Finite Group Databasebeta

← C109×#24031 #42142025

Subgroups — C109×#24031 #42142025

Order 27904.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3488C211yesmaximal, characteristic
2C109×#3093C211yesmaximal, characteristic, complemented
3C109×#2896C211yesmaximal, characteristic, complemented
4C109×#2500C211yesmaximal, characteristic, complemented
5C109×#2040C211yesmaximal, characteristic, complemented
6C109×#2039C211yesmaximal, characteristic, complemented
7C109×#2037C211yesmaximal, characteristic, complemented
8C109×#2037C211yesmaximal, characteristic, complemented
9C109×#1900C211yesmaximal, characteristic, complemented
10C109×#1871C211yesmaximal, characteristic, complemented
11C109×#1860C211yesmaximal, characteristic, complemented
12C109×#1859C211yesmaximal, characteristic, complemented
13C109×#1792C211yesmaximal, characteristic, complemented
14C109×#1792C211yesmaximal, characteristic, complemented
15C109×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18C22×M16×C109C2211yescharacteristic, complemented
19#550×C109—21no—
20#548×C109—21no—
21#546×C109—21no—
22#546×C109—22no—
23D42×C109—22no—
24D42×C109—21no—
25#537×C109—21no—
26#537×C109C2211yescharacteristic
27#535×C109—21no—
28#535×C109C2211yescharacteristic
29#525×C109—21no—
30#525×C109C2211yescharacteristic
31C2×#121×C109—21no—
32C2×#121×C109C2211yescharacteristic
33#520×C109C2211yescharacteristic
34C2×#117×C109C2211yescharacteristic, complemented
35#485×C109—21no—
36#485×C109—21no—
37#482×C109—21no—
38#482×C109—21no—
39#428×C109C2211yescharacteristic, complemented
40#428×C109C2211yescharacteristic, complemented
41C2×#104×C109C2211yescharacteristic
42C2×#104×C109C2211yescharacteristic
43C2×#104×C109C2211yescharacteristic, complemented
44C2×#104×C109C2211yescharacteristic, complemented
45C2×#104×C109C2211yescharacteristic, complemented
46C2×#104×C109C2211yescharacteristic, complemented
47#419×C109—21no—
48#418×C109—21no—
49#417×C109C2211yescharacteristic
50#417×C109C2211yescharacteristic
51#417×C109C2211yescharacteristic, complemented
52#417×C109C2211yescharacteristic, complemented
53#417×C109C2211yescharacteristic, complemented
54#417×C109C2211yescharacteristic, complemented
55#416×C109—21no—
56#416×C109—21no—
57C2×#100×C109C2211yescharacteristic, complemented
58C2×#100×C109C2211yescharacteristic, complemented
59#407×C109C2211yescharacteristic, complemented
60#394×C109—22no—
61#390×C109C2211yescharacteristic, complemented
62#390×C109C2211yescharacteristic, complemented
63#388×C109—22no—
64#384×C109C2211yescharacteristic, complemented
65#382×C109C2211yescharacteristic, complemented
66C4×C22⋊C4×C109C2211yescharacteristic, complemented
67#343×C109C2211yescharacteristic, complemented
68#343×C109C2211yescharacteristic, complemented
69#339×C109C2211yescharacteristic, complemented
70#339×C109C2211yescharacteristic, complemented
71H(5,𝔽2)×C109—22no—
72H(5,𝔽2)×C109—22no—
73H(5,𝔽2)×C109—41no—
74H(5,𝔽2)×C109—41no—
75C2×#41×C109—21no—
76C2×#41×C109—21no—
77C2×#41×C109—21no—
78C2×#41×C109—21no—
79C2×#41×C109—22no—
80C2×#41×C109—22no—
81C2×#41×C109—41no—
82C2×#41×C109—41no—
83C2×#41×C109D411yescharacteristic
84C2×#41×C109D411yescharacteristic
85C2×#41×C109C2311yescharacteristic
86C2×#41×C109C2311yescharacteristic
87C2×#41×C109C2311yescharacteristic
88C22×Q8×C109D411yescharacteristic
89C22×D4×C109—21no—
90C22×D4×C109—22no—
91C22×D4×C109—22no—
