Finite Group Databasebeta

← #13168239

Subgroups — #13168239

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
1#11723691C211yesmaximal, characteristic
2C4×#6293C211yesmaximal, characteristic, complemented
3#11723501C211yesmaximal, characteristic
4#11723450C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic
7C3×#63872C211yesmaximal, characteristic, complemented
8#11722979C212yesmaximal, complemented
9#11722974C212yesmaximal, complemented
10#11722972C212yesmaximal, complemented
11#11722908C212yesmaximal, complemented
12#10594470—31nomaximal
13#10594452—31nomaximal
14#10593956—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×#6294C2212yes—
17C2×#6293C2211yescharacteristic
18C2×Dic3×C3⋊D3C2212yes—
19C2×C3×#627C2212yes—
20C2×C3×#624C2212yes—
21C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4×Dic3C2211yescharacteristic
27#88814C2212yes—
28#88807C2211yescharacteristic
29#88807C2212yes—
30#88806C2211yescharacteristic
31Dic3⋊(C3⋊Dic3)C2211yescharacteristic
32Dic3⋊(C3⋊Dic3)C2212yes—
33#88803C2212yes—
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×#3722C2212yes—
38#64102—31no—
39#64099—31no—
40C4×#634—31no—
41C3×#893—31no—
42C3×#890—31no—
43C3×#890—31no—
44C3×#888—31no—
45C3×C4×D12—31no—
46C3×#869—31no—
47#63918D311yescharacteristic, complemented
48C4×#627—31no—
49C4×#627—31no—
50C4×#627—61no—
51#63899—32no—
52#63898—31no—
53#63898—31no—
54#63898—31no—
55#63898—61no—
56#63895—32no—
57#63894—31no—
58#63894D311yescharacteristic
59#63893—32no—
60Dic3×D12—31no—
61D3×C4⋊Dic3—32no—
62D3×C4⋊Dic3—32no—
63#63888—32no—
64#63887—32no—
65#63887—32no—
66#63883—32no—
67#63872—31no—
68#63872—31no—
69#63872—61no—
70#63872D311yescharacteristic, complemented
71#63871—32no—
72#63857—32no—
73#63851—32no—
74C22×C3×C3⋊D3C2312yes—
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C3×C4⋊(C3⋊D3)Q814yescomplemented
82C2×C32×Dic3C2312yes—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86#6294—42no—
87#6293—22no—
88Dic3×C3⋊D3—42no—
89C3×#627—42no—
90C3×#624—24no—
91#5730—91no—
92#5690—91no—
93#5543—91no—
94C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
95C2×C4×C3⋊D3—32no—
96C2×#634—31no—
97C2×C3×D12—31no—
98C2×C3×D12—31no—
99C2×C3×D12—61no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3—32no—
102C2×C3×Dic6—32no—
103C2×C3×Dic6—32no—
104C2×#627—31no—
105C2×#627—31no—
106C2×#627—61no—
107C2×#627C2×D312yes—
108C2×#624—32no—
109C2×#624C2×D312yes—
110C2×D3×Dic3—32no—
111C2×D3×Dic3—32no—
112C2×D3×Dic3—32no—
113C2×D3×Dic3—32no—
114C2×D3×Dic3—62no—
115C32×C4⋊C4—31no—
116C32×C4⋊C4—31no—
117C32×C42—31no—
118#3752—32no—
119C4⋊(C3⋊Dic3)—31no—
120C4⋊(C3⋊Dic3)—32no—
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×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
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×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—31no—
157#3724—31no—
158#3724—61no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—62no—
168Dic3⋊Dic3—61no—
169Dic3⋊Dic3—62no—
170Dic3⋊Dic3—61no—
171Dic3⋊Dic3C2×D312yes—
172Dic3⋊Dic3C2×D312yes—
173Dic3⋊Dic3C2×D312yes—
174#3722—32no—
175#3722C2×D312yes—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—62no—
181C22×C33C2411yescharacteristic
