Finite Group Databasebeta

← #13176476

Subgroups — #13176476

Order 1728.

1976 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89019C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
3#11723937C211yesmaximal, characteristic, complemented
4C3×#64105C211yesmaximal, characteristic, complemented
5C32×#888C211yesmaximal, characteristic, complemented
6#11723512C211yesmaximal, characteristic
7#11723502C211yesmaximal, characteristic, complemented
8#11723495C211yesmaximal, characteristic, complemented
9#11723477C211yesmaximal, characteristic, complemented
10#11723476C211yesmaximal, characteristic, complemented
11#11723472C211yesmaximal, characteristic
12#11723471C211yesmaximal, characteristic
13#11723395C211yesmaximal, characteristic, complemented
14#11723394C211yesmaximal, characteristic, complemented
15#11723389C211yesmaximal, characteristic, complemented
16#10596198—31nomaximal
17#10594378—34nomaximal
18C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×#6308C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6293C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic
32#89019—24no—
33C3⋊D3×Dic6—24no—
34C33×C4⋊C4C2211yescharacteristic
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic
37#88857C2211yescharacteristic
38#88857C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C32×C4⋊Dic3C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×C4×Dic3C2211yescharacteristic
47#88807C2211yescharacteristic
48#88806C2211yescharacteristic
49Dic3⋊(C3⋊Dic3)C2211yescharacteristic
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic
51#88804C2211yescharacteristic
52#88803C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×Q8×C3⋊D3—31no—
56C2×Q8×C3⋊D3—31no—
57C2×#3797—34no—
58C2×D3×Dic6—34no—
59C32×C4⋊Q8—31no—
60#64155—31no—
61#64155—31no—
62#64105—31no—
63#64105—31no—
64#64105—31no—
65#64105—34no—
66#64105—64no—
67#64105D311yescharacteristic, complemented
68#64102—31no—
69#64102—31no—
70#64097—31no—
71#64097—31no—
72C4×C4⋊(C3⋊D3)—31no—
73C4×#634—31no—
74C3×#896—34no—
75C3×#888D314yescomplemented
76#63904—34no—
77#63899—34no—
78#63895—34no—
79#63888—34no—
80#63887—34no—
81#63881—34no—
82#63880—34no—
83#63840—34no—
84#63839—34no—
85#63837—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C4×C3⋊(C3⋊D3)—22no—
95#6308—22no—
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C3×C4×C3⋊D3—22no—
100C3×#634—22no—
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C32×Dic6—22no—
106C32×Dic6—22no—
107#6293—22no—
108#6293—22no—
109#6293D414yescomplemented
110#6292Q814yescomplemented
111#6289—22no—
112#6289—22no—
113Dic3×C3⋊D3—22no—
114Dic3×C3⋊D3—22no—
115#5727—94no—
116#5632—91no—
117C2×C32×Q8—31no—
118C2×C32×Q8—31no—
119Q8×C3⋊D3—64no—
120Q8×C3⋊D3—64no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—34no—
126C2×C4×C3⋊D3—31no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—64no—
129C2×C4×C3⋊D3C2×D311yescharacteristic
130C2×#634—31no—
131C2×#634—31no—
