Finite Group Databasebeta

← C109×#32732 #42150726

Subgroups — C109×#32732 #42150726

Order 27904.

724 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2624C211yesmaximal, characteristic
2C109×#2621C211yesmaximal, characteristic, complemented
3C109×#2101C211yesmaximal, characteristic, complemented
4C109×#2092C211yesmaximal, characteristic, complemented
5C109×#2068C211yesmaximal, characteristic, complemented
6C109×#2066C211yesmaximal, characteristic, complemented
7C109×#2055C211yesmaximal, characteristic, complemented
8C109×#2055C211yesmaximal, characteristic, complemented
9C109×#2043C211yesmaximal, characteristic, complemented
10C109×#2036C211yesmaximal, characteristic, complemented
11C109×#2035C211yesmaximal, characteristic, complemented
12C109×#2013C211yesmaximal, characteristic, complemented
13C109×#2000C211yesmaximal, characteristic
14C109×#2000C211yesmaximal, characteristic
15C109×#1798C211yesmaximal, characteristic, complemented
16C22×SD16×C109C2211yescharacteristic
17C22×SD16×C109C2211yescharacteristic
18C2×C4⋊Q8×C109C2211yescharacteristic
19C2×C22⋊Q8×C109C2211yescharacteristic
20C2×C22⋊Q8×C109C2211yescharacteristic
21C2×#121×C109C2211yescharacteristic
22C2×#117×C109C2211yescharacteristic
23C2×#107×C109C2211yescharacteristic
24C2×#106×C109C2211yescharacteristic
25C2×C4⋊C8×C109C2211yescharacteristic
26C2×C4⋊C8×C109C2211yescharacteristic
27C2×#103×C109C2211yescharacteristic
28C2×#103×C109C2211yescharacteristic
29C2×#103×C109C2211yescharacteristic
30C2×#103×C109C2211yescharacteristic
31C2×#103×C109C2211yescharacteristic
32C2×#103×C109C2211yescharacteristic
33C2×#102×C109C2211yescharacteristic
34C2×#102×C109C2211yescharacteristic
35C2×C22⋊C8×C109C2211yescharacteristic
36C2×C22⋊C8×C109C2211yescharacteristic
37#399×C109—21no—
38#398×C109—21no—
39#398×C109—21no—
40#397×C109—21no—
41#397×C109—21no—
42#397×C109—21no—
43#394×C109—21no—
44#394×C109—21no—
45#391×C109C2211yescharacteristic
46#391×C109C2211yescharacteristic
47#390×C109C2211yescharacteristic
48#390×C109C2211yescharacteristic
49#389×C109C2211yescharacteristic
50#389×C109C2211yescharacteristic
51#382×C109C2211yescharacteristic
52#380×C109C2211yescharacteristic
53#340×C109C2211yescharacteristic
54#340×C109C2211yescharacteristic
55#340×C109C2211yescharacteristic
56#340×C109C2211yescharacteristic
57#336×C109C2211yescharacteristic
58#336×C109C2211yescharacteristic
59C22×Q8×C109C2311yescharacteristic
60C22×Q8×C109C2311yescharacteristic
61C22×D4×C109—21no—
62C22×D4×C109C2311yescharacteristic
63C23×C4×C109C2311yescharacteristic
64C2×SD16×C109—41no—
65C2×SD16×C109—41no—
66C2×SD16×C109—41no—
67C2×SD16×C109—41no—
68C2×SD16×C109—41no—
69C2×SD16×C109—41no—
70C22×C8×C109C2311yescharacteristic
71C22×C8×C109C2311yescharacteristic
72C22×C8×C109C2311yescharacteristic
73C22×C8×C109C2311yescharacteristic
74C4⋊Q8×C109—41no—
75C4⋊Q8×C109—41no—
76C22⋊Q8×C109—41no—
77C22⋊Q8×C109—41no—
78C22⋊Q8×C109—41no—
79C22⋊Q8×C109—41no—
80#121×C109—41no—
81#121×C109—41no—
82#117×C109—41no—
83#117×C109—41no—
84C2×C4⋊C4×C109—21no—
