Finite Group Databasebeta

← C109×#18416 #42136410

Subgroups — C109×#18416 #42136410

Order 27904.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3535C211yesmaximal, characteristic, complemented
2C109×#3194C211yesmaximal, characteristic, complemented
3C109×#3187C211yesmaximal, characteristic, complemented
4C109×#2661C211yesmaximal, characteristic, complemented
5C109×#1612C211yesmaximal, characteristic, complemented
6C109×#1611C211yesmaximal, characteristic, complemented
7C109×#1609C211yesmaximal, characteristic, complemented
8C109×#1608C211yesmaximal, characteristic, complemented
9C109×#1600C211yesmaximal, characteristic, complemented
10C109×#1599C211yesmaximal, characteristic, complemented
11C109×#1597C211yesmaximal, characteristic, complemented
12C109×#1596C211yesmaximal, characteristic, complemented
13C109×#1508C211yesmaximal, characteristic, complemented
14C109×#1501C211yesmaximal, characteristic, complemented
15C109×#1468C211yesmaximal, characteristic, complemented
16#563×C109—21no—
17#562×C109—21no—
18#554×C109—21no—
19#552×C109—21no—
20#551×C109—21no—
21#551×C109—21no—
22#547×C109—21no—
23#546×C109—21no—
24#544×C109C2211yescharacteristic
25#543×C109C2211yescharacteristic
26#542×C109—21no—
27#539×C109—21no—
28#539×C109—21no—
29#539×C109C2211yescharacteristic
30#538×C109C2211yescharacteristic
31#536×C109—21no—
32#525×C109C2211yescharacteristic
33C2×#123×C109C2211yescharacteristic
34C2×C22⋊Q8×C109C2211yescharacteristic
35C2×#121×C109C2211yescharacteristic
36#483×C109C2211yescharacteristic
37#483×C109C2211yescharacteristic
38#483×C109C2211yescharacteristic
39#482×C109—21no—
40#481×C109—21no—
41#480×C109C2211yescharacteristic
42#469×C109—21no—
43#468×C109—21no—
44#465×C109—21no—
45#465×C109—21no—
46#450×C109C2211yescharacteristic
47#450×C109C2211yescharacteristic
48#450×C109C2211yescharacteristic
49#449×C109—21no—
50#448×C109—21no—
51#447×C109C2211yescharacteristic
52#407×C109C2211yescharacteristic
53C2×C22⋊C8×C109C2211yescharacteristic
54#398×C109C2211yescharacteristic
55#397×C109C2211yescharacteristic
56#394×C109—21no—
57#394×C109C2211yescharacteristic
58#392×C109—21no—
59#392×C109C2211yescharacteristic
60#390×C109—21no—
61#388×C109—21no—
62C4×C22⋊C4×C109C2211yescharacteristic
63#328×C109C2211yescharacteristic
64#328×C109C2211yescharacteristic
65#328×C109C2211yescharacteristic
66#328×C109C2211yescharacteristic
67#328×C109C2211yescharacteristic
68#328×C109C2211yescharacteristic
69#327×C109C2211yescharacteristic
70#327×C109C2211yescharacteristic
71#324×C109C2211yescharacteristic
72#324×C109C2211yescharacteristic
73#323×C109C2211yescharacteristic
74#323×C109C2211yescharacteristic
75C2×#41×C109—21no—
76C2×#41×C109D411yescharacteristic, complemented
77C22×Q8×C109D411yescharacteristic, complemented
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109D411yescharacteristic
81C22×D4×C109C2311yescharacteristic
82C23×C4×C109C2311yescharacteristic
83C2×SD16×C109—21no—
84C2×SD16×C109—21no—
85C2×SD16×C109—21no—
86C2×D8×C109—21no—
87C2×M16×C109—21no—
