Finite Group Databasebeta

← #11878610

Subgroups — #11878610

Order 1152.

866 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595398C211yesmaximal, characteristic, complemented
2#10594523C211yesmaximal, characteristic, complemented
3#10592506C211yesmaximal, characteristic, complemented
4C3×#4808C211yesmaximal, characteristic, complemented
5C3×#4805C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591600C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10590958C211yesmaximal, characteristic, complemented
10#10590843C211yesmaximal, characteristic, complemented
11#10590823C211yesmaximal, characteristic, complemented
12#10590677C211yesmaximal, characteristic, complemented
13#10590508C211yesmaximal, characteristic, complemented
14#10590500C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#81444—31nomaximal
17#80240—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3798C2211yescharacteristic
21#64155C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×C8×C3⋊D3C2211yescharacteristic
24#64104C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C3×#897C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30#63916C2211yescharacteristic
31#63910—21no—
32#63909—21no—
33#63909C2211yescharacteristic
34#63908C2211yescharacteristic
35#63906—21no—
36#63906—21no—
37#63895—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63886—21no—
40#63885—21no—
41#63871C2211yescharacteristic
42#63851—21no—
43C2×#3714C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C32×#103C2211yescharacteristic
46#63648C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5833—31no—
62#5629—31no—
63#5629—31no—
64#5510—31no—
65C3×#483—31no—
66C3×#452—31no—
67#5238—31no—
68#5189—31no—
69#5187—31no—
70#5172—31no—
71#5171—31no—
72#5047—31no—
73#5043—31no—
74#4968—31no—
75#4865—31no—
76#4864—31no—
77#4863—31no—
78#4862—31no—
79#4816—31no—
80#4810—31no—
81#4808D311yescharacteristic, complemented
82#4807—31no—
83#4807—31no—
84#4807—61no—
85#4805D311yescharacteristic, complemented
86#4782—31no—
87#4777—31no—
88#4735—31no—
89#4734—31no—
90#4727—31no—
91#4727—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C3×#239—41no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627D411yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×#626D411yescharacteristic
111C2×#625—21no—
112C2×#625D411yescharacteristic
113C2×#624—21no—
114C2×D3×Dic3—21no—
115#3799—41no—
116#3799—41no—
117#3798—41no—
118#3798—41no—
119C2×C32×C8C2311yescharacteristic
120C32×C4⋊C4C2311yescharacteristic
121#3755—41no—
122#3752—21no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C8×C3⋊D3—41no—
128C3×#216—41no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—41no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142#3722—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3714—41no—
146#3712—41no—
147#3204—91noSylow
148C2×C3×#41—31no—
149C2×#239—31no—
150C2×#239C2×D311yescharacteristic
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—31no—
154C2×C3×Q16—31no—
155C2×C3×SD16—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C2×C3×C4⋊C4—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic
164C2×#216C2×D311yescharacteristic
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—61no—
168#939—61no—
169#939—61no—
170#938—31no—
171#938—31no—
172C2×#213—31no—
173#930—31no—
174#930—31no—
175#930—61no—
176#930—61no—
177#930—61no—
178C2×C4⋊Dic3—31no—
179#924—61no—
180C2×D24—31no—
181C2×#204C2×D311yescharacteristic
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186C2×D3×C8—61no—
187#897—31no—
188#897—61no—
189#897C2×D311yescharacteristic
190#896—61no—
191#896—61no—
192#895—31no—
193#895—31no—
194#895—31no—
195#895—31no—
196#895—61no—
197#895—61no—
198#895—61no—
199#895—61no—
200D3×C4⋊C4—31no—
201D3×C4⋊C4C2×D311yescharacteristic
202#884—61no—
203#884—61no—
204#884—61no—
205#884—61no—
206C3×#106—31no—
207C3×#106—31no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#102—31no—
213C3×C22⋊C8—31no—
214C3×C22⋊C8—31no—
215#835—31no—
216#835—31no—
217#835C2×D311yescharacteristic
218#832—31no—
219#830—31no—
220#830—31no—
221#821—31no—
222#821—31no—
223#821—31no—
224#821—61no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8C2×D311yescharacteristic
228(C2×D3)⋊C8C2×D311yescharacteristic
229#817—31no—
230#817C2×D311yescharacteristic