132C2×#634—34no—
133C2×#634—31no—
134C2×#634—31no—
135C2×#634—64no—
136C2×#634C2×D311yescharacteristic
137C2×C3×C4×D3—34no—
138C2×C3×Dic6—34no—
139C2×C3×Dic6C2×D314yes—
140C2×C3×Dic6C2×D314yes—
141C2×#627—34no—
142C2×#627—34no—
143C2×#627—34no—
144C2×#626—34no—
145C2×#624—34no—
146C2×#624—34no—
147C2×D3×Dic3—34no—
148C2×D3×Dic3—34no—
149#3797—616no—
150D3×Dic6—616no—
151C32×C4⋊C4—24no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154C32×C4⋊C4—31no—
155C32×C4⋊C4C2×D314yes—
156C32×C4⋊C4C2×D311yescharacteristic
157C32×C42—31no—
158#3752—31no—
159#3752—31no—
160#3752—31no—
161#3752—34no—
162#3752—34no—
163#3752—31no—
164#3752—64no—
165#3752—64no—
166#3752C2×D311yescharacteristic
167#3752C2×D311yescharacteristic
168C4⋊(C3⋊Dic3)—31no—
169C4⋊(C3⋊Dic3)—31no—
170#3750—31no—
171#3750—31no—
172#3750—34no—
173#3750—34no—
174#3750—31no—
175#3750—31no—
176#3750—64no—
177#3750—64no—
178#3750C2×D311yescharacteristic
179#3750C2×D311yescharacteristic
180C4×C3⋊Dic3—31no—
181C4×C3⋊Dic3—31no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4—34no—
184C3×C4⋊Dic3C2×D314yes—
185C3×Dic3⋊C4—34no—
186C3×Dic3⋊C4—34no—
187C3×Dic3⋊C4C2×D314yes—
188C3×Dic3⋊C4C2×D314yes—
189C3×C4×Dic3C2×D314yes—
190#3724—34no—
191Dic3⋊Dic3—34no—
192Dic3⋊Dic3—34no—
193Dic3⋊Dic3—34no—
194#3722—34no—
195(C2×D3)⋊Dic3—34no—
196Dic32—34no—
197Dic32—34no—
198C22×C33C2411yescharacteristic
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)C2×Q812yescomplemented
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3C2×Q812yescomplemented
205C33×C4—21no—
206C33×C4—21no—
207C33×C4—21no—
208C3⋊(C3⋊Dic3)—21no—
209C3⋊(C3⋊Dic3)—21no—
210C3⋊(C3⋊Dic3)C2×D412yes—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3C2×D412yes—
214C32×Dic3—21no—
215C32×Dic3—21no—
216C32×Dic3C2×D412yes—
217C32×Dic3C2×Q812yescomplemented
218C2×D3×Q8—94no—
219C2×D3×Q8—94no—
220C2×D3×Q8—91no—
221C22×Dic6—91no—
222C3×C4⋊Q8—34no—
223C3×C22⋊Q8—91no—
224#946—94no—
225#946—94no—
226#944—91no—
227C4×#67—91no—
228#897—91no—
229#896—34no—
230#896—94no—
231#896—94no—
232#896—91no—
233#896—94no—
234#896—91no—
235#896—184no—
236#893—94no—
237#893—94no—
238#888—94no—
239#888—94no—
240#888—91no—
241#888C3⋊D311yescharacteristic, complemented
242#887—91no—
243#67⋊C4—91no—
244#67⋊C4—91no—
245#878—91no—
246#878—91no—
247C4×D12—94no—
248C4×Dic6—94no—
249C22×C3⋊D3—31no—
250C22×C3⋊D3—34no—
251C22×C3⋊D3—64no—
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—34no—
254C32×Q8—62no—
255C32×Q8—62no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—24no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—34no—
273C2×C3⋊Dic3—34no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—64no—
276C2×C3⋊Dic3—64no—
277C2×C3⋊Dic3—64no—
278C2×C3⋊Dic3C22×D311yescharacteristic
279C2×C3⋊Dic3C22×D311yescharacteristic
280C2×C3⋊Dic3C22×D311yescharacteristic
281C4⋊(C3⋊D3)—34no—
282C4×C3⋊D3—22no—
283C4×C3⋊D3—62no—
284C4×C3⋊D3—62no—
285C4×C3⋊D3—62no—
286C4×C3⋊D3—62no—