88C22×C8×C109—21no—
89C4⋊Q8×C109—21no—
90C4⋊Q8×C109—21no—
91C4⋊Q8×C109—21no—
92#126×C109—21no—
93#126×C109—21no—
94#126×C109—21no—
95#126×C109—21no—
96#126×C109—21no—
97#126×C109—21no—
98#125×C109—21no—
99#125×C109—21no—
100#125×C109—21no—
101#125×C109—21no—
102#125×C109—21no—
103#124×C109—21no—
104#124×C109—21no—
105#124×C109—21no—
106#124×C109—21no—
107#123×C109—21no—
108#123×C109—21no—
109#123×C109—21no—
110#123×C109—21no—
111#123×C109—21no—
112#123×C109—21no—
113#123×C109—21no—
114#123×C109—21no—
115#123×C109—21no—
116#123×C109—21no—
117#123×C109—21no—
118#123×C109—21no—
119#123×C109—21no—
120#123×C109—21no—
121C22⋊Q8×C109—21no—
122C22⋊Q8×C109—21no—
123C22⋊Q8×C109—21no—
124C22⋊Q8×C109—21no—
125C22⋊Q8×C109—21no—
126C22⋊Q8×C109—21no—
127C22⋊Q8×C109—21no—
128C22⋊Q8×C109—21no—
129C22⋊Q8×C109—21no—
130C22⋊Q8×C109—21no—
131C22⋊Q8×C109—21no—
132C22⋊Q8×C109—21no—
133C22⋊Q8×C109—21no—
134C22⋊Q8×C109—21no—
135C22⋊Q8×C109D411yescharacteristic, complemented
136C22⋊Q8×C109D411yescharacteristic, complemented
137C22⋊Q8×C109D411yescharacteristic, complemented
138C22⋊Q8×C109C2311yescharacteristic
139C22⋊Q8×C109C2311yescharacteristic
140C22⋊Q8×C109C2311yescharacteristic
141#121×C109—21no—
142#121×C109—21no—
143#121×C109—21no—
144#121×C109—21no—
145#121×C109—21no—
146#121×C109—21no—
147#121×C109—21no—
148#121×C109—21no—
149#121×C109D411yescharacteristic, complemented
150#121×C109C2311yescharacteristic
151#120×C109—21no—
152#120×C109—21no—
153C4×Q8×C109—21no—
154C4×D4×C109—21no—
155C4×D4×C109—21no—
156C4×D4×C109—21no—
157C4×D4×C109—21no—
158C4×D4×C109—21no—
159C4×D4×C109—21no—
160C4×D4×C109—21no—
161#117×C109—21no—
162#117×C109—21no—
163#117×C109—21no—
164#117×C109D411yescharacteristic, complemented
165C2×C4⋊C4×C109—21no—
166C2×C4⋊C4×C109—21no—
167C2×C4⋊C4×C109—21no—
168C2×C4⋊C4×C109D411yescharacteristic
169C2×C4⋊C4×C109D411yescharacteristic, complemented
170C2×C4⋊C4×C109C2311yescharacteristic
171C2×C4⋊C4×C109C2311yescharacteristic
172C2×C22⋊C4×C109—21no—
173C2×C22⋊C4×C109—21no—
174C2×C22⋊C4×C109—21no—
175C2×C22⋊C4×C109—21no—
176C2×C22⋊C4×C109—21no—
177C2×C22⋊C4×C109—21no—
178C2×C22⋊C4×C109—21no—
179C2×C22⋊C4×C109—21no—
180C2×C22⋊C4×C109D411yescharacteristic
181C2×C22⋊C4×C109D411yescharacteristic
182C2×C22⋊C4×C109C2311yescharacteristic
183C2×C42×C109—21no—
184#107×C109—21no—
185#106×C109—21no—
186#106×C109—21no—
187#106×C109—21no—
188#103×C109—21no—
189#103×C109—21no—
190#103×C109—21no—
191#102×C109—21no—
192#102×C109—21no—
193#102×C109—21no—
194#102×C109—21no—
195#102×C109—21no—
196C22⋊C8×C109—21no—
197C22⋊C8×C109—21no—
198C22⋊C8×C109C2311yescharacteristic
199C22⋊C8×C109C2311yescharacteristic
200C22⋊C8×C109C2311yescharacteristic
201C22⋊C8×C109C2311yescharacteristic
202#95×C109—21no—
203#95×C109—21no—
204#95×C109C2311yescharacteristic
205#95×C109C2311yescharacteristic
206C24×C109—21no—
207C24×C109C2×D411yescharacteristic
208C24×C109C2×D411yescharacteristic
209#41×C109—82no—
210#41×C109—81no—
211C2×Q8×C109—21no—
212C2×Q8×C109—21no—
213C2×Q8×C109—21no—
214C2×Q8×C109—81no—
