Finite Group Databasebeta

← #13169393

Subgroups — #13169393

Order 1728.

1166 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723674C211yesmaximal, characteristic
2C4×Dic3×C3⋊D3C211yesmaximal, characteristic
3#11723410C211yesmaximal, characteristic, complemented
4#11723397C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×#63871C211yesmaximal, characteristic
7C3×#63866C211yesmaximal, characteristic, complemented
8#11723013C212yesmaximal, complemented
9#11722974C212yesmaximal
10#11722941C212yesmaximal, complemented
11#11722921C212yesmaximal
12#10595368—31nomaximal
13#10594387—31nomaximal
14#10593866—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×Dic3×C3⋊D3C2211yescharacteristic
19C2×Dic3×C3⋊D3C2211yescharacteristic
20C2×C3×#627C2212yes—
21C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25#88815C2212yes—
26#88814C2212yes—
27#88807C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29Dic3×C3⋊Dic3C2211yescharacteristic
30Dic3×C3⋊Dic3C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32Dic3×C3⋊Dic3C2211yescharacteristic
33C3×Dic3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×#3722C2212yes—
38Q8×C3⋊Dic3—31no—
39#64096—31no—
40C42×C3⋊D3—31no—
41C3×#946—31no—
42C3×#944—31no—
43C3×#897—31no—
44C3×#888—31no—
45C3×#869—31no—
46C3×#869—31no—
47#63918D311yescharacteristic, complemented
48#63893—32no—
49#63887—32no—
50#63878—32no—
51#63878—32no—
52C4×D3×Dic3—31no—
53C4×D3×Dic3—31no—
54C4×D3×Dic3—61no—
55#63872—32no—
56#63871—31no—
57#63871—32no—
58#63871D311yescharacteristic
59#63866D311yescharacteristic, complemented
60#63857—31no—
61#63856—31no—
62#63849—32no—
63#63846—32no—
64#63845—32no—
65#63843—31no—
66#63843—31no—
67#63843—31no—
68#63843—31no—
69#63843—32no—
70#63843—32no—
71#63843—61no—
72#63843—61no—
73#63838—32no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
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×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×Dic6—22no—
88Dic3×C3⋊D3—22no—
89Dic3×C3⋊D3Q814yescomplemented
90C3×#627—24no—
91#5728—91no—
92#5728—91no—
93#5622—91no—
94C2×C32×Q8—31no—
95C2×C4×C3⋊D3—31no—
96C2×C4×C3⋊D3—31no—
97C2×C4×C3⋊D3C2×D311yescharacteristic
98C2×#634C2×D311yescharacteristic
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—61no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—31no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—32no—
106C2×C3×Dic6—32no—
107C2×C3×Dic6—61no—
108C2×C3×Dic6C2×D311yescharacteristic
109C2×C3×Dic6C2×D311yescharacteristic
110C2×#627C2×D312yes—
111C2×D3×Dic3—31no—
112C2×D3×Dic3—31no—
113C2×D3×Dic3—31no—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—61no—
116C2×D3×Dic3—61no—
117C32×C4⋊C4—31no—
118C32×C42—31no—
119C4⋊(C3⋊Dic3)—32no—
120C4⋊(C3⋊Dic3)C2×D311yescharacteristic
121#3750—32no—
122C4×C3⋊Dic3—31no—
123C4×C3⋊Dic3—31no—
124C4×C3⋊Dic3—31no—
125C4×C3⋊Dic3—31no—
126C4×C3⋊Dic3—31no—
127C4×C3⋊Dic3—32no—
128C4×C3⋊Dic3—32no—
129C4×C3⋊Dic3—61no—
130C4×C3⋊Dic3—61no—
131C4×C3⋊Dic3—61no—
132C4×C3⋊Dic3—121no—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—32no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—61no—
143C3×C4⋊Dic3C2×D311yescharacteristic
144C3×C4⋊Dic3C2×D311yescharacteristic
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×C4×Dic3—21no—
150C3×C4×Dic3C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152#3724—32no—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—32no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—62no—
160Dic3⋊Dic3—62no—
161Dic3⋊Dic3C2×D312yes—
162Dic3⋊Dic3C2×D312yes—