85C2×C4⋊C4×C109—21no—
86C2×C4⋊C4×C109—21no—
87C2×C4⋊C4×C109—21no—
88C2×C4⋊C4×C109—21no—
89C2×C4⋊C4×C109—21no—
90C2×C4⋊C4×C109D411yescharacteristic
91C2×C4⋊C4×C109D411yescharacteristic
92C2×C4⋊C4×C109C2311yescharacteristic
93C2×C4⋊C4×C109C2311yescharacteristic
94C2×C4⋊C4×C109C2311yescharacteristic
95C2×C4⋊C4×C109C2311yescharacteristic
96C2×C4⋊C4×C109C2311yescharacteristic
97C2×C22⋊C4×C109—21no—
98C2×C22⋊C4×C109—21no—
99C2×C22⋊C4×C109—21no—
100C2×C22⋊C4×C109—21no—
101C2×C22⋊C4×C109—21no—
102C2×C22⋊C4×C109—21no—
103C2×C22⋊C4×C109—21no—
104C2×C22⋊C4×C109—21no—
105C2×C22⋊C4×C109D411yescharacteristic
106C2×C22⋊C4×C109D411yescharacteristic
107C2×C42×C109C2311yescharacteristic
108C2×C42×C109C2311yescharacteristic
109#107×C109—41no—
110#106×C109—41no—
111C4⋊C8×C109—41no—
112C4⋊C8×C109—41no—
113#103×C109—41no—
114#103×C109—41no—
115#103×C109—41no—
116#103×C109—41no—
117#103×C109—41no—
118#103×C109—41no—
119#102×C109—41no—
120#102×C109—41no—
121C22⋊C8×C109—41no—
122C22⋊C8×C109—41no—
123#95×C109—21no—
124#95×C109—21no—
125#95×C109—21no—
126#95×C109—21no—
127#95×C109—21no—
128#95×C109—21no—
129#95×C109—21no—
130#95×C109—21no—
131#95×C109—21no—
132C24×C109—21no—
133C24×C109C2×D411yescharacteristic
134C2×Q8×C109—21no—
135C2×Q8×C109—21no—
136C2×Q8×C109—21no—
137C2×Q8×C109—21no—
138C2×Q8×C109—21no—
139C2×Q8×C109—21no—
140C2×Q8×C109—21no—
141C2×Q8×C109—21no—
142C2×Q8×C109—21no—
143C2×Q8×C109—21no—
144C2×Q8×C109—21no—
145C2×Q8×C109—21no—
146C2×D4×C109—21no—
147C2×D4×C109—21no—
148C2×D4×C109—21no—
149C2×D4×C109—21no—
150C2×D4×C109—21no—
151C2×D4×C109—21no—
152C2×D4×C109—42no—
153C2×D4×C109—81no—
154C2×D4×C109—81no—
155C22×C4×C109—21no—
156C22×C4×C109—21no—
157C22×C4×C109—21no—
158C22×C4×C109—21no—
159C22×C4×C109—21no—
160C22×C4×C109—21no—
161C22×C4×C109—21no—
162C22×C4×C109—21no—
163C22×C4×C109—21no—
164C22×C4×C109—21no—
165C22×C4×C109—21no—
166C22×C4×C109—21no—
167C22×C4×C109—21no—
168C22×C4×C109C2×D411yescharacteristic
169C22×C4×C109C2×D411yescharacteristic
170C22×C4×C109C2×D411yescharacteristic
171C22×C4×C109C2×D411yescharacteristic
172C22×C4×C109C2×D411yescharacteristic
173C22×C4×C109C2411yescharacteristic
174SD16×C109—44no—
175SD16×C109—44no—
176C2×C8×C109—21no—
177C2×C8×C109—21no—
178C2×C8×C109—21no—
179C2×C8×C109—21no—
180C2×C8×C109—21no—
181C2×C8×C109—21no—
182C2×C8×C109—21no—
183C2×C8×C109—21no—
184C2×C8×C109—21no—
185C2×C8×C109—21no—
186C2×C8×C109—21no—
187C2×C8×C109—21no—
188C4⋊C4×C109—21no—
189C4⋊C4×C109—21no—
190C4⋊C4×C109—21no—
191C4⋊C4×C109—21no—
192C4⋊C4×C109—21no—
193C4⋊C4×C109—21no—
194C4⋊C4×C109—21no—
195C4⋊C4×C109—21no—
196C4⋊C4×C109—21no—
197C4⋊C4×C109—21no—
198C4⋊C4×C109—41no—
199C4⋊C4×C109—41no—
200C4⋊C4×C109—42no—
201C4⋊C4×C109—42no—
202C4⋊C4×C109—42no—
203C4⋊C4×C109—42no—
204C4⋊C4×C109—81no—
205C4⋊C4×C109—81no—
206C22⋊C4×C109—41no—
207C22⋊C4×C109—41no—
208C22⋊C4×C109—42no—
209C22⋊C4×C109—42no—
210C22⋊C4×C109—42no—
211C22⋊C4×C109—81no—
212C22⋊C4×C109—81no—
213C22⋊C4×C109—81no—
214C22⋊C4×C109—81no—
215C22⋊C4×C109—81no—
216C42×C109—21no—
217C42×C109—21no—