215C2×Q8×C109C2×D411yescharacteristic
216C2×Q8×C109C2×D411yescharacteristic
217C2×Q8×C109C2×D411yescharacteristic
218C2×D4×C109—21no—
219C2×D4×C109—21no—
220C2×D4×C109—21no—
221C2×D4×C109—21no—
222C2×D4×C109—21no—
223C2×D4×C109—21no—
224C2×D4×C109—21no—
225C2×D4×C109—21no—
226C2×D4×C109—21no—
227C2×D4×C109—42no—
228C2×D4×C109—41no—
229C2×D4×C109—41no—
230C2×D4×C109—81no—
231C2×D4×C109—81no—
232C2×D4×C109—81no—
233C2×D4×C109—81no—
234C2×D4×C109—81no—
235C2×D4×C109—81no—
236C2×D4×C109C2×D411yescharacteristic
237C22×C4×C109—21no—
238C22×C4×C109—21no—
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
245C22×C4×C109—21no—
246C22×C4×C109—21no—
247C22×C4×C109—81no—
248C22×C4×C109C2×D411yescharacteristic
249C22×C4×C109C2×D411yescharacteristic
250C22×C4×C109C2×D411yescharacteristic
251C22×C4×C109C2×D411yescharacteristic
252C22×C4×C109C2×D411yescharacteristic
253C22×C4×C109C2×D411yescharacteristic
254C22×C4×C109C2×D411yescharacteristic
255C22×C4×C109C2×D411yescharacteristic
256C22×C4×C109C2411yescharacteristic
257SD16×C109—81no—
258SD16×C109—81no—
259SD16×C109—81no—
260D8×C109—81no—
261M16×C109—81no—
262C2×C8×C109—21no—
263C2×C8×C109—21no—
264C2×C8×C109—21no—
265C2×C8×C109—21no—
266C2×C8×C109—81no—
267C4⋊C4×C109—21no—
268C4⋊C4×C109—21no—
269C4⋊C4×C109—21no—
270C4⋊C4×C109—21no—
271C4⋊C4×C109—21no—
272C4⋊C4×C109—21no—
273C4⋊C4×C109—21no—
274C4⋊C4×C109—21no—
275C4⋊C4×C109—21no—
276C4⋊C4×C109—21no—
277C4⋊C4×C109—21no—
278C4⋊C4×C109—21no—
279C4⋊C4×C109—21no—
280C4⋊C4×C109—21no—
281C4⋊C4×C109—21no—
282C4⋊C4×C109—21no—
283C4⋊C4×C109—21no—
284C4⋊C4×C109—21no—
285C4⋊C4×C109—21no—
286C4⋊C4×C109—21no—
287C4⋊C4×C109—21no—
288C4⋊C4×C109—21no—
289C4⋊C4×C109—21no—
290C4⋊C4×C109—21no—
291C4⋊C4×C109—21no—
292C4⋊C4×C109—81no—
293C4⋊C4×C109C2×D411yescharacteristic
294C4⋊C4×C109C2×D411yescharacteristic
295C4⋊C4×C109C2×D411yescharacteristic
296C4⋊C4×C109C2×D411yescharacteristic
297C22⋊C4×C109—21no—
298C22⋊C4×C109—21no—
299C22⋊C4×C109—21no—
300C22⋊C4×C109—21no—
301C22⋊C4×C109—21no—
302C22⋊C4×C109—21no—
303C22⋊C4×C109—21no—
304C22⋊C4×C109—21no—
305C22⋊C4×C109—21no—
306C22⋊C4×C109—21no—
307C22⋊C4×C109—21no—
308C22⋊C4×C109—21no—
309C22⋊C4×C109—21no—
310C22⋊C4×C109—21no—
311C22⋊C4×C109—21no—
312C22⋊C4×C109—21no—
313C22⋊C4×C109—21no—
314C22⋊C4×C109—21no—
315C22⋊C4×C109—21no—
316C22⋊C4×C109—21no—
317C22⋊C4×C109—21no—
318C22⋊C4×C109—21no—
319C22⋊C4×C109—21no—
320C22⋊C4×C109—42no—
321C22⋊C4×C109—42no—
322C22⋊C4×C109—41no—
323C22⋊C4×C109—41no—
324C22⋊C4×C109—81no—
325C22⋊C4×C109—81no—
326C22⋊C4×C109—81no—
327C42×C109—21no—
328C42×C109—21no—
329C42×C109—21no—
330C42×C109—21no—
331C42×C109—21no—
332C42×C109—81no—
333C23×C109—21no—
334C23×C109—21no—
335C23×C109—21no—
336C23×C109—21no—
337C23×C109—21no—
338C23×C109—21no—
339C23×C109—41no—
340C23×C109—41no—
341C23×C109—41no—
342C23×C109—41no—
343C23×C109—41no—
344C23×C109—41no—
345C23×C109—41no—
346C23×C109—41no—
347C23×C109—41no—
348C23×C109—41no—
349C23×C109—41no—
350C23×C109#12011yescharacteristic
351C23×C109#12011yescharacteristic
