic3—121no—
464C3×Dic3—122no—
465C4⋊Q8—271no—
466#125—91no—
467#125—271no—
468C22⋊Q8—272no—
469C22⋊Q8—272no—
470C22⋊Q8—272no—
471C4×Q8—271no—
472C4×D4—91no—
473C4×D4—91no—
474C4×D4—271no—
475C2×C4⋊C4—272no—
476C33#55411yescharacteristic, complemented, Sylow
477C23×C3—32no—
478C23×C3—32no—
479C23×C3—62no—
480C22×D3C2×D3212yes—
481C3×D4—34no—
482C3×D4—34no—
483C3×D4—64no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—32no—
490C2×C3×C4—31no—
491C2×C3×C4—32no—
492C2×C3×C4—31no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—62no—
497C2×C3×C4—91no—
498C2×C3×C4—92no—
499C2×C3×C4—91no—
500C2×C3×C4—92no—
501C2×C3×C4—184no—
502C2×C3×C4—362no—
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—64no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—91no—
522C2×Dic3—91no—
523C2×Dic3—91no—
524C2×Dic3—91no—
525C2×Dic3—122no—
526C2×Dic3—181no—
527C2×Dic3—181no—
528C2×Dic3—181no—
529C2×Dic3—181no—
530C2×Dic3—181no—
531C2×Dic3—181no—
532C2×Dic3—361no—
533C2×Dic3—361no—
534C2×Dic3—362no—
535C2×Dic3—362no—
536C2×Dic3—364no—
537C2×Dic3C2×D3211yescharacteristic
538C2×Dic3C2×D3211yescharacteristic
539C2×Dic3C2×D3212yes—
540D12#62714yescomplemented
541C4×D3—64no—
542C4×D3—122no—
543C4×D3—362no—
544Dic6—182no—
545Dic6—182no—
546Dic6—182no—
547Dic6—184no—
548Dic6—362no—
549Dic6—362no—
550Dic6—362no—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—41no—
561C2×C32—41no—
562C2×C32—41no—
563C2×C32—64no—
564C2×C32C22×Dic611yescharacteristic
565C2×C32C22×Dic611yescharacteristic
566C2×C32C2×#23711yescharacteristic
567C2×C32#100411yescharacteristic
568C2×C32C2×D3×Q811yescharacteristic
569C2×C32D3×#4111yescharacteristic
570C2×C32D3×#4111yescharacteristic
571C2×C32#100911yescharacteristic
572C2×C32#100911yescharacteristic
573C3×D3—24no—
574C3×D3—24no—
575C3×D3—44no—
576C2×Q8—271no—
577C2×Q8—272no—
578C2×D4—31no—
579C22×C4—92no—
580C22×C4—92no—
581C22×C4—272no—
582C4⋊C4—31no—
583C4⋊C4—92no—
584C4⋊C4—92no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—271no—
588C4⋊C4—272no—
589C4⋊C4—271no—
590C4⋊C4—271no—
591C4⋊C4—272no—
592C4⋊C4—272no—
593C22⋊C4—92no—
594C22⋊C4—92no—
595C22⋊C4—272no—
596C42—31no—
597C42—91no—
598C42—271no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—34no—
603C22×C3—34no—
604C22×C3—41no—
605C22×C3—64no—
606C22×C3—62no—
607C22×C3—62no—
608C22×C3—62no—
609C22×C3—62no—
610C22×C3—122no—
611C22×C3—122no—
612C22×C3C22×D3211yescharacteristic
613C22×C3C22×D3211yescharacteristic
614C22×C3C22×D3211yescharacteristic
615C2×D3—22no—
616C2×D3—22no—
617C2×D3C2×#62714yes—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—62no—
623C3×C4—62no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—62no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—92no—
630C3×C4—122no—
631C3×C4—121no—
632C3×C4—181no—
633C3×C4—182no—
634C3×C4—182no—
635C3×C4D3×Dic612yes—
636C3×C4D3×Dic612yes—
637C3×C4C2×#62712yes—
638Dic3—21no—
639Dic3—21no—
640Dic3—22no—
641Dic3—32no—
642Dic3—32no—
643Dic3—62no—
644Dic3—62no—
645Dic3—62no—
646Dic3—61no—
647Dic3—62no—
648Dic3—61no—
649Dic3—62no—
650Dic3—122no—
651Dic3—122no—
652Dic3—121no—
653Dic3—182no—
654Dic3—182no—
655Dic3—181no—
656Dic3—181no—
657Dic3—181no—
658Dic3—181no—
659Dic3—181no—
660Dic3—181no—
661Dic3—361no—
662Dic3—361no—
663Dic3—361no—
664Dic3—361no—
665Dic3—362no—
666Dic3—362no—
667C32—21no—
668C32—21no—
669C32—21no—
670C32—41no—
671C32#553911yescharacteristic, complemented
672C32#554311yescharacteristic, complemented
673C32#569011yescharacteristic, complemented
674C23—32no—
675Q8—542no—
676Q8—1082no—
677D4—34no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—32no—
681C2×C4—91no—
682C2×C4—91no—
683C2×C4—92no—
684C2×C4—92no—
685C2×C4—184no—
686C2×C4—271no—
687C2×C4—271no—
688C2×C4—362no—
689C2×C4—1082no—
690C2×C4D3311yescharacteristic
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—21no—
700C2×C3—41no—
701C2×C3—41no—
702C2×C3—41no—
703C2×C3—64no—
704C2×C3—64no—
705C2×C3—124no—
706C2×C3C2×D3×Dic611yescharacteristic
707C2×C3C2×D3×Dic611yescharacteristic
708C2×C3#6430611yescharacteristic
709C2×C3#6430711yescharacteristic
710C2×C3D3×#23711yescharacteristic
711C2×C3D3×#23711yescharacteristic
712C2×C3#6431411yescharacteristic
713C2×C3#6432011yescharacteristic
714C2×C3C22×#62711yescharacteristic
715D3—24no—
716C22—34no—
717C22—62no—
718C22—62no—
719C22C2×D3311yescharacteristic
720C4—62no—
721C4—61no—
722C4—61no—
723C4—92no—
724C4—182no—
725C4—182no—
726C4—181no—
727C4—541no—
728C4—541no—
729C4D3×#62712yes—
730C3—21no—
731C3—21no—
732C3—21no—
733C3—41no—
734C3#1059394111yescharacteristic, complemented
735C3#1059445211yescharacteristic, complemented
736C3#1059527211yescharacteristic, complemented
737C2—64no—
738C2#1172437311yescharacteristic
739C2#1172438511yescharacteristic
740C2C2×D3×#62711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C32×D12C22
hypercenterC2×C4D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C4⋊#6296C2semidirect
2. C4×#6293C2semidirect
4. #11723450C2semidirect
7. C3×#63869C2semidirect
8. #11722981C2semidirect
9. #11722978C2semidirect
10. #11722975C2semidirect
11. D3×Dic3⋊Dic3C2semidirect
71. #63869D3semidirect
85. C32×D12Q8semidirect
290. C3×D12Dic6semidirect
291. C3×D12Dic6semidirect
476. C33#554semidirect
540. D12#627semidirect
671. C32#5539semidirect
672. C32#5543semidirect
673. C32#5690semidirect
734. C3#10593941semidirect
735. C3#10594452semidirect
736. C3#10595272semidirect

Maximal subgroups

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

subgroupindex
C4⋊#62962
C4×#62932
#117234992
#117234502
C3×#638982
C3×Dic3×D122
C3×#638692
#117229812
#117229782
#117229752
D3×Dic3⋊Dic32
#105952723
#105944523
#105939413