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3C2×Q814yes—
185C33×C4C2×Q812yes—
186C3⋊(C3⋊Dic3)—21no—
187C3⋊(C3⋊Dic3)—21no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C32×Dic3—22no—
192C32×Dic3—21no—
193C32×Dic3—22no—
194C32×Dic3#4112yes—
195C3×C4⋊Q8—91no—
196C3×#125—91no—
197C3×C4×D4—91no—
198#946—92no—
199#946—92no—
200D4×Dic3—91no—
201D4×Dic3—91no—
202C2×C4⋊Dic3—92no—
203#924—92no—
204#897—92no—
205#897—92no—
206#896—92no—
207#896—92no—
208#893—31no—
209#893—91no—
210#893—91no—
211#893—91no—
212#893—181no—
213D3×C4⋊C4—92no—
214D3×C4⋊C4—92no—
215#890—31no—
216#890—31no—
217#890—91no—
218#890—91no—
219#890—91no—
220#890—181no—
221#888—31no—
222#878—92no—
223#878—92no—
224C4×D12—31no—
225C4×D12—91no—
226#869—31no—
227C4×Dic6—91no—
228C4×Dic6—91no—
229C4×Dic6—91no—
230C4×Dic6—181no—
231C22×C3⋊D3C22×D312yes—
232C22×C3×D3—32no—
233C22×C3×D3—32no—
234C22×C3×D3—62no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—31no—
239C2×C32×C4—32no—
240C2×C32×C4—32no—
241C2×C32×C4—31no—
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⋊Dic3C22×D311yescharacteristic
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D311yescharacteristic
263C4⋊(C3⋊D3)Dic614yescomplemented
264C4×C3⋊D3—122no—
265#634—62no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—62no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3C22×D312yes—
280C2×C3×Dic3C22×D312yes—
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D312yes—
283C2×C3×Dic3C22×D312yes—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C3×D12—34no—
288C3×D12—34no—
289C3×D12—64no—
290C3×C4×D3—64no—
291C3×C4×D3—64no—
292C3×Dic6—122no—
293C3×Dic6—122no—
294#627—42no—
295#627—64no—
296#627—62no—
297#627—62no—
298#624—24no—
299#624—122no—
300D3×Dic3—122no—
301D3×Dic3—122no—
302D3×Dic3—124no—
303D3×Dic3—122no—
304D3×Dic3—122no—
305#554—271noSylow
306C2×C33C22×Q811yescharacteristic
307C2×C33C2×#4111yescharacteristic
308C2×C33H(5,𝔽2)11yescharacteristic
309C3×C3⋊D3—24no—
310C2×C3×Q8—92no—
311C2×C3×D4—91no—
312C22×C3×C4—92no—
313C22×Dic3—92no—
314C22×Dic3—92no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×C4×D3—32no—
319C2×C4×D3—32no—
320C2×C4×D3—92no—
321C2×C4×D3—92no—
322C2×C4×D3—92no—
323C2×C4×D3—92no—
324C2×C4×D3—182no—
325C2×Dic6—32no—
326C2×Dic6—32no—
327C2×Dic6—91no—
328C2×Dic6—91no—
329C2×Dic6—91no—
330C2×Dic6—181no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—92no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—92no—
340C3×C4⋊C4—91no—
341C3×C22⋊C4—92no—
342C3×C42—31no—
343C3×C42—31no—
344C3×C42—61no—
345C3×C42—91no—
346#217—92no—
347#217—92no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352(C2×D3)⋊C4—92no—
353(C2×D3)⋊C4—92no—
354(C2×D3)⋊C4—182no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—32no—
358C4⋊Dic3—32no—
359C4⋊Dic3—32no—
360C4⋊Dic3—61no—
361C4⋊Dic3—91no—
362C4⋊Dic3—91no—
363C4⋊Dic3—92no—
364C4⋊Dic3—92no—
365C4⋊Dic3—91no—
366C4⋊Dic3—92no—
367C4⋊Dic3—181no—
368C4⋊Dic3—182no—
369C4⋊Dic3D3211yescharacteristic
370C4⋊Dic3D3211yescharacteristic
371Dic3⋊C4—32no—
372Dic3⋊C4—32no—
373Dic3⋊C4—32no—
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—41no—
401C22×C32C23×D311yescharacteristic
402C22×C32C23×D311yescharacteristic
