Finite Group Databasebeta

← #13176475

Subgroups — #13176475

Order 1728.

1952 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
2C2×D3×#634C211yesmaximal, characteristic, complemented
3#11723929C211yesmaximal, characteristic, complemented
4C3×#64105C211yesmaximal, characteristic, complemented
5C32×#896C211yesmaximal, characteristic, complemented
6#11723508C211yesmaximal, characteristic
7#11723507C211yesmaximal, characteristic
8#11723506C211yesmaximal, characteristic
9#11723497C211yesmaximal, characteristic, complemented
10#11723496C211yesmaximal, characteristic, complemented
11#11723491C211yesmaximal, characteristic, complemented
12#11723483C211yesmaximal, characteristic, complemented
13#11723394C211yesmaximal, characteristic, complemented
14#11723393C211yesmaximal, characteristic, complemented
15#11723391C211yesmaximal, characteristic, complemented
16#10596103—31nomaximal
17#10594377—34nomaximal
18C2×#6308C2211yescharacteristic
19C2×#6308C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6293C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C3⋊D3×Dic6—24no—
33D3×#634—24no—
34C33×C4⋊C4C2211yescharacteristic
35C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
36#88857C2211yescharacteristic
37#88857C2211yescharacteristic
38C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47#88807C2211yescharacteristic
48#88806C2211yescharacteristic
49#88806C2211yescharacteristic
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic
51#88803C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×Q8×C3⋊D3—31no—
56C22×#634—31no—
57C2×D3×Dic6—34no—
58C2×D3×Dic6—34no—
59C32×C22⋊Q8—31no—
60#64153—31no—
61C4×#638—31no—
62#64106—31no—
63#64105—31no—
64#64105D311yescharacteristic, complemented
65#64097—31no—
66#64097—31no—
67#64097—34no—
68#64097—64no—
69#64096—31no—
70#64090—31no—
71#64090—31no—
72#64087—31no—
73#64087—31no—
74C3×#896—34no—
75C3×#896D314yescomplemented
76#63902—34no—
77#63896—34no—
78#63896—34no—
79#63893—34no—
80#63893—34no—
81#63879—34no—
82#63879—34no—
83#63839—34no—
84#63839—34no—
85#63838—34no—
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C32×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
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95#6308—22no—
96#6308—22no—
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C3×C4×C3⋊D3—22no—
101C3×#634—22no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C32×C4×D3—22no—
106C32×Dic6—22no—
107#6293—22no—
108#6293—22no—
109#6293D414yescomplemented
110#6290Q814yescomplemented
111Dic3×C3⋊D3—22no—
112Dic3×C3⋊D3—22no—
113D3×C3⋊Dic3—22no—
114D3×C3⋊Dic3—22no—
115#5632—94no—
116#5632—91no—
117C2×C32×Q8—31no—
118C22×C32×C4—31no—
119C2×#638—31no—
120C22×C3⋊Dic3—31no—
121C22×C3⋊Dic3—31no—
122Q8×C3⋊D3—64no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3C2×D311yescharacteristic
126C2×#634—31no—
127C2×#634—31no—