163Dic3⋊Dic3C2×D312yes—
164Dic3⋊Dic3C2×D312yes—
165#3722—32no—
166#3722C2×D312yes—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169Dic32—31no—
170Dic32—32no—
171Dic32—32no—
172Dic32—32no—
173Dic32—31no—
174Dic32—32no—
175Dic32—31no—
176Dic32—31no—
177Dic32—62no—
178Dic32—62no—
179Dic32—61no—
180Dic32—61no—
181C22×C33C2411yescharacteristic
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3C2×Q812yes—
185C33×C4#4112yes—
186C3⋊(C3⋊Dic3)—21no—
187C3⋊(C3⋊Dic3)C2×Q812yes—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C32×Dic3—22no—
192C32×Dic3—22no—
193C32×Dic3C2×Q812yes—
194C32×Dic3#4112yes—
195C3×C4⋊Q8—91no—
196C3×C4⋊Q8—91no—
197C3×C22⋊Q8—91no—
198#946—31no—
199#946—92no—
200#946—91no—
201Q8×Dic3—92no—
202Q8×Dic3—91no—
203Q8×Dic3—91no—
204Q8×Dic3—91no—
205Q8×Dic3—181no—
206#944—31no—
207#924—91no—
208C2×C4×Dic3—91no—
209#897—31no—
210#897—92no—
211#897—91no—
212#892—92no—
213#892—92no—
214#890—92no—
215#890—92no—
216#889—92no—
217#888—31no—
218#887—92no—
219#887—92no—
220#887—91no—
221#887—91no—
222#887—91no—
223#887—181no—
224#878—92no—
225#877—92no—
226C42×D3—91no—
227C42×D3—91no—
228C42×D3—181no—
229#869—31no—
230#869—31no—
231C22×C3⋊D3C22×D311yescharacteristic
232C22×C3×D3—31no—
233C22×C3×D3—31no—
234C22×C3×D3—61no—
235C32×Q8—62no—
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—32no—
243C2×C32×C4—41no—
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—31no—
249C2×C3⋊Dic3—31no—
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—31no—
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—61no—
254C2×C3⋊Dic3—61no—
255C2×C3⋊Dic3—61no—
256C2×C3⋊Dic3—61no—
257C2×C3⋊Dic3—61no—
258C2×C3⋊Dic3—61no—
259C2×C3⋊Dic3—121no—
260C2×C3⋊Dic3—121no—
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D311yescharacteristic
264C4×C3⋊D3—22no—
265C4×C3⋊D3—34no—
266C4×C3⋊D3—62no—
267#634—22no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3C22×D312yes—
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D312yes—
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C3×C4×D3—64no—
290C3×C4×D3—62no—
291C3×C4×D3—62no—
292C3×Dic6—24no—
293C3×Dic6—22no—
294C3×Dic6—22no—
295C3×Dic6—64no—
296C3×Dic6—64no—
297C3×Dic6—62no—
298C3×Dic6—62no—
299C3×Dic6—64no—
300#627—24no—
301D3×Dic3—34no—
302D3×Dic3—34no—
303D3×Dic3—64no—
304D3×Dic3—64no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307#533—271noSylow
308C2×C33C22×Q811yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—22no—
312C2×C3×Q8—31no—
313C2×C3×Q8—31no—
314C2×C3×Q8—61no—
315C2×C3×Q8—92no—
316C2×C3×Q8—91no—
317C22×C3×C4—91no—
318C22×Dic3—91no—
319C22×Dic3—91no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—61no—
323C2×C4×D3—91no—
324C2×C4×D3—91no—
325C2×C4×D3—91no—
326C2×C4×D3—91no—
327C2×C4×D3—181no—
328C2×C4×D3—181no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—32no—
332C2×Dic6—32no—
333C2×Dic6—61no—
334C2×Dic6D3211yescharacteristic
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—92no—
340C3×C4⋊C4—92no—
341C3×C4⋊C4—92no—
342C3×C4⋊C4—91no—
343C3×C22⋊C4—92no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—61no—
347#217—92no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—32no—
355C4⋊Dic3—32no—
356C4⋊Dic3—32no—
357C4⋊Dic3—32no—
358C4⋊Dic3—61no—
359C4⋊Dic3—92no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362C4⋊Dic3—92no—
363C4⋊Dic3—182no—
364C4⋊Dic3D3211yescharacteristic
365Dic3⋊C4—32no—
366Dic3⋊C4—32no—
367Dic3⋊C4—32no—
368Dic3⋊C4—32no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—182no—
375C4×Dic3—91no—
