Finite Group Databasebeta

← #13168203

Subgroups — #13168203

Order 1728.

1156 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723691C211yesmaximal, characteristic
2#11723534C211yesmaximal, characteristic, complemented
3Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
4#11723447C211yesmaximal, characteristic, complemented
5C3×C4×#627C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic
7C3×#63869C211yesmaximal, characteristic, complemented
8#11722984C212yesmaximal, complemented
9#11722983C212yesmaximal, complemented
10#11722970C212yesmaximal, complemented
11#11722908C212yesmaximal, complemented
12#10594452—31nomaximal
13#10593960—31nomaximal
14#10593938—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×#6294C2212yes—
17C2×#6293C2212yes—
18C2×Dic3×C3⋊D3C2212yes—
19C2×C3×#627C2211yescharacteristic
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#88806C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31#88803C2212yes—
32C3×#3724C2212yes—
33C3×#3724C2211yescharacteristic
34C3×Dic3⋊Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2211yescharacteristic
37C3×#3722C2212yes—
38#64099—31no—
39C4×C4⋊(C3⋊D3)—31no—
40#64078—31no—
41C3×#893—31no—
42C3×#890—31no—
43C3×C4×D12—31no—
44C3×#870—31no—
45C3×C4×Dic6—31no—
46C3×C4×Dic6—31no—
47#63918—31no—
48#63918—31no—
49#63918—61no—
50C4×#627D311yescharacteristic, complemented
51#63899—32no—
52#63898—31no—
53#63896—32no—
54#63896—32no—
55#63895—32no—
56#63894—31no—
57#63894D311yescharacteristic
58#63893—32no—
59Dic3×D12—31no—
60Dic3×D12—31no—
61Dic3×D12—31no—
62Dic3×D12—61no—
63D3×C4⋊Dic3—32no—
64D3×C4⋊Dic3—32no—
65#63888—32no—
66#63883—32no—
67#63869—31no—
68#63869—31no—
69#63869—61no—
70#63869D311yescharacteristic, complemented
71#63865—32no—
72#63856—32no—
73#63851—32no—
74C22×C3×C3⋊D3C2312yes—
75C2×C33×C4C2311yescharacteristic
76C2×C3⋊(C3⋊Dic3)C2312yes—
77C2×C3×C3⋊Dic3C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C3×C4⋊(C3⋊D3)Q814yescomplemented
81C2×C32×Dic3C2312yes—
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86#6294—42no—
87#6293—42no—
88Dic3×C3⋊D3—42no—
89C3×#627—22no—
90C3×#624—24no—
91#5690—91no—
92#5579—91no—
93#5543—91no—
94C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
95C2×C4×C3⋊D3—32no—
96C2×#634—32no—
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—31no—
103C2×C3×Dic6—31no—
104C2×#627—32no—
105C2×#627—32no—
106C2×#627—62no—
107C2×#627C2×D311yescharacteristic
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×C42—31no—
117C32×C42—31no—
118#3752—32no—
119C4⋊(C3⋊Dic3)—31no—
120C4⋊(C3⋊Dic3)—31no—
121C4⋊(C3⋊Dic3)—31no—
122C4⋊(C3⋊Dic3)—32no—
123C4⋊(C3⋊Dic3)—32no—
124C4⋊(C3⋊Dic3)—61no—
125C4⋊(C3⋊Dic3)—61no—
126C4⋊(C3⋊Dic3)—61no—
127C4⋊(C3⋊Dic3)—121no—
128C4⋊(C3⋊Dic3)C2×D311yescharacteristic
129#3750—32no—
130C4×C3⋊Dic3C2×D311yescharacteristic
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—32no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—61no—
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×C4×Dic3—21no—
150C3×C4×Dic3—21no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—61no—
154C3×C4×Dic3C2×D311yescharacteristic
155C3×C4×Dic3C2×D311yescharacteristic
156C3×C4×Dic3C2×D311yescharacteristic
157C3×C4×Dic3C2×D311yescharacteristic
158#3724—32no—
159#3724—32no—
160#3724—62no—
161#3724C2×D312yes—
162#3724C2×D311yescharacteristic
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—62no—