218C42×C109—21no—
219C42×C109—21no—
220C23×C109—21no—
221C23×C109—21no—
222C23×C109—21no—
223C23×C109—21no—
224C23×C109—21no—
225C23×C109—21no—
226C23×C109—21no—
227C23×C109—41no—
228C23×C109—41no—
229C23×C109—41no—
230C23×C109—41no—
231C23×C109—41no—
232C23×C109—41no—
233C23×C109—41no—
234C23×C109C22×D411yescharacteristic
235Q8×C109—41no—
236Q8×C109—41no—
237Q8×C109—41no—
238Q8×C109—41no—
239Q8×C109—41no—
240Q8×C109—41no—
241Q8×C109—41no—
242Q8×C109—41no—
243D4×C109—41no—
244D4×C109—41no—
245D4×C109—41no—
246D4×C109—41no—
247D4×C109—84no—
248C2×C4×C109—21no—
249C2×C4×C109—21no—
250C2×C4×C109—21no—
251C2×C4×C109—21no—
252C2×C4×C109—21no—
253C2×C4×C109—21no—
254C2×C4×C109—21no—
255C2×C4×C109—21no—
256C2×C4×C109—21no—
257C2×C4×C109—21no—
258C2×C4×C109—21no—
259C2×C4×C109—21no—
260C2×C4×C109—21no—
261C2×C4×C109—21no—
262C2×C4×C109—21no—
263C2×C4×C109—41no—
264C2×C4×C109—41no—
265C2×C4×C109—41no—
266C2×C4×C109—41no—
267C2×C4×C109—41no—
268C2×C4×C109—41no—
269C2×C4×C109—41no—
270C2×C4×C109—41no—
271C2×C4×C109—41no—
272C2×C4×C109—41no—
273C2×C4×C109—41no—
274C2×C4×C109—41no—
275C2×C4×C109—41no—
276C2×C4×C109—41no—
277C2×C4×C109—41no—
278C2×C4×C109—41no—
279C2×C4×C109—41no—
280C2×C4×C109—41no—
281C2×C4×C109—41no—
282C2×C4×C109—41no—
283C2×C4×C109—41no—
284C2×C4×C109—41no—
285C2×C4×C109—41no—
286C2×C4×C109—41no—
287C2×C4×C109—41no—
288C2×C4×C109H(5,𝔽2)11yescharacteristic
289C2×C4×C109H(5,𝔽2)11yescharacteristic
290C2×C4×C109H(5,𝔽2)11yescharacteristic
291C2×C4×C109H(5,𝔽2)11yescharacteristic
292C2×C4×C109H(5,𝔽2)11yescharacteristic
293C2×C4×C1092−1+411yescharacteristic
294C8×C109—41no—
295C8×C109—41no—
296C8×C109—41no—
297C8×C109—41no—
298C22×C109—41no—
299C22×C109—41no—
300C22×C109—41no—
301C22×C109—41no—
302C22×C109—41no—
303C22×C109—41no—
304C22×C109—41no—
305C22×C109—81no—
306C22×C109—81no—
307C22×C109—81no—
308C22×C109—81no—
309C22×C109—81no—
310C22×C109—81no—
311C22×C109—81no—
312C22×C109#53411yescharacteristic
313C22×C109#53511yescharacteristic
314C22×C109#53711yescharacteristic
315C22×C109#57711yescharacteristic
316C22×C109#57711yescharacteristic
317C22×C109#57711yescharacteristic
318C22×C109#57811yescharacteristic
319C4×C109—41no—
320C4×C109—41no—
321C4×C109—41no—
322C4×C109—41no—
323C4×C109—41no—
324C4×C109—81no—
325C4×C109—81no—
326C4×C109—81no—
327C4×C109—81no—
328C4×C109—81no—
329C4×C109—81no—
330C4×C109—81no—
331C4×C109#56011yescharacteristic
332C4×C109#56011yescharacteristic
333C4×C109#56211yescharacteristic
334C4×C109#56211yescharacteristic
335#32732C10911yesmaximal, characteristic, direct product factor, Sylow
336C2×C109—81no—
337C2×C109—161no—
338C2×C109#281311yescharacteristic
339C2×C109#320011yescharacteristic
340C2×C109#320111yescharacteristic
341C2×C109#322111yescharacteristic
342C2×C109#322511yescharacteristic
343C2×C109#325811yescharacteristic
344C2×C109#326011yescharacteristic
345#2624C2×C10911yescharacteristic
346#2621C2×C10911yescharacteristic, complemented
347#2101C2×C10911yescharacteristic, complemented
348#2092C2×C10911yescharacteristic, complemented
