Finite Group Databasebeta

← C109×#18447 #42136441

Subgroups — C109×#18447 #42136441

Order 27904.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3534C211yesmaximal, characteristic
2C109×#3193C211yesmaximal, characteristic, complemented
3C109×#3190C211yesmaximal, characteristic, complemented
4C109×#2814C211yesmaximal, characteristic, complemented
5C109×#1612C211yesmaximal, characteristic, complemented
6C109×#1610C211yesmaximal, characteristic, complemented
7C109×#1609C211yesmaximal, characteristic, complemented
8C109×#1607C211yesmaximal, characteristic, complemented
9C109×#1606C211yesmaximal, characteristic, complemented
10C109×#1604C211yesmaximal, characteristic, complemented
11C109×#1603C211yesmaximal, characteristic, complemented
12C109×#1601C211yesmaximal, characteristic, complemented
13C109×#1519C211yesmaximal, characteristic, complemented
14C109×#1513C211yesmaximal, characteristic, complemented
15C109×#1468C211yesmaximal, characteristic, complemented
16#562×C109—21no—
17#560×C109—21no—
18#553×C109—21no—
19#551×C109—21no—
20#546×C109—21no—
21#546×C109—21no—
22#546×C109—21no—
23D42×C109—21no—
24#540×C109—21no—
25#539×C109—21no—
26#539×C109C2211yescharacteristic
27#538×C109—21no—
28#538×C109C2211yescharacteristic
29#537×C109C2211yescharacteristic
30#534×C109—21no—
31#534×C109C2211yescharacteristic
32#525×C109C2211yescharacteristic
33C2×#123×C109C2211yescharacteristic
34C2×C22⋊Q8×C109C2211yescharacteristic, complemented
35C2×#121×C109C2211yescharacteristic
36#485×C109—21no—
37#484×C109—21no—
38#483×C109C2211yescharacteristic, complemented
39#480×C109C2211yescharacteristic
40#480×C109C2211yescharacteristic, complemented
41#480×C109C2211yescharacteristic, complemented
42#468×C109—21no—
43#468×C109—21no—
44#467×C109—21no—
45#465×C109—21no—
46#452×C109—21no—
47#451×C109C2211yescharacteristic, complemented
48#450×C109—21no—
49#448×C109C2211yescharacteristic
50#448×C109C2211yescharacteristic, complemented
51#448×C109C2211yescharacteristic, complemented
52#407×C109C2211yescharacteristic, complemented
53C2×C22⋊C8×C109C2211yescharacteristic, complemented
54#398×C109—21no—
55#398×C109C2211yescharacteristic, complemented
56#397×C109—21no—
57#397×C109C2211yescharacteristic, complemented
58#396×C109—21no—
59#395×C109C2211yescharacteristic, complemented
60#394×C109—21no—
61#393×C109C2211yescharacteristic, complemented
62#380×C109C2211yescharacteristic, complemented
63#328×C109C2211yescharacteristic, complemented
64#328×C109C2211yescharacteristic, complemented
65#327×C109C2211yescharacteristic
66#327×C109C2211yescharacteristic
67#327×C109C2211yescharacteristic, complemented
68#327×C109C2211yescharacteristic, complemented
69#327×C109C2211yescharacteristic, complemented
70#327×C109C2211yescharacteristic, complemented
71#324×C109C2211yescharacteristic, complemented
72#324×C109C2211yescharacteristic, complemented
73#323×C109C2211yescharacteristic, complemented
74#323×C109C2211yescharacteristic, complemented
75C2×#41×C109—21no—
76C2×#41×C109D411yescharacteristic
77C22×Q8×C109C2311yescharacteristic
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109D411yescharacteristic