287C4×C3⋊D3—62no—
288C4×C3⋊D3—68no—
289C4×C3⋊D3—128no—
290#634—22no—
291#634—34no—
292#634—62no—
293#634—62no—
294#634—62no—
295#634—68no—
296#634—128no—
297C2×C3×Dic3—34no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3C22×D314yes—
301C2×C3×Dic3C22×D314yes—
302C2×C3×Dic3C22×D314yes—
303C2×C3×Dic3C22×D314yes—
304C3×C4×D3—68no—
305C3×Dic6—28no—
306C3×Dic6—28no—
307C3×Dic6—68no—
308#627—316no—
309#627—68no—
310#627—68no—
311#626—316no—
312#624—68no—
313#624—68no—
314D3×Dic3—68no—
315D3×Dic3—68no—
316D4×Q8—271noSylow
317C2×C33C22×D411yescharacteristic
318C2×C33C22×Q811yescharacteristic
319C2×C332−1+411yescharacteristic
320C3⋊(C3⋊D3)—22no—
321C3×C3⋊D3—22no—
322C2×C3×Q8—34no—
323C2×C3×Q8—34no—
324C2×C3×Q8—91no—
325C22×C3×C4—91no—
326C2×#67—91no—
327C22×Dic3—91no—
328C22×Dic3—91no—
329D3×Q8—184no—
330D3×Q8—1816no—
331D3×Q8—1816no—
332C2×D12—94no—
333C2×C4×D3—34no—
334C2×C4×D3—94no—
335C2×C4×D3—94no—
336C2×C4×D3—94no—
337C2×C4×D3—94no—
338C2×C4×D3—94no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—184no—
343C2×Dic6—34no—
344C2×Dic6—94no—
345C2×Dic6—91no—
346C2×Dic6—94no—
347C2×Dic6—94no—
348C2×Dic6—94no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—91no—
352C2×Dic6—184no—
353C2×Dic6—184no—
354C2×Dic6C2×C3⋊D311yescharacteristic
355C2×Dic6C2×C3⋊D311yescharacteristic
356C3×C4⋊C4—24no—
357C3×C4⋊C4—34no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4—34no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4—91no—
362C3×C4⋊C4D3214yes—
363C3×C4⋊C4C2×C3⋊D311yescharacteristic
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C42—34no—
367#217—91no—
368(C2×D3)⋊C4—34no—
369(C2×D3)⋊C4—34no—
370(C2×D3)⋊C4—94no—
371(C2×D3)⋊C4—94no—
372(C2×D3)⋊C4—94no—
373(C2×D3)⋊C4—94no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—184no—
378(C2×D3)⋊C4—184no—
379C4⋊Dic3—94no—
380C4⋊Dic3—94no—
381C4⋊Dic3—91no—
382C4⋊Dic3C2×C3⋊D311yescharacteristic
383Dic3⋊C4—34no—
384Dic3⋊C4—34no—
385Dic3⋊C4—94no—
386Dic3⋊C4—94no—
387Dic3⋊C4—94no—
388Dic3⋊C4—94no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—184no—
395Dic3⋊C4—184no—
396Dic3⋊C4C2×C3⋊D311yescharacteristic
397Dic3⋊C4C2×C3⋊D311yescharacteristic
398C4×Dic3—94no—
399C4×Dic3—94no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3C2×C3⋊D311yescharacteristic
403C22×C32—24no—
404C22×C32C23×D314yes—
405C22×C32C23×D311yescharacteristic
406C2×C3⋊D3—21no—
407C2×C3⋊D3—21no—
408C2×C3⋊D3—32no—
409C2×C3⋊D3—38no—
410C2×C3⋊D3—68no—
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—64no—
414C2×C3⋊D3—64no—
415C2×C3⋊D3—124no—
416C2×C3⋊D3—124no—
417C2×C3⋊D3D3×Q812yescomplemented
418C2×C3×D3—38no—
419C2×C3×D3—64no—
420C2×C3×D3—64no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—24no—
425C32×C4—24no—
426C32×C4—24no—
427C32×C4—32no—
428C32×C4—32no—
429C32×C4—44no—
430C32×C4—44no—
431C32×C4—44no—
432C32×C4—61no—
433C32×C4—61no—
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—32no—
437C3⋊Dic3—38no—
438C3⋊Dic3—68no—