168Dic3⋊Dic3—62no—
169Dic3⋊Dic3C2×D312yes—
170Dic3⋊Dic3C2×D311yescharacteristic
171Dic3⋊Dic3C2×D311yescharacteristic
172#3722—32no—
173#3722C2×D312yes—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—62no—
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3C2×Q814yes—
183C33×C4C2×Q812yes—
184C3⋊(C3⋊Dic3)—22no—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3—22no—
187C3×C3⋊Dic3—21no—
188C32×Dic3—22no—
189C32×Dic3—21no—
190C32×Dic3—21no—
191C32×Dic3—21no—
192C32×Dic3#4112yes—
193C3×#125—91no—
194C3×C4×Q8—91no—
195C3×C4×D4—91no—
196#946—92no—
197D4×Dic3—91no—
198D4×Dic3—91no—
199C2×C4⋊Dic3—92no—
200#924—92no—
201#897—92no—
202#896—92no—
203#896—92no—
204#896—92no—
205#896—92no—
206#893—31no—
207#893—91no—
208D3×C4⋊C4—92no—
209D3×C4⋊C4—92no—
210#890—31no—
211#890—91no—
212#890—91no—
213#890—181no—
214#888—91no—
215#878—92no—
216#878—92no—
217C4×D12—31no—
218C4×D12—91no—
219C4×D12—91no—
220C4×D12—91no—
221C4×D12—181no—
222#870—31no—
223#870—91no—
224#869—91no—
225#869—91no—
226#869—181no—
227C4×Dic6—31no—
228C4×Dic6—31no—
229C22×C3⋊D3C22×D312yes—
230C22×C3×D3—32no—
231C22×C3×D3—32no—
232C22×C3×D3—62no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—31no—
237C2×C32×C4—31no—
238C2×C32×C4—31no—
239C2×C32×C4—31no—
240C2×C32×C4—32no—
241C2×C32×C4—41no—
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C3⋊Dic3—32no—
246C2×C3⋊Dic3—32no—
247C2×C3⋊Dic3—32no—
248C2×C3⋊Dic3—62no—
249C2×C3⋊Dic3—62no—
250C2×C3⋊Dic3—62no—
251C2×C3⋊Dic3—122no—
252C2×C3⋊Dic3C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D312yes—
254C2×C3⋊Dic3C22×D311yescharacteristic
255C4⋊(C3⋊D3)Dic614yescomplemented
256C4×C3⋊D3—122no—
257#634—122no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D312yes—
276C2×C3×Dic3C22×D312yes—
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C3×D12—34no—
283C3×D12—34no—
284C3×D12—64no—
285C3×C4×D3—64no—
286C3×C4×D3—64no—
287C3×Dic6—62no—
288C3×Dic6—62no—
289#627—22no—
290#627—122no—
291#627—122no—
292#627—124no—
293#624—24no—
294#624—122no—
295D3×Dic3—122no—
296D3×Dic3—122no—
297D3×Dic3—124no—
298D3×Dic3—122no—
299D3×Dic3—122no—
300#554—271noSylow
301C2×C33C22×Q811yescharacteristic
302C2×C33C2×#4111yescharacteristic
303C2×C33H(5,𝔽2)11yescharacteristic
304C3×C3⋊D3—24no—
305C2×C3×Q8—91no—
306C2×C3×D4—91no—
307C22×C3×C4—92no—
308C22×Dic3—92no—
309C22×Dic3—92no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×C4×D3—32no—
314C2×C4×D3—32no—
315C2×C4×D3—92no—
316C2×C4×D3—92no—
317C2×C4×D3—92no—
318C2×C4×D3—92no—
319C2×C4×D3—182no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—92no—
323C2×Dic6—92no—
324C2×Dic6—92no—
325C2×Dic6—182no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—92no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—92no—
334C3×C4⋊C4—91no—
335C3×C22⋊C4—92no—
336C3×C42—31no—
337C3×C42—31no—
338C3×C42—31no—
339C3×C42—31no—
340C3×C42—61no—
341C3×C42—61no—
342C3×C42—91no—
343#217—92no—
344#217—92no—
345(C2×D3)⋊C4—32no—
346(C2×D3)⋊C4—32no—
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—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—32no—
357C4⋊Dic3—61no—
358C4⋊Dic3—92no—
359C4⋊Dic3—92no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362C4⋊Dic3—91no—
363C4⋊Dic3—91no—
364C4⋊Dic3—91no—
365C4⋊Dic3—182no—
366C4⋊Dic3—182no—
367C4⋊Dic3—181no—
368C4⋊Dic3—181no—
369C4⋊Dic3—181no—
370C4⋊Dic3—361no—
371C4⋊Dic3D3211yescharacteristic