352C23×C109C22×D411yescharacteristic
353Q8×C109—41no—
354Q8×C109—41no—
355Q8×C109—41no—
356Q8×C109—81no—
357Q8×C109—81no—
358Q8×C109—81no—
359D4×C109—41no—
360D4×C109—41no—
361D4×C109—41no—
362D4×C109—41no—
363D4×C109—41no—
364D4×C109—42no—
365D4×C109—42no—
366D4×C109—41no—
367D4×C109—41no—
368D4×C109—81no—
369D4×C109—81no—
370D4×C109—81no—
371D4×C109—81no—
372D4×C109—84no—
373D4×C109—82no—
374D4×C109—82no—
375C2×C4×C109—22no—
376C2×C4×C109—21no—
377C2×C4×C109—21no—
378C2×C4×C109—21no—
379C2×C4×C109—21no—
380C2×C4×C109—21no—
381C2×C4×C109—21no—
382C2×C4×C109—21no—
383C2×C4×C109—21no—
384C2×C4×C109—21no—
385C2×C4×C109—21no—
386C2×C4×C109—21no—
387C2×C4×C109—21no—
388C2×C4×C109—41no—
389C2×C4×C109—41no—
390C2×C4×C109—41no—
391C2×C4×C109—41no—
392C2×C4×C109—41no—
393C2×C4×C109—41no—
394C2×C4×C109—41no—
395C2×C4×C109—42no—
396C2×C4×C109—41no—
397C2×C4×C109—41no—
398C2×C4×C109—41no—
399C2×C4×C109—41no—
400C2×C4×C109—41no—
401C2×C4×C109—41no—
402C2×C4×C109—41no—
403C2×C4×C109—41no—
404C2×C4×C109—41no—
405C2×C4×C109—81no—
406C2×C4×C109—81no—
407C2×C4×C109—81no—
408C2×C4×C109—81no—
409C2×C4×C109—81no—
410C2×C4×C109—81no—
411C2×C4×C109#12011yescharacteristic
412C2×C4×C109#12011yescharacteristic
413C2×C4×C109C22×D411yescharacteristic
414C2×C4×C109C22×D411yescharacteristic
415C8×C109—41no—
416C8×C109—41no—
417C8×C109—41no—
418C8×C109—41no—
419C22×C109—21no—
420C22×C109—21no—
421C22×C109—21no—
422C22×C109—21no—
423C22×C109—21no—
424C22×C109—21no—
425C22×C109—21no—
426C22×C109—21no—
427C22×C109—41no—
428C22×C109—41no—
429C22×C109—41no—
430C22×C109—41no—
431C22×C109—41no—
432C22×C109—41no—
433C22×C109—81no—
434C22×C109—81no—
435C22×C109—81no—
436C22×C109—81no—
437C22×C109—81no—
438C22×C109—81no—
439C22×C109—81no—
440C22×C109—81no—
441C22×C109—81no—
442C22×C109—81no—
443C22×C109—81no—
444C22×C109C2×#12011yescharacteristic
445C22×C109#57711yescharacteristic
446C22×C109#57711yescharacteristic
447C4×C109—21no—
448C4×C109—21no—
449C4×C109—21no—
450C4×C109—21no—
451C4×C109—42no—
452C4×C109—41no—
453C4×C109—41no—
454C4×C109—41no—
455C4×C109—41no—
456C4×C109—41no—
457C4×C109—41no—
458C4×C109—41no—
459C4×C109—41no—
460C4×C109—41no—
461C4×C109—41no—
462C4×C109—81no—
463C4×C109—81no—
464#18416C10911yesmaximal, characteristic, direct product factor, Sylow
465C2×C109—21no—
466C2×C109—21no—
467C2×C109—41no—
468C2×C109—41no—
469C2×C109—81no—
470C2×C109—81no—
471C2×C109—161no—
472C2×C109#301011yescharacteristic
473C2×C109#301811yescharacteristic
474C2×C109#302611yescharacteristic
475#3535C2×C10911yescharacteristic, complemented
476#3194C2×C10911yescharacteristic, complemented
477#3187C2×C10911yescharacteristic, complemented
478#2661C2×C10911yescharacteristic, complemented
479#1612C2×C10911yescharacteristic, complemented
480#1611C2×C10911yescharacteristic, complemented
481#1609C2×C10911yescharacteristic, complemented
482#1608C2×C10911yescharacteristic, complemented
483#1600C2×C10911yescharacteristic, complemented
484#1599C2×C10911yescharacteristic, complemented