128C2×#634—31no—
129C2×#634—34no—
130C2×#634—34no—
131C2×#634—31no—
132C2×#634—31no—
133C2×#634—64no—
134C2×#634—64no—
135C2×#634—64no—
136C2×#634C2×D311yescharacteristic
137C2×C3×C4×D3—34no—
138C2×C3×C4×D3C2×D314yes—
139C2×C3×Dic6—34no—
140C2×C3×Dic6C2×D314yes—
141C2×#627—34no—
142C2×#627—34no—
143C2×#627—34no—
144C2×#625—34no—
145C2×D3×Dic3—34no—
146C2×D3×Dic3—34no—
147C2×D3×Dic3—34no—
148C2×D3×Dic3—34no—
149D3×Dic6—616no—
150D3×Dic6—616no—
151C32×C4⋊C4—24no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154C32×C4⋊C4C2×D314yes—
155C32×C4⋊C4C2×D311yescharacteristic
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158#3757—31no—
159#3752—31no—
160#3752C2×D311yescharacteristic
161#3752C2×D311yescharacteristic
162C4⋊(C3⋊Dic3)—31no—
163C4⋊(C3⋊Dic3)—34no—
164C4⋊(C3⋊Dic3)—31no—
165C4⋊(C3⋊Dic3)—64no—
166#3750—31no—
167#3750—31no—
168#3750—34no—
169#3750—34no—
170#3750—31no—
171#3750—31no—
172#3750—31no—
173#3750—64no—
174#3750—64no—
175#3750C2×D311yescharacteristic
176#3750C2×D311yescharacteristic
177C4×C3⋊Dic3—31no—
178C4×C3⋊Dic3—34no—
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3—31no—
181C4×C3⋊Dic3—64no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4—34no—
184C3×(C2×D3)⋊C4C2×D314yes—
185C3×(C2×D3)⋊C4C2×D314yes—
186C3×Dic3⋊C4—34no—
187C3×Dic3⋊C4—34no—
188C3×Dic3⋊C4C2×D314yes—
189C3×Dic3⋊C4C2×D314yes—
190#3724—34no—
191#3724—34no—
192Dic3⋊Dic3—34no—
193Dic3⋊Dic3—34no—
194(C2×D3)⋊Dic3—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⋊D3C2×Q812yescomplemented
202C2×C32×D3—21no—
203C2×C32×D3—21no—
204C2×C32×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)C2×Q812yescomplemented
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3—21no—
214C3×C3⋊Dic3C2×D412yes—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3C2×D412yes—
218C2×D3×Q8—94no—
219C2×D3×Q8—91no—
220C22×Dic6—94no—
221C22×Dic6—91no—
222C3×C22⋊Q8—34no—
223C3×C22⋊Q8—91no—
224#944—94no—
225#944—91no—
226C4×#67—94no—
227C4×#67—91no—
228#897—94no—
229#897—91no—
230#896—34no—
231#896—94no—
232#896—91no—
233#896C3⋊D311yescharacteristic, complemented
234#888—94no—
235#888—91no—
236#888—94no—
237#888—91no—
238#888—184no—
239#887—94no—
240#887—91no—
241#67⋊C4—94no—
242#67⋊C4—94no—
243#67⋊C4—91no—
244#67⋊C4—91no—
245#878—94no—
246#878—94no—
247#878—91no—
248#878—91no—
249C23×C32—31no—
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3×D3—34no—
252C22×C3×D3C22×D314yes—
253C32×Q8—62no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—62no—
261C2×C32×C4C22×D314yes—
262C2×C32×C4C22×D314yes—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267#638—34no—
268C2×C3⋊Dic3—31no—
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—34no—
276C2×C3⋊Dic3—64no—
277C2×C3⋊Dic3—64no—
278C2×C3⋊Dic3—64no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—62no—
281C2×C3⋊Dic3—62no—
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C4×C3⋊D3—22no—