82C22×D4×C109D411yescharacteristic
83C23×C4×C109C2311yescharacteristic
84C2×Q16×C109—21no—
85C2×SD16×C109—21no—
86C2×SD16×C109—21no—
87C2×SD16×C109—21no—
88C2×M16×C109—21no—
89C22×C8×C109—21no—
90#127×C109—21no—
91#126×C109—21no—
92#126×C109—21no—
93#126×C109—21no—
94#126×C109—21no—
95#125×C109—21no—
96#125×C109—21no—
97#124×C109—21no—
98#124×C109—21no—
99#124×C109—21no—
100#123×C109—21no—
101#123×C109—21no—
102#123×C109—21no—
103#123×C109—21no—
104#123×C109—21no—
105#123×C109—21no—
106#123×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—
114C22⋊Q8×C109—21no—
115C22⋊Q8×C109—21no—
116C22⋊Q8×C109—21no—
117C22⋊Q8×C109—21no—
118C22⋊Q8×C109—21no—
119C22⋊Q8×C109—21no—
120C22⋊Q8×C109—21no—
121C22⋊Q8×C109—21no—
122C22⋊Q8×C109—21no—
123C22⋊Q8×C109D411yescharacteristic
124C22⋊Q8×C109C2311yescharacteristic
125#121×C109—21no—
126#121×C109—21no—
127#121×C109—21no—
128#121×C109—21no—
129#121×C109—21no—
130#121×C109—21no—
131#121×C109—21no—
132#121×C109—21no—
133#121×C109—21no—
134#121×C109—21no—
135#121×C109—21no—
136#121×C109—21no—
137#121×C109—21no—
138#121×C109—21no—
139#121×C109—21no—
140#121×C109D411yescharacteristic
141#121×C109D411yescharacteristic
142#121×C109D411yescharacteristic
143#121×C109C2311yescharacteristic
144#121×C109C2311yescharacteristic
145#121×C109C2311yescharacteristic
146#120×C109—21no—
147#120×C109—21no—
148#120×C109—21no—
149#120×C109—21no—
150#120×C109—21no—
151#120×C109—21no—
152#120×C109—21no—
153#120×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—
161C4×D4×C109—21no—
162#117×C109—21no—
163#117×C109D411yescharacteristic
164C2×C4⋊C4×C109—21no—
165C2×C4⋊C4×C109—21no—
166C2×C4⋊C4×C109—21no—
167C2×C4⋊C4×C109—21no—
168C2×C4⋊C4×C109D411yescharacteristic
169C2×C4⋊C4×C109D411yescharacteristic
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×C109D411yescharacteristic
180C2×C22⋊C4×C109D411yescharacteristic
181C2×C22⋊C4×C109C2311yescharacteristic
182#107×C109—21no—
183#107×C109—21no—
184#107×C109—21no—
185#106×C109—21no—
186#103×C109—21no—
187#103×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—
194C22⋊C8×C109—21no—
195C22⋊C8×C109—21no—
196C22⋊C8×C109C2311yescharacteristic
197C22⋊C8×C109C2311yescharacteristic
198C22⋊C8×C109C2311yescharacteristic
199C22⋊C8×C109C2311yescharacteristic
200#95×C109—21no—
201#95×C109—21no—
202#95×C109—21no—
203#95×C109—21no—
204#95×C109C2311yescharacteristic
205#95×C109C2311yescharacteristic
206C24×C109—21no—
207C24×C109—21no—
208C24×C109C2×D411yescharacteristic
209C24×C109C2×D411yescharacteristic
210#41×C109—81no—
211#41×C109—81no—
212#41×C109—81no—
213C2×Q8×C109—21no—
214C2×Q8×C109—21no—
215C2×Q8×C109—21no—
216C2×Q8×C109—81no—
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—21no—
228C2×D4×C109—21no—
229C2×D4×C109—21no—
230C2×D4×C109—21no—
231C2×D4×C109—21no—
232C2×D4×C109—21no—
233C2×D4×C109—21no—
234C2×D4×C109—21no—
235C2×D4×C109—81no—
236C2×D4×C109—81no—
237C2×D4×C109—81no—
238C2×D4×C109—81no—
239C2×D4×C109—81no—
240C2×D4×C109—81no—
241C2×D4×C109—82no—
242C2×D4×C109C2×D411yescharacteristic
243C2×D4×C109C2×D411yescharacteristic