485#1597C2×C10911yescharacteristic, complemented
486#1596C2×C10911yescharacteristic, complemented
487#1508C2×C10911yescharacteristic, complemented
488#1501C2×C10911yescharacteristic, complemented
489#1468C2×C10911yescharacteristic, complemented
490C109#1841611yescharacteristic, direct product factor, Sylow
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C10911yescharacteristic
500#543C22×C10911yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C10911yescharacteristic
505#538C22×C10911yescharacteristic
506#536—21no—
507#525C22×C10911yescharacteristic
508C2×#123C22×C10911yescharacteristic
509C2×C22⋊Q8C22×C10911yescharacteristic
510C2×#121C22×C10911yescharacteristic
511#483C22×C10911yescharacteristic
512#483C22×C10911yescharacteristic
513#483C22×C10911yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C10911yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C10911yescharacteristic
522#450C22×C10911yescharacteristic
523#450C22×C10911yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C10911yescharacteristic
527#407C22×C10911yescharacteristic
528C2×C22⋊C8C22×C10911yescharacteristic
529#398C22×C10911yescharacteristic
530#397C22×C10911yescharacteristic
531#394—21no—
532#394C22×C10911yescharacteristic
533#392—21no—
534#392C22×C10911yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C10911yescharacteristic
538#328C22×C10911yescharacteristic
539#328C22×C10911yescharacteristic
540#328C22×C10911yescharacteristic
541#328C22×C10911yescharacteristic
542#328C22×C10911yescharacteristic
543#328C22×C10911yescharacteristic
544#327C22×C10911yescharacteristic
545#327C22×C10911yescharacteristic
546#324C22×C10911yescharacteristic
547#324C22×C10911yescharacteristic
548#323C22×C10911yescharacteristic
549#323C22×C10911yescharacteristic
550C2×#41—21no—
551C2×#41D4×C10911yescharacteristic, complemented
552C22×Q8D4×C10911yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C10911yescharacteristic
556C22×D4C23×C10911yescharacteristic
557C23×C4C23×C10911yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C10911yescharacteristic, complemented
611C22⋊Q8D4×C10911yescharacteristic, complemented
612C22⋊Q8D4×C10911yescharacteristic, complemented
613C22⋊Q8C23×C10911yescharacteristic
614C22⋊Q8C23×C10911yescharacteristic
615C22⋊Q8C23×C10911yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C10911yescharacteristic, complemented
625#121C23×C10911yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C10911yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C10911yescharacteristic
644C2×C4⋊C4D4×C10911yescharacteristic, complemented
645C2×C4⋊C4C23×C10911yescharacteristic
646C2×C4⋊C4C23×C10911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C10911yescharacteristic
656C2×C22⋊C4D4×C10911yescharacteristic
657C2×C22⋊C4C23×C10911yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C10911yescharacteristic
674C22⋊C8C23×C10911yescharacteristic
675C22⋊C8C23×C10911yescharacteristic
676C22⋊C8C23×C10911yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C10911yescharacteristic