92C22×D4×C109—21no—
93C22×D4×C109—21no—
94C22×D4×C109D411yescharacteristic
95C22×D4×C109D412yes—
96C22×D4×C109C2311yescharacteristic
97C23×C4×C109—21no—
98C23×C4×C109C2311yescharacteristic
99C2×M16×C109—21no—
100C2×M16×C109—41no—
101C2×M16×C109—41no—
102C2×M16×C109C2311yescharacteristic
103C2×M16×C109C2311yescharacteristic
104C2×M16×C109C2311yescharacteristic
105C2×M16×C109C2311yescharacteristic
106C22×C8×C109—21no—
107#127×C109—22no—
108#127×C109—21no—
109#124×C109—22no—
110#124×C109—21no—
111#123×C109—22no—
112#123×C109—21no—
113C22⋊Q8×C109—22no—
114C22⋊Q8×C109—21no—
115C22⋊Q8×C109—21no—
116C22⋊Q8×C109D411yescharacteristic
117C22⋊Q8×C109D411yescharacteristic
118#121×C109—22no—
119#121×C109—22no—
120#121×C109—22no—
121#121×C109—22no—
122#121×C109—22no—
123#121×C109—21no—
124#121×C109—21no—
125#121×C109—21no—
126#121×C109—21no—
127#121×C109—21no—
128#121×C109—21no—
129#121×C109—22no—
130#121×C109—21no—
131#121×C109—21no—
132#121×C109D411yescharacteristic
133#121×C109D411yescharacteristic
134#120×C109—22no—
135#120×C109—22no—
136#120×C109—22no—
137#120×C109—21no—
138#120×C109—22no—
139C4×Q8×C109—21no—
140C4×D4×C109—22no—
141C4×D4×C109—22no—
142C4×D4×C109—21no—
143C4×D4×C109—22no—
144C4×D4×C109—21no—
145C4×D4×C109—21no—
146#117×C109—21no—
147#117×C109—21no—
148#117×C109—21no—
149#117×C109—21no—
150#117×C109—21no—
151#117×C109C2311yescharacteristic
152C2×C4⋊C4×C109—21no—
153C2×C4⋊C4×C109—22no—
154C2×C4⋊C4×C109C2311yescharacteristic
155C2×C4⋊C4×C109C2311yescharacteristic
156C2×C4⋊C4×C109C2311yescharacteristic
157C2×C22⋊C4×C109—22no—
158C2×C22⋊C4×C109—21no—
159C2×C22⋊C4×C109—21no—
160C2×C22⋊C4×C109—22no—
161C2×C22⋊C4×C109—22no—
162C2×C22⋊C4×C109D412yes—
163C2×C42×C109—21no—
164C2×C42×C109C2311yescharacteristic
165C2×C42×C109C2311yescharacteristic
166#107×C109—21no—
167#107×C109—21no—
168#106×C109—21no—
169#106×C109—21no—
170#104×C109—22no—
171#104×C109—22no—
172#104×C109—41no—
173#104×C109—41no—
174#104×C109—41no—
175#104×C109—41no—
176#103×C109—21no—
177#103×C109—21no—
178#103×C109—21no—
179#103×C109—21no—
180#103×C109—21no—
181#103×C109—21no—
182#102×C109—21no—
183#102×C109—21no—
184#102×C109—21no—
185#102×C109—21no—
186#102×C109—21no—
187#102×C109—21no—
188#100×C109—41no—
189#100×C109—41no—
190C22⋊C8×C109—21no—
191C22⋊C8×C109—21no—
192#95×C109—21no—
193#95×C109—22no—
194C24×C109—22no—
195C24×C109—21no—
196C24×C109C2×D412yes—
197C24×C109C2×D411yescharacteristic
198#41×C109—21no—
199#41×C109—21no—
200#41×C109—22no—
201#41×C109—22no—
202#41×C109—21no—
203#41×C109—21no—
204#41×C109—21no—
205#41×C109—21no—
206#41×C109—21no—
207#41×C109—21no—
208#41×C109—21no—
209#41×C109—21no—
210#41×C109—42no—
211#41×C109—42no—
212#41×C109—41no—
213#41×C109—41no—
214#41×C109—42no—
215#41×C109—42no—
216#41×C109—42no—
217#41×C109—42no—
218#41×C109—42no—
219#41×C109—42no—
220#41×C109#4112yes—
221#41×C109#4112yes—
222C2×Q8×C109—21no—
223C2×Q8×C109—22no—
224C2×Q8×C109—41no—
225C2×Q8×C109C2×D411yescharacteristic
226C2×Q8×C109C2×D411yescharacteristic
227C2×Q8×C109C2×D411yescharacteristic
228C2×D4×C109—21no—
229C2×D4×C109—22no—
230C2×D4×C109—22no—
231C2×D4×C109—22no—
232C2×D4×C109—22no—
233C2×D4×C109—21no—
234C2×D4×C109—21no—
235C2×D4×C109—21no—
236C2×D4×C109—21no—
237C2×D4×C109—21no—
238C2×D4×C109—22no—
239C2×D4×C109—22no—
240C2×D4×C109—22no—
241C2×D4×C109—21no—
242C2×D4×C109—22no—
243C2×D4×C109—21no—
244C2×D4×C109—21no—
245C2×D4×C109—21no—