403C22×C32C23×D311yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3C2×Dic614yes—
407C2×C3×D3—34no—
408C2×C3×D3—34no—
409C2×C3×D3—64no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—62no—
413C2×C3×D3—62no—
414C2×C3×D3—122no—
415C2×C3×D3—122no—
416C32×C4—22no—
417C32×C4—22no—
418C32×C4—22no—
419C32×C4—32no—
420C32×C4—42no—
421C32×C4—62no—
422C32×C4—61no—
423C32×C4—62no—
424C32×C4C2×Dic612yes—
425C32×C4D3×Q812yes—
426C32×C4D3×Q812yes—
427C3⋊Dic3—21no—
428C3⋊Dic3—22no—
429C3⋊Dic3—21no—
430C3⋊Dic3—61no—
431C3⋊Dic3—61no—
432C3⋊Dic3—62no—
433C3⋊Dic3—62no—
434C3⋊Dic3—61no—
435C3⋊Dic3—61no—
436C3⋊Dic3—61no—
437C3⋊Dic3—61no—
438C3⋊Dic3—121no—
439C3⋊Dic3—121no—
440C3⋊Dic3—121no—
441C3⋊Dic3—121no—
442C3⋊Dic3—122no—
443C3⋊Dic3—122no—
444C3×Dic3—22no—
445C3×Dic3—22no—
446C3×Dic3—21no—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—21no—
450C3×Dic3—22no—
451C3×Dic3—42no—
452C3×Dic3—41no—
453C3×Dic3—42no—
454C3×Dic3—62no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3—62no—
459C3×Dic3—61no—
460C3×Dic3—62no—
461C3×Dic3—121no—
462C3×Dic3—122no—
463C3×Dic3#23712yes—
464C3×Dic3#23912yes—
465C4⋊Q8—91no—
466#125—91no—
467#125—271no—
468C22⋊Q8—272no—
469C22⋊Q8—272no—
470C22⋊Q8—272no—
471C4×Q8—271no—
472C4×D4—91no—
473C4×D4—271no—
474C4×D4—271no—
475C2×C4⋊C4—272no—
476C33#55411yescharacteristic, complemented, Sylow
477C23×C3—92no—
478C22×D3—32no—
479C22×D3—32no—
480C22×D3—62no—
481C3×Q8—362no—
482C3×D4—94no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—32no—
494C2×C3×C4—41no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—91no—
500C2×C3×C4—92no—
501C2×C3×C4—91no—
502C2×C3×C4—184no—
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—61no—
513C2×Dic3—61no—
514C2×Dic3—62no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—181no—
522C2×Dic3—181no—
523C2×Dic3—181no—
524C2×Dic3—181no—
525C2×Dic3—181no—
526C2×Dic3—181no—
527C2×Dic3—361no—
528C2×Dic3—361no—
529C2×Dic3—362no—
530C2×Dic3—362no—
531C2×Dic3C2×D3211yescharacteristic
532C2×Dic3C2×D3212yes—
533C2×Dic3C2×D3212yes—
534C2×Dic3C2×D3211yescharacteristic
535D12—34no—
536D12—34no—
537D12—64no—
538C4×D3—64no—
539C4×D3—64no—
540C4×D3—362no—
541C4×D3—362no—
542C4×D3—362no—
543C4×D3—362no—
544C4×D3—364no—
545Dic6—122no—
546Dic6—122no—
547Dic6—182no—
548Dic6—182no—
549Dic6—184no—
550Dic6—182no—
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×C32C22×Dic611yescharacteristic
564C2×C32C2×#23711yescharacteristic
565C2×C32#100411yescharacteristic
566C2×C32C2×D3×Q811yescharacteristic
567C2×C32C2×D3×Q811yescharacteristic
568C2×C32C2×#23911yescharacteristic
569C2×C32D3×#4111yescharacteristic
570C2×C32#100911yescharacteristic
571C2×C32#100911yescharacteristic
572C3⋊D3—24no—
573C3×D3—64no—
574C3×D3—64no—
575C3×D3—124no—
576C2×Q8—92no—
577C2×Q8—271no—
578C2×D4—91no—
579C22×C4—92no—
580C22×C4—272no—
581C22×C4—272no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—92no—
585C4⋊C4—92no—
586C4⋊C4—92no—
587C4⋊C4—91no—
588C4⋊C4—271no—
589C4⋊C4—272no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C4⋊C4—272no—
593C22⋊C4—92no—
594C22⋊C4—272no—
595C22⋊C4—272no—
596C42—31no—
597C42—91no—
598C42—271no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—41no—
603C22×C3—94no—
604C22×C3—182no—