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—32no—
377Dic3⋊C4—32no—
378Dic3⋊C4—32no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—92no—
382Dic3⋊C4—92no—
383Dic3⋊C4—92no—
384Dic3⋊C4—182no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3D3211yescharacteristic
389C4×Dic3D3211yescharacteristic
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—41no—
394C22×C32C23×D311yescharacteristic
395C22×C32C23×D311yescharacteristic
396C22×C32C23×D311yescharacteristic
397C2×C3⋊D3—22no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3C2×Dic614yes—
400C2×C3×D3—34no—
401C2×C3×D3—34no—
402C2×C3×D3—64no—
403C2×C3×D3—62no—
404C2×C3×D3—62no—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—122no—
408C2×C3×D3—122no—
409C32×C4—22no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—32no—
413C32×C4—42no—
414C32×C4—61no—
415C32×C4—61no—
416C32×C4—62no—
417C32×C4—61no—
418C32×C4C2×Dic612yes—
419C32×C4D3×Q812yes—
420C32×C4D3×Q812yes—
421C3⋊Dic3—21no—
422C3⋊Dic3—21no—
423C3⋊Dic3—22no—
424C3⋊Dic3—62no—
425C3⋊Dic3—62no—
426C3⋊Dic3—62no—
427C3⋊Dic3—122no—
428C3⋊Dic3—122no—
429C3⋊Dic3—122no—
430C3⋊Dic3—242no—
431C3×Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—22no—
435C3×Dic3—21no—
436C3×Dic3—22no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—22no—
442C3×Dic3—41no—
443C3×Dic3—42no—
444C3×Dic3—61no—
445C3×Dic3—61no—
446C3×Dic3—61no—
447C3×Dic3—62no—
448C3×Dic3—61no—
449C3×Dic3—62no—
450C3×Dic3—122no—
451C3×Dic3—121no—
452C3×Dic3—121no—
453C3×Dic3#23512yes—
454C3×Dic3#23712yes—
455C4⋊Q8—271no—
456#125—91no—
457#125—271no—
458C22⋊Q8—272no—
459C22⋊Q8—272no—
460C22⋊Q8—272no—
461C4×Q8—91no—
462C4×D4—91no—
463C4×D4—271no—
464C4×D4—271no—
465C2×C4⋊C4—272no—
466C33#55411yescharacteristic, complemented, Sylow
467C23×C3—92no—
468C22×D3—32no—
469C22×D3—32no—
470C22×D3—62no—
471C3×Q8—182no—
472C3×D4—94no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—62no—
491C2×C3×C4—61no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—92no—
495C2×C3×C4—184no—
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—62no—
508C2×Dic3—92no—
509C2×Dic3—92no—
510C2×Dic3—92no—
511C2×Dic3—182no—
512C2×Dic3—182no—
513C2×Dic3—182no—
514C2×Dic3—362no—
515C2×Dic3—362no—
516C2×Dic3—362no—
517C2×Dic3C2×D3211yescharacteristic
518C2×Dic3C2×D3211yescharacteristic
519C2×Dic3C2×D3211yescharacteristic
520C2×Dic3C2×D3212yes—
521C2×Dic3C2×D3211yescharacteristic
522D12—34no—
523D12—34no—
524D12—64no—
525C4×D3—64no—
526C4×D3—64no—
527C4×D3—362no—
528C4×D3—362no—
529C4×D3—362no—
530C4×D3—362no—
531C4×D3—364no—
532Dic6—62no—
533Dic6—62no—
534Dic6—362no—
535Dic6—362no—
536Dic6—362no—
537Dic6—364no—
538C2×C32—21no—
539C2×C32—21no—
540C2×C32—21no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—41no—
548C2×C32—41no—
549C2×C32—41no—
550C2×C32C22×Dic611yescharacteristic
551C2×C32C2×#23511yescharacteristic
552C2×C32C2×#23711yescharacteristic
553C2×C32C2×D3×Q811yescharacteristic
554C2×C32C2×D3×Q811yescharacteristic
555C2×C32D3×#4111yescharacteristic
556C2×C32#100911yescharacteristic
557C2×C32#100911yescharacteristic
558C2×C32#100911yescharacteristic
559C3⋊D3—24no—
560C3×D3—64no—
561C3×D3—64no—
562C3×D3—124no—
563C2×Q8—91no—
564C2×Q8—272no—
565C2×D4—91no—
566C22×C4—92no—
567C22×C4—272no—
568C22×C4—272no—
569C4⋊C4—31no—
570C4⋊C4—91no—
571C4⋊C4—92no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4—92no—
575C4⋊C4—91no—
576C4⋊C4—272no—