244C2×D4×C109C2×D411yescharacteristic
245C22×C4×C109—21no—
246C22×C4×C109—21no—
247C22×C4×C109—21no—
248C22×C4×C109—21no—
249C22×C4×C109—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109—21no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—81no—
257C22×C4×C109C2×D411yescharacteristic
258C22×C4×C109C2×D411yescharacteristic
259C22×C4×C109C2×D411yescharacteristic
260C22×C4×C109C2×D411yescharacteristic
261C22×C4×C109C2×D411yescharacteristic
262C22×C4×C109C2×D411yescharacteristic
263C22×C4×C109C2×D411yescharacteristic
264C22×C4×C109C2×D411yescharacteristic
265C22×C4×C109C2411yescharacteristic
266Q16×C109—81no—
267SD16×C109—81no—
268SD16×C109—81no—
269SD16×C109—81no—
270M16×C109—81no—
271C2×C8×C109—21no—
272C2×C8×C109—21no—
273C2×C8×C109—21no—
274C2×C8×C109—21no—
275C2×C8×C109—81no—
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—41no—
292C4⋊C4×C109—41no—
293C4⋊C4×C109—81no—
294C4⋊C4×C109—81no—
295C4⋊C4×C109—81no—
296C4⋊C4×C109C2×D411yescharacteristic
297C4⋊C4×C109C2×D411yescharacteristic
298C4⋊C4×C109C2×D411yescharacteristic
299C4⋊C4×C109C2×D411yescharacteristic
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—21no—
321C22⋊C4×C109—21no—
322C22⋊C4×C109—21no—
323C22⋊C4×C109—21no—
324C22⋊C4×C109—21no—
325C22⋊C4×C109—41no—
326C22⋊C4×C109—41no—
327C22⋊C4×C109—81no—
328C22⋊C4×C109—81no—
329C22⋊C4×C109—81no—
330C42×C109—21no—
331C42×C109—21no—
332C42×C109—21no—
333C23×C109—21no—
334C23×C109—21no—
335C23×C109—21no—
336C23×C109—21no—
337C23×C109—21no—
338C23×C109—21no—
339C23×C109—21no—
340C23×C109—21no—
341C23×C109—41no—
342C23×C109—41no—
343C23×C109—42no—
344C23×C109—41no—
345C23×C109—41no—
346C23×C109—81no—
347C23×C109—81no—
348C23×C109—81no—
349C23×C109—81no—
350C23×C109—81no—
351C23×C109#12011yescharacteristic
352C23×C109#12011yescharacteristic
353C23×C109C22×D411yescharacteristic
354Q8×C109—41no—
355Q8×C109—41no—
356Q8×C109—41no—
357Q8×C109—41no—
358Q8×C109—41no—
359Q8×C109—81no—
360D4×C109—41no—
361D4×C109—41no—
362D4×C109—41no—
363D4×C109—42no—
364D4×C109—42no—
365D4×C109—41no—
366D4×C109—41no—
367D4×C109—41no—
368D4×C109—41no—
369D4×C109—41no—
370D4×C109—41no—
371D4×C109—81no—
372D4×C109—81no—
373D4×C109—81no—
374D4×C109—81no—
375D4×C109—81no—
376D4×C109—81no—
377D4×C109—81no—
378D4×C109—81no—
379D4×C109—81no—
380D4×C109—81no—
381D4×C109—81no—
382D4×C109—81no—
383C2×C4×C109—21no—
384C2×C4×C109—21no—
385C2×C4×C109—21no—
386C2×C4×C109—21no—
387C2×C4×C109—21no—
388C2×C4×C109—21no—
389C2×C4×C109—21no—
390C2×C4×C109—21no—
391C2×C4×C109—21no—
392C2×C4×C109—21no—
393C2×C4×C109—41no—
394C2×C4×C109—41no—
395C2×C4×C109—41no—
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—41no—
406C2×C4×C109—41no—
407C2×C4×C109—41no—
408C2×C4×C109—41no—
409C2×C4×C109—41no—
410C2×C4×C109—41no—
411C2×C4×C109—41no—
412C2×C4×C109—41no—
413C2×C4×C109—81no—
414C2×C4×C109—81no—
415C2×C4×C109—81no—
416C2×C4×C109—81no—
417C2×C4×C109—81no—
418C2×C4×C109—81no—
419C2×C4×C109—81no—
420C2×C4×C109#12011yescharacteristic
421C2×C4×C109#12011yescharacteristic
422C2×C4×C109C22×D411yescharacteristic
423C2×C4×C109C22×D411yescharacteristic
424C8×C109—41no—