605C22×C3—182no—
606C22×C3C22×D3211yescharacteristic
607C22×C3C22×D3211yescharacteristic
608C22×C3C22×D3211yescharacteristic
609C2×D3—34no—
610C2×D3—34no—
611C2×D3—64no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—62no—
616C2×D3—122no—
617C2×D3—122no—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—32no—
622C3×C4—32no—
623C3×C4—42no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—62no—
627C3×C4—61no—
628C3×C4—62no—
629C3×C4—62no—
630C3×C4—61no—
631C3×C4—122no—
632C3×C4—122no—
633C3×C4—121no—
634C3×C4—181no—
635C3×C4—181no—
636C3×C4—182no—
637C3×C4D3×Dic612yes—
638C3×C4D3×Dic612yes—
639C3×C4#379712yes—
640Dic3—21no—
641Dic3—22no—
642Dic3—22no—
643Dic3—62no—
644Dic3—62no—
645Dic3—61no—
646Dic3—62no—
647Dic3—61no—
648Dic3—61no—
649Dic3—61no—
650Dic3—121no—
651Dic3—122no—
652Dic3—182no—
653Dic3—182no—
654Dic3—181no—
655Dic3—181no—
656Dic3—181no—
657Dic3—181no—
658Dic3—181no—
659Dic3—181no—
660Dic3—361no—
661Dic3—361no—
662Dic3—361no—
663Dic3—361no—
664Dic3—362no—
665Dic3—362no—
666Dic3#379612yes—
667C32—21no—
668C32—21no—
669C32—21no—
670C32—41no—
671C32#554311yescharacteristic, complemented
672C32#569011yescharacteristic, complemented
673C32#573011yescharacteristic, complemented
674C23—92no—
675Q8—362no—
676Q8—542no—
677D4—94no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—91no—
683C2×C4—91no—
684C2×C4—92no—
685C2×C4—184no—
686C2×C4—271no—
687C2×C4—271no—
688C2×C4—1082no—
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—184no—
704C2×C3C2×D3×Dic611yescharacteristic
705C2×C3C2×D3×Dic611yescharacteristic
706C2×C3C2×#379611yescharacteristic
707C2×C3C2×#379711yescharacteristic
708C2×C3#6430711yescharacteristic
709C2×C3D3×#23711yescharacteristic
710C2×C3#6431411yescharacteristic
711C2×C3D3×#23911yescharacteristic
712C2×C3#6432011yescharacteristic
713D3—64no—
714D3—64no—
715D3—124no—
716C22—94no—
717C22—182no—
718C22—182no—
719C22C2×D3311yescharacteristic
720C4—32no—
721C4—62no—
722C4—62no—
723C4—61no—
724C4—181no—
725C4—181no—
726C4—182no—
727C4—541no—
728C4—541no—
729C4#8895712yes—
730C3—21no—
731C3—21no—
732C3—21no—
733C3—41no—
734C3#1059395611yescharacteristic, complemented
735C3#1059445211yescharacteristic, complemented
736C3#1059447011yescharacteristic, complemented
737C2—184no—
738C2D3×#379611yescharacteristic
739C2#1172438511yescharacteristic
740C2C2×#8895711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×C4⋊(C3⋊D3)C22
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
2. C4×#6293C2semidirect
4. #11723450C2semidirect
5. C3×#63918C2semidirect
7. C3×#63872C2semidirect
8. #11722979C2semidirect
9. #11722974C2semidirect
10. #11722972C2semidirect
11. #11722908C2semidirect
47. #63918D3semidirect
70. #63872D3semidirect
81. C3×C4⋊(C3⋊D3)Q8semidirect
263. C4⋊(C3⋊D3)Dic6semidirect
476. C33#554semidirect
671. C32#5543semidirect
672. C32#5690semidirect
673. C32#5730semidirect
734. C3#10593956semidirect
735. C3#10594452semidirect
736. C3#10594470semidirect

Maximal subgroups

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

subgroupindex
#117236912
C4×#62932
#117235012
#117234502
C3×#639182
C3×#638942
C3×#638722
#117229792
#117229742
#117229722
#117229082
#105944703
#105944523
#105939563