246C2×D4×C109—21no—
247C2×D4×C109—21no—
248C2×D4×C109—21no—
249C2×D4×C109—21no—
250C2×D4×C109—41no—
251C2×D4×C109—42no—
252C2×D4×C109—42no—
253C2×D4×C109—42no—
254C2×D4×C109—42no—
255C2×D4×C109—44no—
256C2×D4×C109—44no—
257C2×D4×C109—42no—
258C2×D4×C109—42no—
259C2×D4×C109—82no—
260C2×D4×C109—84no—
261C2×D4×C109C2×D411yescharacteristic
262C2×D4×C109C2×D411yescharacteristic
263C2×D4×C109C2×D411yescharacteristic
264C22×C4×C109—21no—
265C22×C4×C109—21no—
266C22×C4×C109—21no—
267C22×C4×C109—21no—
268C22×C4×C109—21no—
269C22×C4×C109—22no—
270C22×C4×C109—21no—
271C22×C4×C109—21no—
272C22×C4×C109—22no—
273C22×C4×C109—21no—
274C22×C4×C109—21no—
275C22×C4×C109—21no—
276C22×C4×C109—21no—
277C22×C4×C109—21no—
278C22×C4×C109—21no—
279C22×C4×C109—21no—
280C22×C4×C109—42no—
281C22×C4×C109—42no—
282C22×C4×C109C2×D411yescharacteristic
283C22×C4×C109C2×D411yescharacteristic
284C22×C4×C109C2×D411yescharacteristic
285C22×C4×C109C2×D411yescharacteristic
286C22×C4×C109C2×D411yescharacteristic
287C22×C4×C109C2×D412yes—
288C22×C4×C109C2411yescharacteristic
289M16×C109—21no—
290M16×C109—21no—
291M16×C109—21no—
292M16×C109—21no—
293M16×C109—21no—
294M16×C109—21no—
295M16×C109—21no—
296M16×C109—21no—
297M16×C109—42no—
298C2×C8×C109—21no—
299C2×C8×C109—21no—
300C2×C8×C109—21no—
301C2×C8×C109—21no—
302C2×C8×C109—42no—
303C4⋊C4×C109—22no—
304C4⋊C4×C109—22no—
305C4⋊C4×C109—21no—
306C4⋊C4×C109—21no—
307C4⋊C4×C109—21no—
308C4⋊C4×C109—21no—
309C4⋊C4×C109—21no—
310C4⋊C4×C109—21no—
311C4⋊C4×C109—21no—
312C4⋊C4×C109—21no—
313C4⋊C4×C109—82no—
314C4⋊C4×C109C2×D411yescharacteristic
315C4⋊C4×C109C2×D411yescharacteristic
316C22⋊C4×C109—22no—
317C22⋊C4×C109—22no—
318C22⋊C4×C109—22no—
319C22⋊C4×C109—22no—
320C22⋊C4×C109—22no—
321C22⋊C4×C109—21no—
322C22⋊C4×C109—21no—
323C22⋊C4×C109—21no—
324C22⋊C4×C109—21no—
325C22⋊C4×C109—22no—
326C22⋊C4×C109—22no—
327C22⋊C4×C109—21no—
328C22⋊C4×C109—42no—
329C22⋊C4×C109—44no—
330C22⋊C4×C109—41no—
331C22⋊C4×C109—41no—
332C22⋊C4×C109—82no—
333C42×C109—22no—
334C42×C109—21no—
335C42×C109—21no—
336C42×C109—21no—
337C42×C109—21no—
338C42×C109—21no—
339C42×C109—41no—
340C42×C109—41no—
341C23×C109—21no—
342C23×C109—21no—
343C23×C109—21no—
344C23×C109—22no—
345C23×C109—21no—
346C23×C109—21no—
347C23×C109—22no—
348C23×C109—22no—
349C23×C109—41no—
350C23×C109—41no—
351C23×C109—42no—
352C23×C109—42no—
353C23×C109—44no—
354C23×C109—42no—
355C23×C109—42no—
356C23×C109—81no—
357C23×C109—82no—
358C23×C109—82no—
359C23×C109#12011yescharacteristic
360C23×C109#12011yescharacteristic
361C23×C109C22×D411yescharacteristic
362Q8×C109—21no—
363Q8×C109—21no—
364Q8×C109—21no—
365Q8×C109—21no—
366Q8×C109—21no—
367Q8×C109—42no—
368Q8×C109#12312yes—
369D4×C109—22no—
370D4×C109—22no—
371D4×C109—21no—
372D4×C109—21no—
373D4×C109—21no—
374D4×C109—21no—
375D4×C109—21no—
376D4×C109—42no—
377D4×C109—42no—
378D4×C109—44no—
379D4×C109—42no—
380D4×C109—44no—
381D4×C109—44no—
382D4×C109—42no—
383D4×C109—41no—
384D4×C109—41no—
385D4×C109—41no—
386D4×C109—41no—
387D4×C109—41no—
388D4×C109—41no—
389D4×C109—41no—
390D4×C109—41no—
391D4×C109—81no—
392D4×C109—82no—
393D4×C109—82no—
394D4×C109—82no—
395D4×C109—82no—
396D4×C109#12312yes—
397C2×C4×C109—21no—
398C2×C4×C109—21no—
399C2×C4×C109—21no—
400C2×C4×C109—21no—
401C2×C4×C109—21no—
402C2×C4×C109—21no—
403C2×C4×C109—21no—
404C2×C4×C109—21no—
405C2×C4×C109—21no—
406C2×C4×C109—21no—