425C8×C109—41no—
426C8×C109—41no—
427C8×C109—41no—
428C22×C109—21no—
429C22×C109—21no—
430C22×C109—21no—
431C22×C109—21no—
432C22×C109—21no—
433C22×C109—21no—
434C22×C109—21no—
435C22×C109—21no—
436C22×C109—41no—
437C22×C109—41no—
438C22×C109—41no—
439C22×C109—41no—
440C22×C109—41no—
441C22×C109—41no—
442C22×C109—41no—
443C22×C109—41no—
444C22×C109—41no—
445C22×C109—41no—
446C22×C109—41no—
447C22×C109—41no—
448C22×C109—81no—
449C22×C109—81no—
450C22×C109—81no—
451C22×C109—81no—
452C22×C109—162no—
453C22×C109—162no—
454C22×C109C2×#12011yescharacteristic
455C22×C109#57611yescharacteristic
456C22×C109#57711yescharacteristic
457C4×C109—21no—
458C4×C109—21no—
459C4×C109—21no—
460C4×C109—21no—
461C4×C109—41no—
462C4×C109—41no—
463C4×C109—41no—
464C4×C109—41no—
465C4×C109—41no—
466C4×C109—41no—
467C4×C109—41no—
468C4×C109—41no—
469C4×C109—81no—
470C4×C109—81no—
471C4×C109—81no—
472C4×C109—81no—
473#18447C10911yesmaximal, characteristic, direct product factor, Sylow
474C2×C109—21no—
475C2×C109—21no—
476C2×C109—41no—
477C2×C109—41no—
478C2×C109—81no—
479C2×C109—81no—
480C2×C109—81no—
481C2×C109—81no—
482C2×C109#301211yescharacteristic
483C2×C109#302211yescharacteristic
484C2×C109#302611yescharacteristic
485#3534C2×C10911yescharacteristic
486#3193C2×C10911yescharacteristic, complemented
487#3190C2×C10911yescharacteristic, complemented
488#2814C2×C10911yescharacteristic, complemented
489#1612C2×C10911yescharacteristic, complemented
490#1610C2×C10911yescharacteristic, complemented
491#1609C2×C10911yescharacteristic, complemented
492#1607C2×C10911yescharacteristic, complemented
493#1606C2×C10911yescharacteristic, complemented
494#1604C2×C10911yescharacteristic, complemented
495#1603C2×C10911yescharacteristic, complemented
496#1601C2×C10911yescharacteristic, complemented
497#1519C2×C10911yescharacteristic, complemented
498#1513C2×C10911yescharacteristic, complemented
499#1468C2×C10911yescharacteristic, complemented
500C109#1844711yescharacteristic, direct product factor, Sylow
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C10911yescharacteristic
512#538—21no—
513#538C22×C10911yescharacteristic
514#537C22×C10911yescharacteristic
515#534—21no—
516#534C22×C10911yescharacteristic
517#525C22×C10911yescharacteristic
518C2×#123C22×C10911yescharacteristic
519C2×C22⋊Q8C22×C10911yescharacteristic, complemented
520C2×#121C22×C10911yescharacteristic
521#485—21no—
522#484—21no—
523#483C22×C10911yescharacteristic, complemented
524#480C22×C10911yescharacteristic
525#480C22×C10911yescharacteristic, complemented
526#480C22×C10911yescharacteristic, complemented
527#468—21no—
528#468—21no—
529#467—21no—
530#465—21no—
531#452—21no—
532#451C22×C10911yescharacteristic, complemented
533#450—21no—
534#448C22×C10911yescharacteristic
535#448C22×C10911yescharacteristic, complemented
536#448C22×C10911yescharacteristic, complemented
537#407C22×C10911yescharacteristic, complemented
538C2×C22⋊C8C22×C10911yescharacteristic, complemented
539#398—21no—
540#398C22×C10911yescharacteristic, complemented
541#397—21no—
542#397C22×C10911yescharacteristic, complemented