349#2068C2×C10911yescharacteristic, complemented
350#2066C2×C10911yescharacteristic, complemented
351#2055C2×C10911yescharacteristic, complemented
352#2055C2×C10911yescharacteristic, complemented
353#2043C2×C10911yescharacteristic, complemented
354#2036C2×C10911yescharacteristic, complemented
355#2035C2×C10911yescharacteristic, complemented
356#2013C2×C10911yescharacteristic, complemented
357#2000C2×C10911yescharacteristic
358#2000C2×C10911yescharacteristic
359#1798C2×C10911yescharacteristic, complemented
360C109#3273211yescharacteristic, direct product factor, Sylow
361C22×SD16C22×C10911yescharacteristic
362C22×SD16C22×C10911yescharacteristic
363C2×C4⋊Q8C22×C10911yescharacteristic
364C2×C22⋊Q8C22×C10911yescharacteristic
365C2×C22⋊Q8C22×C10911yescharacteristic
366C2×#121C22×C10911yescharacteristic
367C2×#117C22×C10911yescharacteristic
368C2×#107C22×C10911yescharacteristic
369C2×#106C22×C10911yescharacteristic
370C2×C4⋊C8C22×C10911yescharacteristic
371C2×C4⋊C8C22×C10911yescharacteristic
372C2×#103C22×C10911yescharacteristic
373C2×#103C22×C10911yescharacteristic
374C2×#103C22×C10911yescharacteristic
375C2×#103C22×C10911yescharacteristic
376C2×#103C22×C10911yescharacteristic
377C2×#103C22×C10911yescharacteristic
378C2×#102C22×C10911yescharacteristic
379C2×#102C22×C10911yescharacteristic
380C2×C22⋊C8C22×C10911yescharacteristic
381C2×C22⋊C8C22×C10911yescharacteristic
382#399—21no—
383#398—21no—
384#398—21no—
385#397—21no—
386#397—21no—
387#397—21no—
388#394—21no—
389#394—21no—
390#391C22×C10911yescharacteristic
391#391C22×C10911yescharacteristic
392#390C22×C10911yescharacteristic
393#390C22×C10911yescharacteristic
394#389C22×C10911yescharacteristic
395#389C22×C10911yescharacteristic
396#382C22×C10911yescharacteristic
397#380C22×C10911yescharacteristic
398#340C22×C10911yescharacteristic
399#340C22×C10911yescharacteristic
400#340C22×C10911yescharacteristic
401#340C22×C10911yescharacteristic
402#336C22×C10911yescharacteristic
403#336C22×C10911yescharacteristic
404C22×Q8C23×C10911yescharacteristic
405C22×Q8C23×C10911yescharacteristic
406C22×D4—21no—
407C22×D4C23×C10911yescharacteristic
408C23×C4C23×C10911yescharacteristic
409C2×SD16—41no—
410C2×SD16—41no—
411C2×SD16—41no—
412C2×SD16—41no—
413C2×SD16—41no—
414C2×SD16—41no—
415C22×C8C23×C10911yescharacteristic
416C22×C8C23×C10911yescharacteristic
417C22×C8C23×C10911yescharacteristic
418C22×C8C23×C10911yescharacteristic
419C4⋊Q8—41no—
420C4⋊Q8—41no—
421C22⋊Q8—41no—
422C22⋊Q8—41no—
423C22⋊Q8—41no—
424C22⋊Q8—41no—
425#121—41no—
426#121—41no—
427#117—41no—
428#117—41no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4D4×C10911yescharacteristic
436C2×C4⋊C4D4×C10911yescharacteristic
437C2×C4⋊C4C23×C10911yescharacteristic
438C2×C4⋊C4C23×C10911yescharacteristic
439C2×C4⋊C4C23×C10911yescharacteristic
440C2×C4⋊C4C23×C10911yescharacteristic
441C2×C4⋊C4C23×C10911yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4D4×C10911yescharacteristic
451C2×C22⋊C4D4×C10911yescharacteristic
452C2×C42C23×C10911yescharacteristic