577C4⋊C4—272no—
578C4⋊C4—272no—
579C4⋊C4—271no—
580C22⋊C4—92no—
581C22⋊C4—272no—
582C22⋊C4—272no—
583C42—31no—
584C42—31no—
585C42—91no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—41no—
590C22×C3—94no—
591C22×C3—182no—
592C22×C3—182no—
593C22×C3C22×D3211yescharacteristic
594C22×C3C22×D3211yescharacteristic
595C22×C3C22×D3211yescharacteristic
596C2×D3—34no—
597C2×D3—34no—
598C2×D3—64no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—62no—
603C2×D3—122no—
604C2×D3—122no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—32no—
609C3×C4—32no—
610C3×C4—42no—
611C3×C4—62no—
612C3×C4—62no—
613C3×C4—62no—
614C3×C4—61no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—61no—
620C3×C4—61no—
621C3×C4—61no—
622C3×C4—122no—
623C3×C4—121no—
624C3×C4—182no—
625C3×C4—181no—
626C3×C4—181no—
627C3×C4D3×Dic612yes—
628C3×C4D3×Dic612yes—
629C3×C4#379712yes—
630Dic3—21no—
631Dic3—21no—
632Dic3—21no—
633Dic3—22no—
634Dic3—61no—
635Dic3—61no—
636Dic3—62no—
637Dic3—61no—
638Dic3—61no—
639Dic3—62no—
640Dic3—122no—
641Dic3—121no—
642Dic3—121no—
643Dic3—182no—
644Dic3—182no—
645Dic3—182no—
646Dic3—362no—
647Dic3—362no—
648Dic3—362no—
649Dic3—722no—
650Dic3#379512yes—
651C32—21no—
652C32—21no—
653C32—21no—
654C32—41no—
655C32#554311yescharacteristic, complemented
656C32#557911yescharacteristic, complemented
657C32#569011yescharacteristic, complemented
658C23—92no—
659Q8—182no—
660Q8—1082no—
661D4—94no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—32no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—92no—
670C2×C4—184no—
671C2×C4—272no—
672C2×C4—1082no—
673C2×C4—1082no—
674C2×C4D3311yescharacteristic
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—41no—
685C2×C3—41no—
686C2×C3—41no—
687C2×C3—184no—
688C2×C3C2×D3×Dic611yescharacteristic
689C2×C3C2×D3×Dic611yescharacteristic
690C2×C3C2×#379511yescharacteristic
691C2×C3C2×#379711yescharacteristic
692C2×C3D3×#23511yescharacteristic
693C2×C3#6430811yescharacteristic
694C2×C3#6430811yescharacteristic
695C2×C3D3×#23711yescharacteristic
696C2×C3#6432011yescharacteristic
697D3—64no—
698D3—64no—
699D3—124no—
700C22—94no—
701C22—182no—
702C22—182no—
703C22C2×D3311yescharacteristic
704C4—32no—
705C4—62no—
706C4—61no—
707C4—61no—
708C4—61no—
709C4—181no—
710C4—181no—
711C4—182no—
712C4—542no—
713C4#8895712yes—
714C3—21no—
715C3—21no—
716C3—21no—
717C3—41no—
718C3#1059393811yescharacteristic, complemented
719C3#1059396011yescharacteristic, complemented
720C3#1059445211yescharacteristic, complemented
721C2—184no—
722C2D3×#379511yescharacteristic
723C2#1172439011yescharacteristic
724C2C2×#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. #11723534C2semidirect
4. #11723447C2semidirect
5. C3×C4×#627C2semidirect
7. C3×#63869C2semidirect
8. #11722984C2semidirect
9. #11722983C2semidirect
10. #11722970C2semidirect
11. #11722908C2semidirect
50. C4×#627D3semidirect
70. #63869D3semidirect
80. C3×C4⋊(C3⋊D3)Q8semidirect
255. C4⋊(C3⋊D3)Dic6semidirect
466. C33#554semidirect
655. C32#5543semidirect
656. C32#5579semidirect
657. C32#5690semidirect
718. C3#10593938semidirect
719. C3#10593960semidirect
720. C3#10594452semidirect

Maximal subgroups

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

subgroupindex
#117236912
#117235342
Dic3×C4⋊(C3⋊D3)2
#117234472
C3×C4×#6272
C3×#638942
C3×#638692
#117229842
#117229832
#117229702
#117229082
#105944523
#105939603
#105939383