543#396—21no—
544#395C22×C10911yescharacteristic, complemented
545#394—21no—
546#393C22×C10911yescharacteristic, complemented
547#380C22×C10911yescharacteristic, complemented
548#328C22×C10911yescharacteristic, complemented
549#328C22×C10911yescharacteristic, complemented
550#327C22×C10911yescharacteristic
551#327C22×C10911yescharacteristic
552#327C22×C10911yescharacteristic, complemented
553#327C22×C10911yescharacteristic, complemented
554#327C22×C10911yescharacteristic, complemented
555#327C22×C10911yescharacteristic, complemented
556#324C22×C10911yescharacteristic, complemented
557#324C22×C10911yescharacteristic, complemented
558#323C22×C10911yescharacteristic, complemented
559#323C22×C10911yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C10911yescharacteristic
562C22×Q8C23×C10911yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C10911yescharacteristic
567C22×D4D4×C10911yescharacteristic
568C23×C4C23×C10911yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—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—
596#123—21no—
597#123—21no—
598#123—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⋊Q8D4×C10911yescharacteristic
609C22⋊Q8C23×C10911yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
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#121—21no—
625#121D4×C10911yescharacteristic
626#121D4×C10911yescharacteristic
627#121D4×C10911yescharacteristic
628#121C23×C10911yescharacteristic
629#121C23×C10911yescharacteristic
630#121C23×C10911yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C10911yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4D4×C10911yescharacteristic
654C2×C4⋊C4D4×C10911yescharacteristic
655C2×C4⋊C4C23×C10911yescharacteristic
656C2×C4⋊C4C23×C10911yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4D4×C10911yescharacteristic
665C2×C22⋊C4D4×C10911yescharacteristic
666C2×C22⋊C4C23×C10911yescharacteristic
667#107—21no—
668#107—21no—
669#107—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C10911yescharacteristic
682C22⋊C8C23×C10911yescharacteristic
683C22⋊C8C23×C10911yescharacteristic
684C22⋊C8C23×C10911yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C10911yescharacteristic
690#95C23×C10911yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C10911yescharacteristic
694C24C2×D4×C10911yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C10911yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C10911yescharacteristic
728C2×D4C2×D4×C10911yescharacteristic
729C2×D4C2×D4×C10911yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C10911yescharacteristic
743C22×C4C2×D4×C10911yescharacteristic
744C22×C4C2×D4×C10911yescharacteristic
745C22×C4C2×D4×C10911yescharacteristic
746C22×C4C2×D4×C10911yescharacteristic
747C22×C4C2×D4×C10911yescharacteristic
748C22×C4C2×D4×C10911yescharacteristic
749C22×C4C2×D4×C10911yescharacteristic
750C22×C4C24×C10911yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C10911yescharacteristic
782C4⋊C4C2×D4×C10911yescharacteristic
783C4⋊C4C2×D4×C10911yescharacteristic
784C4⋊C4C2×D4×C10911yescharacteristic