407C2×C4×C109—21no—
408C2×C4×C109—22no—
409C2×C4×C109—22no—
410C2×C4×C109—22no—
411C2×C4×C109—21no—
412C2×C4×C109—22no—
413C2×C4×C109—21no—
414C2×C4×C109—21no—
415C2×C4×C109—21no—
416C2×C4×C109—42no—
417C2×C4×C109—42no—
418C2×C4×C109—42no—
419C2×C4×C109—44no—
420C2×C4×C109—41no—
421C2×C4×C109—41no—
422C2×C4×C109—41no—
423C2×C4×C109—41no—
424C2×C4×C109—41no—
425C2×C4×C109—41no—
426C2×C4×C109—42no—
427C2×C4×C109—41no—
428C2×C4×C109—42no—
429C2×C4×C109—41no—
430C2×C4×C109—42no—
431C2×C4×C109—41no—
432C2×C4×C109—41no—
433C2×C4×C109—41no—
434C2×C4×C109—82no—
435C2×C4×C109#12011yescharacteristic
436C2×C4×C109#12011yescharacteristic
437C2×C4×C109C22×D411yescharacteristic
438C2×C4×C109C22×D411yescharacteristic
439C2×C4×C109C2×#4111yescharacteristic
440C2×C4×C109C2×#4111yescharacteristic
441C2×C4×C109H(5,𝔽2)11yescharacteristic
442C2×C4×C109H(5,𝔽2)11yescharacteristic
443C8×C109—41no—
444C8×C109—41no—
445C8×C109—41no—
446C8×C109—41no—
447C22×C109—21no—
448C22×C109—21no—
449C22×C109—21no—
450C22×C109—21no—
451C22×C109—22no—
452C22×C109—21no—
453C22×C109—21no—
454C22×C109—21no—
455C22×C109—21no—
456C22×C109—41no—
457C22×C109—41no—
458C22×C109—41no—
459C22×C109—41no—
460C22×C109—42no—
461C22×C109—41no—
462C22×C109—42no—
463C22×C109—41no—
464C22×C109—42no—
465C22×C109—41no—
466C22×C109—41no—
467C22×C109—81no—
468C22×C109—81no—
469C22×C109—82no—
470C22×C109—82no—
471C22×C109—84no—
472C22×C109—164no—
473C22×C109C2×#12011yescharacteristic
474C22×C109#54611yescharacteristic
475C22×C109#54611yescharacteristic
476C4×C109—21no—
477C4×C109—21no—
478C4×C109—22no—
479C4×C109—42no—
480C4×C109—41no—
481C4×C109—41no—
482C4×C109—41no—
483C4×C109—42no—
484C4×C109—41no—
485C4×C109—81no—
486C4×C109—81no—
487C4×C109—81no—
488C4×C109C2×#12311yescharacteristic
489C4×C109#53411yescharacteristic
490C4×C109#54611yescharacteristic
491C4×C109#54611yescharacteristic
492#24031C10911yesmaximal, characteristic, direct product factor, Sylow
493C2×C109—21no—
494C2×C109—21no—
495C2×C109—41no—
496C2×C109—41no—
497C2×C109—42no—
498C2×C109—81no—
499C2×C109—82no—
500C2×C109—81no—
501C2×C109#240511yescharacteristic
502C2×C109#301811yescharacteristic
503C2×C109#301911yescharacteristic
504#3488C2×C10911yescharacteristic
505#3093C2×C10911yescharacteristic, complemented
506#2896C2×C10911yescharacteristic, complemented
507#2500C2×C10911yescharacteristic, complemented
508#2040C2×C10911yescharacteristic, complemented
509#2039C2×C10911yescharacteristic, complemented
510#2037C2×C10911yescharacteristic, complemented
511#2037C2×C10911yescharacteristic, complemented
512#1900C2×C10911yescharacteristic, complemented
513#1871C2×C10911yescharacteristic, complemented
514#1860C2×C10911yescharacteristic, complemented
515#1859C2×C10911yescharacteristic, complemented
516#1792C2×C10911yescharacteristic, complemented
517#1792C2×C10911yescharacteristic, complemented
518#1789C2×C10911yescharacteristic, complemented
519C109#2403111yescharacteristic, direct product factor, Sylow
520C2×H(5,𝔽2)C22×C10911yescharacteristic
521C22×#41C22×C10911yescharacteristic
522C22×M16C22×C10911yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C10911yescharacteristic
531#535—21no—
532#535C22×C10911yescharacteristic
533#525—21no—
534#525C22×C10911yescharacteristic
535C2×#121—21no—
536C2×#121C22×C10911yescharacteristic
537#520C22×C10911yescharacteristic