286C4×C3⋊D3—62no—
287C4×C3⋊D3—62no—
288#634—22no—
289#634—34no—
290#634—62no—
291#634—62no—
292#634—62no—
293#634—62no—
294#634—68no—
295#634—68no—
296#634—128no—
297#634—128no—
298C2×C3×Dic3—34no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3C22×D314yes—
302C2×C3×Dic3C22×D314yes—
303C2×C3×Dic3C22×D314yes—
304C3×C4×D3—28no—
305C3×C4×D3—68no—
306C3×Dic6—28no—
307C3×Dic6—68no—
308#627—316no—
309#627—68no—
310#627—68no—
311#625—316no—
312D3×Dic3—68no—
313D3×Dic3—68no—
314D3×Dic3—68no—
315D3×Dic3—68no—
316D4×Q8—271noSylow
317C2×C33C22×D411yescharacteristic
318C2×C33C22×Q811yescharacteristic
319C2×C332−1+411yescharacteristic
320C3×C3⋊D3—22no—
321C32×D3—22no—
322C2×C3×Q8—34no—
323C2×C3×Q8—91no—
324C22×C3×C4—34no—
325C22×C3×C4—91no—
326C2×#67—94no—
327C2×#67—91no—
328C22×Dic3—94no—
329C22×Dic3—94no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332D3×Q8—184no—
333D3×Q8—1816no—
334C2×C4×D3—34no—
335C2×C4×D3—94no—
336C2×C4×D3—94no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3C2×C3⋊D311yescharacteristic
340C2×Dic6—34no—
341C2×Dic6—94no—
342C2×Dic6—91no—
343C2×Dic6—94no—
344C2×Dic6—94no—
345C2×Dic6—94no—
346C2×Dic6—94no—
347C2×Dic6—91no—
348C2×Dic6—91no—
349C2×Dic6—91no—
350C2×Dic6—91no—
351C2×Dic6—184no—
352C2×Dic6—184no—
353C2×Dic6—184no—
354C2×Dic6—1816no—
355C2×Dic6C2×C3⋊D311yescharacteristic
356C3×C4⋊C4—24no—
357C3×C4⋊C4—34no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4D3214yes—
362C3×C4⋊C4C2×C3⋊D311yescharacteristic
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367#217—94no—
368#217—91no—
369(C2×D3)⋊C4—34no—
370(C2×D3)⋊C4—34no—
371(C2×D3)⋊C4—94no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
374(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
375C4⋊Dic3—94no—
376C4⋊Dic3—94no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—184no—
380Dic3⋊C4—34no—
381Dic3⋊C4—34no—
382Dic3⋊C4—94no—
383Dic3⋊C4—94no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—94no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—184no—
393Dic3⋊C4—184no—
394Dic3⋊C4C2×C3⋊D311yescharacteristic
395Dic3⋊C4C2×C3⋊D311yescharacteristic
396C4×Dic3—94no—
397C4×Dic3—94no—
398C4×Dic3—94no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—184no—
403C22×C32—24no—
404C22×C32—32no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32C23×D314yes—
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3D3×Q812yescomplemented
412C2×C3×D3—24no—
413C2×C3×D3—24no—
414C2×C3×D3—38no—
415C2×C3×D3—64no—
416C2×C3×D3—64no—
417C2×C3×D3D3×Q818yescomplemented
418C32×C4—28no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—24no—
422C32×C4—21no—
423C32×C4—24no—
424C32×C4—24no—
425C32×C4—32no—
426C32×C4—44no—
427C32×C4—44no—
428C32×C4—61no—
429C32×C4—61no—
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—32no—
433C3⋊Dic3—32no—
434C3⋊Dic3—38no—
435C3⋊Dic3—38no—
436C3⋊Dic3—68no—