439C3⋊Dic3—61no—
440C3⋊Dic3—61no—
441C3⋊Dic3—64no—
442C3⋊Dic3—64no—
443C3⋊Dic3—124no—
444C3⋊Dic3—124no—
445C3⋊Dic3D3×D412yes—
446C3×Dic3—24no—
447C3×Dic3—24no—
448C3×Dic3—38no—
449C3×Dic3—64no—
450C3×Dic3—64no—
451C3×Dic3D3×D418yes—
452C3×Dic3D3×Q818yescomplemented
453C22×Q8—271no—
454C22×Q8—271no—
455C4⋊Q8—31no—
456C4⋊Q8—271no—
457C4⋊Q8—271no—
458C22⋊Q8—91no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464C4×Q8—271no—
465C4×D4—271no—
466C4×D4—271no—
467C4×D4—271no—
468C33D4×Q811yescharacteristic, complemented, Sylow
469C23×C3—91no—
470C22×D3—34no—
471C22×D3—94no—
472C22×D3—91no—
473C22×D3—184no—
474C3×Q8—68no—
475C3×Q8—68no—
476C3×Q8—182no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—34no—
481C2×C3×C4—34no—
482C2×C3×C4—34no—
483C2×C3×C4—34no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—91no—
487C2×C3×C4—182no—
488C2×C3×C4C2×D3214yes—
489C2×C3×C4C2×D3214yes—
490C2×C3×C4C2×D3214yes—
491C2×C3×C4C22×C3⋊D311yescharacteristic
492C2×C3×C4C22×C3⋊D311yescharacteristic
493C2×C3×C4C22×C3⋊D311yescharacteristic
494#67—94no—
495C2×Dic3—34no—
496C2×Dic3—34no—
497C2×Dic3—34no—
498C2×Dic3—94no—
499C2×Dic3—91no—
500C2×Dic3—94no—
501C2×Dic3—94no—
502C2×Dic3—91no—
503C2×Dic3—91no—
504C2×Dic3—184no—
505C2×Dic3—184no—
506C2×Dic3—184no—
507C2×Dic3—182no—
508C2×Dic3—182no—
509C2×Dic3C22×C3⋊D311yescharacteristic
510C2×Dic3C22×C3⋊D311yescharacteristic
511C2×Dic3C22×C3⋊D311yescharacteristic
512C2×Dic3C22×C3⋊D311yescharacteristic
513D12—916no—
514C4×D3—68no—
515C4×D3—182no—
516C4×D3—188no—
517C4×D3—188no—
518C4×D3—182no—
519C4×D3—188no—
520C4×D3—188no—
521C4×D3—188no—
522C4×D3—182no—
523C4×D3—368no—
524Dic6—22no—
525Dic6—22no—
526Dic6—68no—
527Dic6—916no—
528Dic6—94no—
529Dic6—182no—
530Dic6—182no—
531Dic6—188no—
532Dic6—188no—
533Dic6—182no—
534Dic6—188no—
535Dic6—368no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—24no—
539C2×C32C2×D3×D414yes—
540C2×C32C2×D3×D411yescharacteristic
541C2×C32C2×D3×Q814yes—
542C2×C32C2×D3×Q811yescharacteristic
543C2×C32#100714yes—
544C2×C32#101011yescharacteristic
545C3⋊D3—22no—
546C3⋊D3—62no—
547C3⋊D3—68no—
548C3⋊D3—128no—
549C3×D3—68no—
550C2×Q8—31no—
551C2×Q8—31no—
552C2×Q8—91no—
553C2×Q8—271no—
554C2×Q8—271no—
555C2×Q8—271no—
556C2×Q8—271no—
557C2×Q8—544no—
558C2×Q8—544no—
559C2×D4—271no—
560C22×C4—91no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C4⋊C4—271no—
576C4⋊C4—271no—
577C4⋊C4D3×C3⋊D311yescharacteristic
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C42—31no—
585C42—271no—
586C42—271no—
587C22×C3—24no—
588C22×C3—92no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3C22×D3214yes—
592C22×C3C23×C3⋊D311yescharacteristic
593C2×D3—38no—
594C2×D3—64no—
595C2×D3—64no—
596C2×D3—98no—
597C2×D3—92no—
598C2×D3—188no—
599C2×D3—184no—
600C2×D3—184no—
601C2×D3—181no—
602C2×D3—181no—
603C2×D3—364no—
604C2×D3—364no—
605C3×C4—24no—
606C3×C4—24no—
607C3×C4—24no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—38no—