538C2×#117C22×C10911yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C10911yescharacteristic, complemented
544#428C22×C10911yescharacteristic, complemented
545C2×#104C22×C10911yescharacteristic
546C2×#104C22×C10911yescharacteristic
547C2×#104C22×C10911yescharacteristic, complemented
548C2×#104C22×C10911yescharacteristic, complemented
549C2×#104C22×C10911yescharacteristic, complemented
550C2×#104C22×C10911yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C10911yescharacteristic
554#417C22×C10911yescharacteristic
555#417C22×C10911yescharacteristic, complemented
556#417C22×C10911yescharacteristic, complemented
557#417C22×C10911yescharacteristic, complemented
558#417C22×C10911yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C10911yescharacteristic, complemented
562C2×#100C22×C10911yescharacteristic, complemented
563#407C22×C10911yescharacteristic, complemented
564#394—22no—
565#390C22×C10911yescharacteristic, complemented
566#390C22×C10911yescharacteristic, complemented
567#388—22no—
568#384C22×C10911yescharacteristic, complemented
569#382C22×C10911yescharacteristic, complemented
570C4×C22⋊C4C22×C10911yescharacteristic, complemented
571#343C22×C10911yescharacteristic, complemented
572#343C22×C10911yescharacteristic, complemented
573#339C22×C10911yescharacteristic, complemented
574#339C22×C10911yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C10911yescharacteristic
588C2×#41D4×C10911yescharacteristic
589C2×#41C23×C10911yescharacteristic
590C2×#41C23×C10911yescharacteristic
591C2×#41C23×C10911yescharacteristic
592C22×Q8D4×C10911yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C10911yescharacteristic
599C22×D4D4×C10912yes—
600C22×D4C23×C10911yescharacteristic
601C23×C4—21no—
602C23×C4C23×C10911yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C10911yescharacteristic
607C2×M16C23×C10911yescharacteristic
608C2×M16C23×C10911yescharacteristic
609C2×M16C23×C10911yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C10911yescharacteristic
621C22⋊Q8D4×C10911yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C10911yescharacteristic
637#121D4×C10911yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C10911yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C10911yescharacteristic
659C2×C4⋊C4C23×C10911yescharacteristic
660C2×C4⋊C4C23×C10911yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C10912yes—
667C2×C42—21no—
668C2×C42C23×C10911yescharacteristic
669C2×C42C23×C10911yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C10912yes—
701C24C2×D4×C10911yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C10912yes—
725#41#41×C10912yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C10911yescharacteristic
730C2×Q8C2×D4×C10911yescharacteristic
731C2×Q8C2×D4×C10911yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C10911yescharacteristic
766C2×D4C2×D4×C10911yescharacteristic
767C2×D4C2×D4×C10911yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C10911yescharacteristic
787C22×C4C2×D4×C10911yescharacteristic
788C22×C4C2×D4×C10911yescharacteristic
789C22×C4C2×D4×C10911yescharacteristic
790C22×C4C2×D4×C10911yescharacteristic
791C22×C4C2×D4×C10912yes—
792C22×C4C24×C10911yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C10911yescharacteristic
819C4⋊C4C2×D4×C10911yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C10911yescharacteristic
864C23#120×C10911yescharacteristic