437C3⋊Dic3—68no—
438C3⋊Dic3—61no—
439C3⋊Dic3—61no—
440C3⋊Dic3—64no—
441C3⋊Dic3—64no—
442C3⋊Dic3—124no—
443C3⋊Dic3—124no—
444C3⋊Dic3D3×D412yes—
445C3×Dic3—24no—
446C3×Dic3—24no—
447C3×Dic3—38no—
448C3×Dic3—64no—
449C3×Dic3—64no—
450C3×Dic3D3×D418yes—
451C22×Q8—271no—
452C22×Q8—271no—
453C4⋊Q8—271no—
454C4⋊Q8—271no—
455C4⋊Q8—271no—
456C22⋊Q8—31no—
457C22⋊Q8—91no—
458C22⋊Q8—271no—
459C22⋊Q8—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462C4×Q8—271no—
463C4×D4—271no—
464C4×D4—271no—
465C4×D4—271no—
466C33D4×Q811yescharacteristic, complemented, Sylow
467C23×C3—34no—
468C23×C3—91no—
469C22×D3—34no—
470C22×D3C22×C3⋊D311yescharacteristic
471C3×Q8—68no—
472C3×Q8—182no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—34no—
477C2×C3×C4—34no—
478C2×C3×C4—34no—
479C2×C3×C4—68no—
480C2×C3×C4—91no—
481C2×C3×C4—91no—
482C2×C3×C4—91no—
483C2×C3×C4—182no—
484C2×C3×C4C2×D3214yes—
485C2×C3×C4C2×D3214yes—
486C2×C3×C4C2×D3214yes—
487C2×C3×C4C22×C3⋊D311yescharacteristic
488C2×C3×C4C22×C3⋊D311yescharacteristic
489C2×C3×C4C22×C3⋊D311yescharacteristic
490#67—916no—
491#67—94no—
492C2×Dic3—34no—
493C2×Dic3—34no—
494C2×Dic3—34no—
495C2×Dic3—94no—
496C2×Dic3—94no—
497C2×Dic3—91no—
498C2×Dic3—91no—
499C2×Dic3—94no—
500C2×Dic3—94no—
501C2×Dic3—91no—
502C2×Dic3—91no—
503C2×Dic3—184no—
504C2×Dic3—184no—
505C2×Dic3—184no—
506C2×Dic3—184no—
507C2×Dic3—182no—
508C2×Dic3—188no—
509C2×Dic3—188no—
510C2×Dic3—182no—
511C2×Dic3C22×C3⋊D311yescharacteristic
512C2×Dic3C22×C3⋊D311yescharacteristic
513C2×Dic3C22×C3⋊D311yescharacteristic
514C4×D3—22no—
515C4×D3—68no—
516C4×D3—188no—
517C4×D3—182no—
518C4×D3—188no—
519C4×D3—182no—
520Dic6—22no—
521Dic6—68no—
522Dic6—916no—
523Dic6—94no—
524Dic6—182no—
525Dic6—188no—
526Dic6—188no—
527Dic6—182no—
528Dic6—182no—
529Dic6—188no—
530Dic6—188no—
531Dic6—182no—
532Dic6—368no—
533Dic6—368no—
534C2×C32—24no—
535C2×C32—24no—
536C2×C32—24no—
537C2×C32—62no—
538C2×C32C2×D3×D414yes—
539C2×C32C2×D3×D411yescharacteristic
540C2×C32C2×D3×Q814yes—
541C2×C32C2×D3×Q811yescharacteristic
542C2×C32#101014yes—
543C2×C32#101011yescharacteristic
544C3⋊D3—22no—
545C3×D3—28no—
546C3×D3—68no—
547C2×Q8—31no—
548C2×Q8—91no—
549C2×Q8—271no—
550C2×Q8—271no—
551C2×Q8—271no—
552C2×Q8—271no—
553C2×Q8—271no—
554C2×Q8—544no—
555C2×Q8—544no—
556C2×D4—271no—
557C22×C4—31no—
558C22×C4—91no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4D3×C3⋊D311yescharacteristic
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C42—271no—
582C42—271no—
583C42—271no—
584C22×C3—24no—
585C22×C3—38no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—92no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3C22×D3214yes—
592C22×C3C23×C3⋊D311yescharacteristic
593C2×D3—21no—
594C2×D3—21no—
595C2×D3—38no—
596C2×D3—64no—
597C2×D3—64no—
598C2×D3Q8×C3⋊D312yescomplemented
599C3×C4—28no—
600C3×C4—24no—
601C3×C4—24no—