376C4×Dic3—91no—
377C4×Dic3—91no—
378C4×Dic3—91no—
379C4×Dic3—92no—
380C4×Dic3—92no—
381C4×Dic3—92no—
382C4×Dic3—92no—
383C4×Dic3—91no—
384C4×Dic3—91no—
385C4×Dic3—91no—
386C4×Dic3—91no—
387C4×Dic3—92no—
388C4×Dic3—92no—
389C4×Dic3—91no—
390C4×Dic3—181no—
391C4×Dic3—181no—
392C4×Dic3—182no—
393C4×Dic3—182no—
394C4×Dic3—181no—
395C4×Dic3—181no—
396C4×Dic3—181no—
397C4×Dic3—361no—
398C4×Dic3D3211yescharacteristic
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—41no—
403C22×C32C23×D311yescharacteristic
404C22×C32C23×D311yescharacteristic
405C22×C32C23×D311yescharacteristic
406C2×C3⋊D3—21no—
407C2×C3⋊D3—21no—
408C2×C3⋊D3D3×Q812yes—
409C2×C3×D3—32no—
410C2×C3×D3—32no—
411C2×C3×D3—62no—
412C2×C3×D3—62no—
413C2×C3×D3—62no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C32×C4—22no—
419C32×C4—22no—
420C32×C4—22no—
421C32×C4—32no—
422C32×C4—32no—
423C32×C4—42no—
424C32×C4—62no—
425C32×C4—62no—
426C32×C4#23712yes—
427C32×C4#23712yes—
428C32×C4#23912yes—
429C3⋊Dic3—22no—
430C3⋊Dic3—21no—
431C3⋊Dic3—22no—
432C3⋊Dic3—32no—
433C3⋊Dic3—32no—
434C3⋊Dic3—32no—
435C3⋊Dic3—62no—
436C3⋊Dic3—62no—
437C3⋊Dic3—62no—
438C3⋊Dic3—61no—
439C3⋊Dic3—62no—
440C3⋊Dic3—61no—
441C3⋊Dic3—61no—
442C3⋊Dic3—122no—
443C3⋊Dic3—121no—
444C3⋊Dic3—121no—
445C3⋊Dic3—122no—
446C3×Dic3—24no—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—42no—
454C3×Dic3—64no—
455C3×Dic3—62no—
456C3×Dic3—62no—
457C3×Dic3—61no—
458C3×Dic3—62no—
459C3×Dic3—62no—
460C3×Dic3—61no—
461C3×Dic3—62no—
462C3×Dic3—122no—
463C3×Dic3#23712yes—
464C3×Dic3D3×Q812yes—
465C3×Dic3D3×Q812yes—
466C3×Dic3#23912yes—
467C4⋊Q8—91no—
468C4⋊Q8—91no—
469#125—272no—
470C22⋊Q8—91no—
471C22⋊Q8—272no—
472C22⋊Q8—271no—
473C4×Q8—271no—
474C4×Q8—272no—
475C4×Q8—271no—
476#117—272no—
477C2×C42—271no—
478C33#53311yescharacteristic, complemented, Sylow
479C23×C3—91no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—61no—
483C3×Q8—64no—
484C3×Q8—62no—
485C3×Q8—62no—
486C3×Q8—184no—
487C3×Q8—182no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—41no—
500C2×C3×C4—62no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
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
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—32no—
517C2×Dic3—61no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—91no—
521C2×Dic3—91no—
522C2×Dic3—91no—
523C2×Dic3—94no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—181no—
528C2×Dic3—181no—
529C2×Dic3—181no—
530C2×Dic3—181no—
531C2×Dic3—181no—
532C2×Dic3—181no—
533C2×Dic3—182no—
534C2×Dic3—361no—
535C2×Dic3—361no—
536C2×Dic3C2×D3212yes—
537C2×Dic3C2×D3212yes—
538C2×Dic3C2×D3211yescharacteristic
539C2×Dic3C2×D3211yescharacteristic
540C4×D3—64no—
541C4×D3—62no—
542C4×D3—62no—
543C4×D3—94no—
544C4×D3—94no—
545C4×D3—184no—
546C4×D3—182no—
547C4×D3—182no—
548C4×D3—184no—
549Dic6—22no—
550Dic6—64no—
551Dic6—64no—
552Dic6—62no—
553Dic6—62no—
554Dic6—64no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—41no—
565C2×C32—41no—
566C2×C32—41no—
567C2×C32C2×#23711yescharacteristic
568C2×C32C2×#23711yescharacteristic
569C2×C32C2×#23711yescharacteristic
570C2×C32C2×D3×Q811yescharacteristic
571C2×C32C2×D3×Q811yescharacteristic
572C2×C32C2×D3×Q811yescharacteristic
573C2×C32C2×#23911yescharacteristic
574C2×C32C2×#23911yescharacteristic
575C2×C32D3×#4111yescharacteristic
576C3⋊D3—22no—
577C3×D3—64no—
578C3×D3—62no—
579C3×D3—62no—
580C2×Q8—31no—
581C2×Q8—92no—
582C2×Q8—91no—
583C22×C4—91no—
584C22×C4—271no—
585C22×C4—271no—
586C4⋊C4—31no—
587C4⋊C4—92no—
588C4⋊C4—92no—