231#816—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#809C2×D311yescharacteristic
236#808—31no—
237#808—31no—
238#808—31no—
239#808—61no—
240#808C2×D311yescharacteristic
241C22×C3⋊D3—21no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—81no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#627—41no—
275#626—41no—
276#626—41no—
277#626—42no—
278#626—81no—
279#626—81no—
280#625—41no—
281#625—81no—
282#624—42no—
283D3×Dic3—81no—
284C32×C8—21no—
285C3⋊(C3⋊C8)—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—91no—
289#537—91no—
290#483—31no—
291#483—91no—
292#481—91no—
293#481—91no—
294#470—91no—
295#469—91no—
296#465—91no—
297#465—91no—
298#452—31no—
299#452—91no—
300#449—91no—
301#449—91no—
302#408—91no—
303C3×#41—121no—
304C3×#41—121no—
305C2×C3×Q8—21no—
306C2×C3×Q8—31no—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—31no—
316C2×#67—31no—
317C2×#67—31no—
318C2×#67—31no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C22×Dic3—61no—
325#239—41no—
326#239—41no—
327#239—121no—
328#239—121no—
329#235—121no—
330#235—121no—
331#235—121no—
332#235—121no—
333#235—121no—
334#235—121no—
335C2×D12—21no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—121no—
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—21no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6—31no—
359C2×Dic6—31no—
360C2×Dic6C22×D311yescharacteristic
361C3×Q16—121no—
362C3×SD16—121no—
363C2×C3×C8—21no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378#217—61no—
379#217—61no—
380#216—41no—
381#215—121no—
382#215—121no—
383#215—122no—
384#213—121no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—121no—
398(C2×D3)⋊C4—121no—
399C4⋊Dic3—21no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3C22×D311yescharacteristic
406C4⋊Dic3C22×D311yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—121no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419D24—121no—
420#204—41no—
421ΓL(1,𝔽25)—121no—
422ΓL(1,𝔽25)—121no—
423D3×C8—121no—
424D3×C8—121no—
425D3×C8—122no—
426C22×C32C22×D411yescharacteristic
427C2×C3⋊D3—21no—
428C2×C3⋊D3—21no—
429C2×C3⋊D3—21no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4H(5,𝔽2)11yescharacteristic
445C32×C4H(5,𝔽2)11yescharacteristic
446C3⋊Dic3—21no—
447C3⋊Dic3—41no—
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—31no—
454C2×#41—91no—
455C2×#41—91no—
456C2×Q16—31no—
457C2×SD16—31no—
458C2×SD16—91no—
459C2×D8—91no—
460C2×M16—91no—
461C22×C8—91no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—181no—
467C22⋊Q8—181no—
468#121—91no—
469#121—91no—
470#121—91no—
471#121—91no—
472#121—181no—
473#121—181no—
474#121—181no—
475#121—181no—
476#121—181no—
477#121—181no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4—91no—
480#106—31no—
481#106—31no—
482#106—91no—
483#106—91no—
484#103—31no—
485#103—91no—
486#103—91no—
487#103D3211yescharacteristic
488#102—31no—
489#102—91no—
490#102—91no—
491#102—91no—
492C22⋊C8—31no—
493C22⋊C8—31no—
494C22⋊C8—91no—
495C22⋊C8—91no—
496C23×C3—31no—
497C23×C3—31no—
498C23×C3—61no—
499C22×D3—21no—
500C22×D3—31no—
501C22×D3—31no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—121no—
506C22×D3D3×D411yescharacteristic
507C22×D3D3×D411yescharacteristic
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—41no—
513C3×Q8—41no—
514C3×Q8—61no—
515C3×Q8—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—122no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—122no—
536C2×C3×C4—241no—
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—121no—
540#67—121no—
541#67—122no—
542#67—121no—
543#67—121no—
544#67—241no—
545#67—241no—
546#67—241no—
547#67—241no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—121no—
557C2×Dic3—241no—
558C2×Dic3D3×D411yescharacteristic
559C2×Dic3D3×D411yescharacteristic
560D12—21no—
561D12—21no—
562D12—42no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—121no—
568D12—121no—
569D12—121no—
570D12—121no—
571D12—122no—
572D12—241no—
573D12—241no—
574D12—242no—
575D12—241no—
576D12—241no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—42no—
582C4×D3—61no—
583C4×D3—61no—
584C4×D3—61no—
585C4×D3—61no—
586C4×D3—81no—
587C4×D3—121no—
588C4×D3—121no—
589C4×D3—122no—
590C4×D3—122no—
591C4×D3—241no—
592Dic6—21no—
593Dic6—21no—
594Dic6—121no—