602C3×C4—24no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—38no—
607C3×C4—44no—
608C3×C4—44no—
609C3×C4—64no—
610C3×C4—64no—
611C3×C4—92no—
612C3×C4—181no—
613C3×C4—181no—
614Dic3—21no—
615Dic3—21no—
616Dic3—38no—
617Dic3—64no—
618Dic3—64no—
619Dic3—98no—
620Dic3—98no—
621Dic3—92no—
622Dic3—92no—
623Dic3—188no—
624Dic3—188no—
625Dic3—184no—
626Dic3—184no—
627Dic3—181no—
628Dic3—181no—
629Dic3—364no—
630Dic3—364no—
631Dic3D4×C3⋊D312yes—
632C32—24no—
633C32#563214yescomplemented
634C32#563211yescharacteristic, complemented
635C23—31no—
636C23—91no—
637Q8—62no—
638Q8—182no—
639Q8—274no—
640Q8—542no—
641Q8—542no—
642Q8—542no—
643Q8—542no—
644D4—274no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—62no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—182no—
653C2×C4—271no—
654C2×C4—271no—
655C2×C4—271no—
656C2×C4—271no—
657C2×C4—542no—
658C2×C4—542no—
659C2×C4—542no—
660C2×C4—542no—
661C2×C4C2×D3×C3⋊D311yescharacteristic
662C2×C4C2×D3×C3⋊D311yescharacteristic
663C2×C4C2×D3×C3⋊D311yescharacteristic
664C2×C3—24no—
665C2×C3—24no—
666C2×C3—24no—
667C2×C3—68no—
668C2×C3—182no—
669C2×C3#6429814yes—
670C2×C3D32×D414yes—
671C2×C3D32×Q814yes—
672C2×C3C2×D4×C3⋊D311yescharacteristic
673C2×C3C2×Q8×C3⋊D311yescharacteristic
674C2×C3#6436711yescharacteristic
675D3—22no—
676D3—68no—
677C22—32no—
678C22—61no—
679C22—61no—
680C22—92no—
681C22—181no—
682C22—181no—
683C22C22×D3×C3⋊D311yescharacteristic
684C4—21no—
685C4—21no—
686C4—21no—
687C4—32no—
688C4—61no—
689C4—61no—
690C4—92no—
691C4—181no—
692C4—181no—
693C4—272no—
694C4—272no—
695C4—541no—
696C4—541no—
697C3—24no—
698C3#1059437714yescomplemented
699C3#1059610311yescharacteristic, complemented
700C2—62no—
701C2—182no—
702C2#1172456311yescharacteristic
703C2D3×D4×C3⋊D311yescharacteristic
704C2D3×Q8×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC2×#6290C22
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×C3⋊D3×Dic6C2semidirect
2. C2×D3×#634C2semidirect
3. #11723929C2semidirect
4. C3×#64105C2semidirect
5. C32×#896C2semidirect
9. #11723497C2semidirect
10. #11723496C2semidirect
11. #11723491C2semidirect
12. #11723483C2semidirect
13. #11723394C2semidirect
14. #11723393C2semidirect
15. #11723391C2semidirect
64. #64105D3semidirect
75. C3×#896D3semidirect
109. #6293D4semidirect
110. #6290Q8semidirect
201. C2×C3×C3⋊D3C2×Q8semidirect
204. C2×C32×D3C2×Q8semidirect
211. C3⋊(C3⋊Dic3)C2×Q8semidirect
233. #896C3⋊D3semidirect
411. C2×C3⋊D3D3×Q8semidirect
417. C2×C3×D3D3×Q8semidirect
466. C33D4×Q8semidirect
598. C2×D3Q8×C3⋊D3semidirect
633. C32#5632semidirect
634. C32#5632semidirect
698. C3#10594377semidirect
699. C3#10596103semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×Dic62
C2×D3×#6342
#117239292
C3×#641052
C32×#8962
#117235082
#117235072
#117235062
#117234972
#117234962
#117234912
#117234832
#117233942
#117233932
#117233912
#105961033
#105943773