589C4⋊C4—92no—
590C4⋊C4—92no—
591C4⋊C4—91no—
592C4⋊C4—272no—
593C4⋊C4—272no—
594C4⋊C4—272no—
595C22⋊C4—92no—
596C22⋊C4—272no—
597C42—31no—
598C42—271no—
599C42—271no—
600C42—272no—
601C42—272no—
602C42—271no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—41no—
607C22×C3—92no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3C22×D3211yescharacteristic
611C22×C3C22×D3211yescharacteristic
612C22×C3C22×D3211yescharacteristic
613C2×D3—32no—
614C2×D3—32no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—61no—
619C2×D3—61no—
620C2×D3—61no—
621C2×D3—61no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—32no—
626C3×C4—32no—
627C3×C4—32no—
628C3×C4—32no—
629C3×C4—42no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—64no—
633C3×C4—62no—
634C3×C4—62no—
635C3×C4—62no—
636C3×C4—62no—
637C3×C4—122no—
638C3×C4—181no—
639C3×C4—182no—
640C3×C4—182no—
641C3×C4#379612yes—
642C3×C4#379612yes—
643C3×C4#380512yes—
644Dic3—22no—
645Dic3—22no—
646Dic3—64no—
647Dic3—62no—
648Dic3—62no—
649Dic3—62no—
650Dic3—61no—
651Dic3—62no—
652Dic3—62no—
653Dic3—61no—
654Dic3—92no—
655Dic3—92no—
656Dic3—92no—
657Dic3—122no—
658Dic3—182no—
659Dic3—182no—
660Dic3—182no—
661Dic3—182no—
662Dic3—181no—
663Dic3—181no—
664Dic3—181no—
665Dic3—362no—
666Dic3—361no—
667Dic3—361no—
668Dic3—362no—
669Dic3#379612yes—
670Dic3#379712yes—
671C32—21no—
672C32—21no—
673C32—21no—
674C32—41no—
675C32#562211yescharacteristic, complemented
676C32#572811yescharacteristic, complemented
677C32#572811yescharacteristic, complemented
678C23—91no—
679Q8—62no—
680Q8—184no—
681Q8—182no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—91no—
687C2×C4—92no—
688C2×C4—92no—
689C2×C4—182no—
690C2×C4—274no—
691C2×C4—271no—
692C2×C4—271no—
693C2×C4—542no—
694C2×C4D3311yescharacteristic
695C2×C3—21no—
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—41no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—182no—
708C2×C3C2×#379611yescharacteristic
709C2×C3C2×#379611yescharacteristic
710C2×C3C2×#379611yescharacteristic
711C2×C3C2×#379711yescharacteristic
712C2×C3D3×#23711yescharacteristic
713C2×C3D32×Q811yescharacteristic
714C2×C3D32×Q811yescharacteristic
715C2×C3D3×#23911yescharacteristic
716C2×C3C2×#380511yescharacteristic
717D3—64no—
718D3—62no—
719D3—62no—
720C22—92no—
721C22—181no—
722C22—181no—
723C22C2×D3311yescharacteristic
724C4—32no—
725C4—32no—
726C4—62no—
727C4—62no—
728C4—182no—
729C4—181no—
730C4—182no—
731C4—272no—
732C4—541no—
733C4#8896412yes—
734C3—21no—
735C3—21no—
736C3—21no—
737C3—41no—
738C3#1059386611yescharacteristic, complemented
739C3#1059438711yescharacteristic, complemented
740C3#1059536811yescharacteristic, complemented
741C2—182no—
742C2D3×#379611yescharacteristic
743C2D3×#379711yescharacteristic
744C2C2×#8896411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×C4D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #11723410C2semidirect
4. #11723397C2semidirect
5. C3×#63918C2semidirect
7. C3×#63866C2semidirect
8. #11723013C2semidirect
10. #11722941C2semidirect
47. #63918D3semidirect
59. #63866D3semidirect
89. Dic3×C3⋊D3Q8semidirect
478. C33#533semidirect
675. C32#5622semidirect
676. C32#5728semidirect
677. C32#5728semidirect
738. C3#10593866semidirect
739. C3#10594387semidirect
740. C3#10595368semidirect

Maximal subgroups

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

subgroupindex
#117236742
C4×Dic3×C3⋊D32
#117234102
#117233972
C3×#639182
C3×#638712
C3×#638662
#117230132
#117229742
#117229412
#117229212
#105953683
#105943873
#105938663