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—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C10911yescharacteristic
837C23#120×C10911yescharacteristic
838C23C22×D4×C10911yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C10911yescharacteristic
906C2×C4#120×C10911yescharacteristic
907C2×C4C22×D4×C10911yescharacteristic
908C2×C4C22×D4×C10911yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C10911yescharacteristic
940C22#576×C10911yescharacteristic
941C22#577×C10911yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C109×#301211yescharacteristic
967C2C109×#302211yescharacteristic
968C2C109×#302611yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#3534C2
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
2. C109×#3193C2semidirect
3. C109×#3190C2semidirect
4. C109×#2814C2semidirect
5. C109×#1612C2semidirect
6. C109×#1610C2semidirect
7. C109×#1609C2semidirect
8. C109×#1607C2semidirect
9. C109×#1606C2semidirect
10. C109×#1604C2semidirect
11. C109×#1603C2semidirect
12. C109×#1601C2semidirect
13. C109×#1519C2semidirect
14. C109×#1513C2semidirect
15. C109×#1468C2semidirect
34. C2×C22⋊Q8×C109C22semidirect
38. #483×C109C22semidirect
40. #480×C109C22semidirect
41. #480×C109C22semidirect
47. #451×C109C22semidirect
50. #448×C109C22semidirect
51. #448×C109C22semidirect
52. #407×C109C22semidirect
53. C2×C22⋊C8×C109C22semidirect
55. #398×C109C22semidirect
57. #397×C109C22semidirect
59. #395×C109C22semidirect
61. #393×C109C22semidirect
62. #380×C109C22semidirect
63. #328×C109C22semidirect
64. #328×C109C22semidirect
67. #327×C109C22semidirect
68. #327×C109C22semidirect
69. #327×C109C22semidirect
70. #327×C109C22semidirect
71. #324×C109C22semidirect
72. #324×C109C22semidirect
73. #323×C109C22semidirect
74. #323×C109C22semidirect
473. #18447C109direct (N × H)
486. #3193C2×C109semidirect
487. #3190C2×C109semidirect
488. #2814C2×C109semidirect
489. #1612C2×C109semidirect
490. #1610C2×C109semidirect
491. #1609C2×C109semidirect
492. #1607C2×C109semidirect
493. #1606C2×C109semidirect
494. #1604C2×C109semidirect
495. #1603C2×C109semidirect
496. #1601C2×C109semidirect
497. #1519C2×C109semidirect
498. #1513C2×C109semidirect
499. #1468C2×C109semidirect
500. C109#18447direct (N × H)
519. C2×C22⋊Q8C22×C109semidirect
523. #483C22×C109semidirect
525. #480C22×C109semidirect
526. #480C22×C109semidirect
532. #451C22×C109semidirect
535. #448C22×C109semidirect
536. #448C22×C109semidirect
537. #407C22×C109semidirect
538. C2×C22⋊C8C22×C109semidirect
540. #398C22×C109semidirect
542. #397C22×C109semidirect
544. #395C22×C109semidirect
546. #393C22×C109semidirect
547. #380C22×C109semidirect
548. #328C22×C109semidirect
549. #328C22×C109semidirect
552. #327C22×C109semidirect
553. #327C22×C109semidirect
554. #327C22×C109semidirect
555. #327C22×C109semidirect
556. #324C22×C109semidirect
557. #324C22×C109semidirect
558. #323C22×C109semidirect
559. #323C22×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35342
C109×#31932
C109×#31902
C109×#28142
C109×#16122
C109×#16102
C109×#16092
C109×#16072
C109×#16062
C109×#16042
C109×#16032
C109×#16012
C109×#15192
C109×#15132
C109×#14682
#18447109