680#95C23×C10911yescharacteristic
681C24—21no—
682C24C2×D4×C10911yescharacteristic
683C24C2×D4×C10911yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C10911yescharacteristic
691C2×Q8C2×D4×C10911yescharacteristic
692C2×Q8C2×D4×C10911yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C10911yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C10911yescharacteristic
724C22×C4C2×D4×C10911yescharacteristic
725C22×C4C2×D4×C10911yescharacteristic
726C22×C4C2×D4×C10911yescharacteristic
727C22×C4C2×D4×C10911yescharacteristic
728C22×C4C2×D4×C10911yescharacteristic
729C22×C4C2×D4×C10911yescharacteristic
730C22×C4C2×D4×C10911yescharacteristic
731C22×C4C24×C10911yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4C2×D4×C10911yescharacteristic
769C4⋊C4C2×D4×C10911yescharacteristic
770C4⋊C4C2×D4×C10911yescharacteristic
771C4⋊C4C2×D4×C10911yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C10911yescharacteristic
826C23#120×C10911yescharacteristic
827C23C22×D4×C10911yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C10911yescharacteristic
887C2×C4#120×C10911yescharacteristic
888C2×C4C22×D4×C10911yescharacteristic
889C2×C4C22×D4×C10911yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C10911yescharacteristic
920C22#577×C10911yescharacteristic
921C22#577×C10911yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C109×#301011yescharacteristic
947C2C109×#301811yescharacteristic
948C2C109×#302611yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3535C2semidirect
2. C109×#3194C2semidirect
3. C109×#3187C2semidirect
4. C109×#2661C2semidirect
5. C109×#1612C2semidirect
6. C109×#1611C2semidirect
7. C109×#1609C2semidirect
8. C109×#1608C2semidirect
9. C109×#1600C2semidirect
10. C109×#1599C2semidirect
11. C109×#1597C2semidirect
12. C109×#1596C2semidirect
13. C109×#1508C2semidirect
14. C109×#1501C2semidirect
15. C109×#1468C2semidirect
76. C2×#41×C109D4semidirect
77. C22×Q8×C109D4semidirect
135. C22⋊Q8×C109D4semidirect
136. C22⋊Q8×C109D4semidirect
137. C22⋊Q8×C109D4semidirect
149. #121×C109D4semidirect
164. #117×C109D4semidirect
169. C2×C4⋊C4×C109D4semidirect
464. #18416C109direct (N × H)
475. #3535C2×C109semidirect
476. #3194C2×C109semidirect
477. #3187C2×C109semidirect
478. #2661C2×C109semidirect
479. #1612C2×C109semidirect
480. #1611C2×C109semidirect
481. #1609C2×C109semidirect
482. #1608C2×C109semidirect
483. #1600C2×C109semidirect
484. #1599C2×C109semidirect
485. #1597C2×C109semidirect
486. #1596C2×C109semidirect
487. #1508C2×C109semidirect
488. #1501C2×C109semidirect
489. #1468C2×C109semidirect
490. C109#18416direct (N × H)
551. C2×#41D4×C109semidirect
552. C22×Q8D4×C109semidirect
610. C22⋊Q8D4×C109semidirect
611. C22⋊Q8D4×C109semidirect
612. C22⋊Q8D4×C109semidirect
624. #121D4×C109semidirect
639. #117D4×C109semidirect
644. C2×C4⋊C4D4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35352
C109×#31942
C109×#31872
C109×#26612
C109×#16122
C109×#16112
C109×#16092
C109×#16082
C109×#16002
C109×#15992
C109×#15972
C109×#15962
C109×#15082
C109×#15012
C109×#14682
#18416109