612C3×C4—38no—
613C3×C4—44no—
614C3×C4—44no—
615C3×C4—44no—
616C3×C4—64no—
617C3×C4—64no—
618C3×C4—92no—
619C3×C4—181no—
620C3×C4—181no—
621Dic3—21no—
622Dic3—21no—
623Dic3—38no—
624Dic3—64no—
625Dic3—64no—
626Dic3—98no—
627Dic3—92no—
628Dic3—188no—
629Dic3—184no—
630Dic3—184no—
631Dic3—181no—
632Dic3—181no—
633Dic3—364no—
634Dic3—364no—
635Dic3D4×C3⋊D312yes—
636Dic3Q8×C3⋊D312yescomplemented
637C32—24no—
638C32#563211yescharacteristic, complemented
639C32#572714yescomplemented
640C23—91no—
641C23—271no—
642Q8—62no—
643Q8—62no—
644Q8—182no—
645Q8—274no—
646Q8—542no—
647Q8—542no—
648Q8—542no—
649D4—274no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—91no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—182no—
658C2×C4—271no—
659C2×C4—271no—
660C2×C4—271no—
661C2×C4—542no—
662C2×C4—542no—
663C2×C4—542no—
664C2×C4—542no—
665C2×C4—542no—
666C2×C4C2×D3×C3⋊D311yescharacteristic
667C2×C4C2×D3×C3⋊D311yescharacteristic
668C2×C4C2×D3×C3⋊D311yescharacteristic
669C2×C3—24no—
670C2×C3—24no—
671C2×C3—24no—
672C2×C3—182no—
673C2×C3#6429714yes—
674C2×C3D32×D414yes—
675C2×C3D32×Q814yes—
676C2×C3C2×D4×C3⋊D311yescharacteristic
677C2×C3C2×Q8×C3⋊D311yescharacteristic
678C2×C3#6436411yescharacteristic
679D3—68no—
680D3—188no—
681D3—182no—
682D3—368no—
683C22—92no—
684C22—181no—
685C22—181no—
686C22—272no—
687C22—541no—
688C22—541no—
689C22C22×D3×C3⋊D311yescharacteristic
690C4—21no—
691C4—21no—
692C4—21no—
693C4—32no—
694C4—32no—
695C4—61no—
696C4—61no—
697C4—92no—
698C4—181no—
699C4—181no—
700C4—272no—
701C4—541no—
702C4—541no—
703C3—24no—
704C3#1059437814yescomplemented
705C3#1059619811yescharacteristic, complemented
706C2—182no—
707C2—542no—
708C2#1172456611yescharacteristic
709C2D3×D4×C3⋊D311yescharacteristic
710C2D3×Q8×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC2×#6292C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33D4×Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89019C2semidirect
2. C2×C3⋊D3×Dic6C2semidirect
3. #11723937C2semidirect
4. C3×#64105C2semidirect
5. C32×#888C2semidirect
7. #11723502C2semidirect
8. #11723495C2semidirect
9. #11723477C2semidirect
10. #11723476C2semidirect
13. #11723395C2semidirect
14. #11723394C2semidirect
15. #11723389C2semidirect
67. #64105D3semidirect
75. C3×#888D3semidirect
109. #6293D4semidirect
110. #6292Q8semidirect
201. C2×C3⋊(C3⋊D3)C2×Q8semidirect
204. C2×C3×C3⋊D3C2×Q8semidirect
217. C32×Dic3C2×Q8semidirect
241. #888C3⋊D3semidirect
417. C2×C3⋊D3D3×Q8semidirect
452. C3×Dic3D3×Q8semidirect
468. C33D4×Q8semidirect
636. Dic3Q8×C3⋊D3semidirect
638. C32#5632semidirect
639. C32#5727semidirect
704. C3#10594378semidirect
705. C3#10596198semidirect

Maximal subgroups

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

subgroupindex
C2×#890192
C2×C3⋊D3×Dic62
#117239372
C3×#641052
C32×#8882
#117235122
#117235022
#117234952
#117234772
#117234762
#117234722
#117234712
#117233952
#117233942
#117233892
#105961983
#105943783