595Dic6—121no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—41no—
599C3×C8—61no—
600C3×C8—61no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C3⋊C8—62no—
604C3⋊C8—61no—
605C3⋊C8—61no—
606C2×C32#53411yescharacteristic
607C2×C32#57711yescharacteristic
608C2×C32#57711yescharacteristic
609C3⋊D3—41no—
610C3⋊D3—81no—
611C3×D3—41no—
612C3×D3—41no—
613C3×D3—81no—
614#41—121no—
615#41—121no—
616#41—361no—
617#41—361no—
618#41—361no—
619#41—361no—
620C2×Q8—31no—
621C2×Q8—91no—
622C2×Q8C2×D3211yescharacteristic
623C2×D4—31no—
624C2×D4—61no—
625C2×D4—91no—
626C2×D4—91no—
627C2×D4—91no—
628C2×D4—91no—
629C2×D4—181no—
630C2×D4—181no—
631C2×D4—181no—
632C2×D4—181no—
633C2×D4—181no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—91no—
639C22×C4—181no—
640C22×C4—181no—
641Q16—121no—
642SD16—121no—
643SD16—361no—
644D8—361no—
645M16—361no—
646C2×C8—31no—
647C2×C8—31no—
648C2×C8—91no—
649C2×C8—361no—
650C2×C8C2×D3211yescharacteristic
651C4⋊C4—31no—
652C4⋊C4—31no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C4⋊C4—91no—
657C4⋊C4—181no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4C2×D3211yescharacteristic
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22×C3—21no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3C2×D3×D411yescharacteristic
680C22×C3C2×D3×D411yescharacteristic
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—62no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—241no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—81no—
717C3×C4—81no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4#100411yescharacteristic
722C3×C4#100411yescharacteristic
723C3×C4#100911yescharacteristic
724C3×C4#100911yescharacteristic
725Dic3—21no—
726Dic3—21no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—61no—
731Dic3—61no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736C32#320411yescharacteristic, complemented, Sylow
737C23—31no—
738C23—31no—
739C23—61no—
740C23—91no—
741C23—181no—
742Q8—21no—
743Q8—21no—
744Q8—61no—
745Q8—61no—
746Q8—361no—
747D4—61no—
748D4—61no—
749D4—122no—
750D4—181no—
751D4—181no—
752D4—361no—
753D4—361no—
754D4—362no—
755D4—361no—
756D4—721no—
757D4—721no—
758D4—721no—
759D4—721no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—91no—
772C2×C4—122no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—241no—
777C2×C4—362no—
778C2×C4—721no—
779C2×C4C22×D3211yescharacteristic
780C8—21no—
781C8—61no—
782C8—61no—
783C8—181no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—121no—
788C2×C3—121no—
789C2×C3—241no—
790C2×C3#558911yescharacteristic
791C2×C3#565311yescharacteristic
792C2×C3#576211yescharacteristic
793C2×C3#577011yescharacteristic
794C2×C3#577811yescharacteristic
795C2×C3#577811yescharacteristic
796D3—41no—
797D3—41no—
798D3—81no—
799D3—122no—
800D3—121no—
801D3—121no—
802D3—241no—
803D3—241no—
804D3—481no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—181no—
815C22—181no—
816C22—181no—
817C22—361no—
818C22—361no—
819C22—361no—
820C22D32×D411yescharacteristic
821C4—41no—
822C4—41no—
823C4—61no—
824C4—61no—
825C4—121no—
826C4—121no—
827C4—121no—
828C4—181no—
829C4—361no—
830C4#6430711yescharacteristic
831C4#6431411yescharacteristic
832C3—21no—
833C3#8024011yescharacteristic, complemented
834C3#8144411yescharacteristic, complemented
835C2—121no—
836C2—121no—
837C2—241no—
838C2—361no—
839C2—721no—
840C2#1059426211yescharacteristic
841C2#1059475311yescharacteristic
842C2#1059476711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3204
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595398C2semidirect
2. #10594523C2semidirect
3. #10592506C2semidirect
4. C3×#4808C2semidirect
5. C3×#4805C2semidirect
6. #10591657C2semidirect
7. #10591600C2semidirect
8. #10591588C2semidirect
9. #10590958C2semidirect
10. #10590843C2semidirect
11. #10590823C2semidirect
12. #10590677C2semidirect
13. #10590508C2semidirect
14. #10590500C2semidirect
15. #10590439C2semidirect
81. #4808D3semidirect
85. #4805D3semidirect
736. C32#3204semidirect
833. C3#80240semidirect
834. C3#81444semidirect

Maximal subgroups

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

subgroupindex
#105953982
#105945232
#105925062
C3×#48082
C3×#48052
#105916572
#105916002
#105915882
#105909582
#105908432
#105908232
#105906772
#105905082
#105905002
#105904392
#814443
#802403