865C23C22×D4×C10911yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C10912yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C10912yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C10911yescharacteristic
940C2×C4#120×C10911yescharacteristic
941C2×C4C22×D4×C10911yescharacteristic
942C2×C4C22×D4×C10911yescharacteristic
943C2×C4C2×#41×C10911yescharacteristic
944C2×C4C2×#41×C10911yescharacteristic
945C2×C4H(5,𝔽2)×C10911yescharacteristic
946C2×C4H(5,𝔽2)×C10911yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C10911yescharacteristic
978C22#546×C10911yescharacteristic
979C22#546×C10911yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—42no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C10911yescharacteristic
993C4#534×C10911yescharacteristic
994C4#546×C10911yescharacteristic
995C4#546×C10911yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C109×#240511yescharacteristic
1005C2C109×#301811yescharacteristic
1006C2C109×#301911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#3093C2semidirect
3. C109×#2896C2semidirect
4. C109×#2500C2semidirect
5. C109×#2040C2semidirect
6. C109×#2039C2semidirect
7. C109×#2037C2semidirect
8. C109×#2037C2semidirect
9. C109×#1900C2semidirect
10. C109×#1871C2semidirect
11. C109×#1860C2semidirect
12. C109×#1859C2semidirect
13. C109×#1792C2semidirect
14. C109×#1792C2semidirect
15. C109×#1789C2semidirect
18. C22×M16×C109C22semidirect
34. C2×#117×C109C22semidirect
39. #428×C109C22semidirect
40. #428×C109C22semidirect
43. C2×#104×C109C22semidirect
44. C2×#104×C109C22semidirect
45. C2×#104×C109C22semidirect
46. C2×#104×C109C22semidirect
51. #417×C109C22semidirect
52. #417×C109C22semidirect
53. #417×C109C22semidirect
54. #417×C109C22semidirect
57. C2×#100×C109C22semidirect
58. C2×#100×C109C22semidirect
59. #407×C109C22semidirect
61. #390×C109C22semidirect
62. #390×C109C22semidirect
64. #384×C109C22semidirect
65. #382×C109C22semidirect
66. C4×C22⋊C4×C109C22semidirect
67. #343×C109C22semidirect
68. #343×C109C22semidirect
69. #339×C109C22semidirect
70. #339×C109C22semidirect
492. #24031C109direct (N × H)
505. #3093C2×C109semidirect
506. #2896C2×C109semidirect
507. #2500C2×C109semidirect
508. #2040C2×C109semidirect
509. #2039C2×C109semidirect
510. #2037C2×C109semidirect
511. #2037C2×C109semidirect
512. #1900C2×C109semidirect
513. #1871C2×C109semidirect
514. #1860C2×C109semidirect
515. #1859C2×C109semidirect
516. #1792C2×C109semidirect
517. #1792C2×C109semidirect
518. #1789C2×C109semidirect
519. C109#24031direct (N × H)
522. C22×M16C22×C109semidirect
538. C2×#117C22×C109semidirect
543. #428C22×C109semidirect
544. #428C22×C109semidirect
547. C2×#104C22×C109semidirect
548. C2×#104C22×C109semidirect
549. C2×#104C22×C109semidirect
550. C2×#104C22×C109semidirect
555. #417C22×C109semidirect
556. #417C22×C109semidirect
557. #417C22×C109semidirect
558. #417C22×C109semidirect
561. C2×#100C22×C109semidirect
562. C2×#100C22×C109semidirect
563. #407C22×C109semidirect
565. #390C22×C109semidirect
566. #390C22×C109semidirect
568. #384C22×C109semidirect
569. #382C22×C109semidirect
570. C4×C22⋊C4C22×C109semidirect
571. #343C22×C109semidirect
572. #343C22×C109semidirect
573. #339C22×C109semidirect
574. #339C22×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#34882
C109×#30932
C109×#28962
C109×#25002
C109×#20402
C109×#20392
C109×#20372
C109×#19002
C109×#18712
C109×#18602
C109×#18592
C109×#17922
C109×#17892
#24031109