453C2×C42C23×C10911yescharacteristic
454#107—41no—
455#106—41no—
456C4⋊C8—41no—
457C4⋊C8—41no—
458#103—41no—
459#103—41no—
460#103—41no—
461#103—41no—
462#103—41no—
463#103—41no—
464#102—41no—
465#102—41no—
466C22⋊C8—41no—
467C22⋊C8—41no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477C24—21no—
478C24C2×D4×C10911yescharacteristic
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—81no—
499C2×D4—81no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4C2×D4×C10911yescharacteristic
514C22×C4C2×D4×C10911yescharacteristic
515C22×C4C2×D4×C10911yescharacteristic
516C22×C4C2×D4×C10911yescharacteristic
517C22×C4C2×D4×C10911yescharacteristic
518C22×C4C24×C10911yescharacteristic
519SD16—44no—
520SD16—44no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C22×D4×C10911yescharacteristic
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—84no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4H(5,𝔽2)×C10911yescharacteristic
634C2×C4H(5,𝔽2)×C10911yescharacteristic
635C2×C4H(5,𝔽2)×C10911yescharacteristic
636C2×C4H(5,𝔽2)×C10911yescharacteristic
637C2×C4H(5,𝔽2)×C10911yescharacteristic
638C2×C42−1+4×C10911yescharacteristic
639C8—41no—
640C8—41no—
641C8—41no—
642C8—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22#534×C10911yescharacteristic
658C22#535×C10911yescharacteristic
659C22#537×C10911yescharacteristic
660C22#577×C10911yescharacteristic
661C22#577×C10911yescharacteristic
662C22#577×C10911yescharacteristic
663C22#578×C10911yescharacteristic
664C4—41no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4—81no—
676C4#560×C10911yescharacteristic
677C4#560×C10911yescharacteristic
678C4#562×C10911yescharacteristic
679C4#562×C10911yescharacteristic
680C2—81no—
681C2—161no—
682C2C109×#281311yescharacteristic
683C2C109×#320011yescharacteristic
684C2C109×#320111yescharacteristic
685C2C109×#322111yescharacteristic
686C2C109×#322511yescharacteristic
687C2C109×#325811yescharacteristic
688C2C109×#326011yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×#121×C109C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×#117×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#2621C2semidirect
3. C109×#2101C2semidirect
4. C109×#2092C2semidirect
5. C109×#2068C2semidirect
6. C109×#2066C2semidirect
7. C109×#2055C2semidirect
8. C109×#2055C2semidirect
9. C109×#2043C2semidirect
10. C109×#2036C2semidirect
11. C109×#2035C2semidirect
12. C109×#2013C2semidirect
15. C109×#1798C2semidirect
335. #32732C109direct (N × H)
346. #2621C2×C109semidirect
347. #2101C2×C109semidirect
348. #2092C2×C109semidirect
349. #2068C2×C109semidirect
350. #2066C2×C109semidirect
351. #2055C2×C109semidirect
352. #2055C2×C109semidirect
353. #2043C2×C109semidirect
354. #2036C2×C109semidirect
355. #2035C2×C109semidirect
356. #2013C2×C109semidirect
359. #1798C2×C109semidirect
360. C109#32732direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#26242
C109×#26212
C109×#21012
C109×#20922
C109×#20682
C109×#20662
C109×#20552
C109×#20432
C109×#20362
C109×#20352
C109×#20132
C109×#20002
C109×#17982
#32732109