Finite Group Databasebeta

← C73×#23033 #32932437

Subgroups — C73×#23033 #32932437

Order 18688.

982 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C73C211yesmaximal, characteristic
2C2×#440×C73C211yesmaximal, characteristic, complemented
3C2×#427×C73C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic
5C73×#2362C211yesmaximal, characteristic, complemented
6C73×#1973C211yesmaximal, characteristic, complemented
7C73×#1944C211yesmaximal, characteristic, complemented
8C73×#1927C211yesmaximal, characteristic, complemented
9C73×#1926C211yesmaximal, characteristic, complemented
10C73×#1875C211yesmaximal, characteristic
11C73×#1873C211yesmaximal, characteristic, complemented
12C73×#1865C211yesmaximal, characteristic, complemented
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1776C211yesmaximal, characteristic, complemented
15C73×#1752C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23C2×#117×C73C2211yescharacteristic
24#465×C73C418yescomplemented
25#440×C73—24no—
26#427×C73—24no—
27C2×#107×C73C2211yescharacteristic
28C2×#107×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31C2×#106×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40C2×#97×C73C2211yescharacteristic
41#391×C73C2211yescharacteristic
42#390×C73—21no—
43#390×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#388×C73—21no—
47#388×C73—21no—
48#388×C73—21no—
49#387×C73—21no—
50#386×C73—21no—
51C4×C4⋊C4×C73—21no—
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73—21no—
55C4×C22⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73—21no—
66C23×C4×C73C2311yescharacteristic
67C2×SD16×C73—22no—
68C2×SD16×C73—22no—
69C2×SD16×C73C2×C414yes—
70C22×C8×C73—22no—
71C22×C8×C73—22no—
72C22×C8×C73C2×C414yescomplemented
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22⋊Q8×C73—22no—
78C22⋊Q8×C73C2×C414yescomplemented
79#121×C73—22no—
80#121×C73C2×C414yes—
81C4×Q8×C73—22no—
82C4×Q8×C73—41no—
83C4×D4×C73—22no—
84C4×D4×C73—41no—
85#117×C73—22no—
86#117×C73—22no—
87#117×C73—41no—
88#117×C73—41no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73D411yescharacteristic
107C2×C22⋊C4×C73D411yescharacteristic
108C2×C42×C73—21no—
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115#107×C73—22no—
116#107×C73D414yescomplemented
117#106×C73—22no—
118#106×C73—22no—
119#106×C73C2×C414yescomplemented
120#103×C73—22no—
121#103×C73—41no—
122#103×C73C2×C414yescomplemented
123#102×C73—22no—
124#102×C73—41no—
125#102×C73C2×C414yes—
126C22⋊C8×C73—22no—
127#97×C73—22no—
128#97×C73—22no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73D411yescharacteristic
136#95×C73D411yescharacteristic
137C24×C73—21no—
138C24×C73C2×D411yescharacteristic
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73C22×C412yes—
145C2×D4×C73—24no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—81no—
152C2×D4×C73—81no—
153C2×D4×C73C22×C412yes—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—81no—
168C22×C4×C73C22×C412yes—
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73#4112yes—
175C22×C4×C73C2411yescharacteristic
176SD16×C73—28no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—28no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73C22×C412yes—
187C2×C8×C73C22×C412yes—
188C2×C8×C73C2×D412yes—
189C2×C8×C73#4112yes—
190C4⋊C4×C73—24no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—42no—
200C4⋊C4×C73—42no—
201C4⋊C4×C73—81no—
202C4⋊C4×C73C22×C412yes—
203C4⋊C4×C73C22×C412yes—
204C4⋊C4×C73C2×D412yes—
205C4⋊C4×C73C2×D412yes—
206C22⋊C4×C73—24no—
207C22⋊C4×C73—24no—
208C22⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—81no—
215C42×C73—21no—
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—42no—
220C42×C73—42no—
221C42×C73—42no—
222C42×C73—42no—
223C42×C73—81no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—22no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73C4×D412yes—
238C23×C73C22×D411yescharacteristic
239Q8×C73—22no—
240Q8×C73—22no—
241Q8×C73—41no—
242Q8×C73—41no—
243D4×C73—22no—
244D4×C73—22no—
245D4×C73—41no—
246D4×C73—41no—
247D4×C73—84no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—22no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—84no—
288C2×C4×C73C4×D412yes—
289C2×C4×C73C23×C411yescharacteristic
290C2×C4×C73C22×D411yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73H(5,𝔽2)11yescharacteristic
294C2×C4×C732−1+411yescharacteristic
295C8×C73—22no—
296C8×C73—41no—
297C8×C73—41no—
298C8×C73C4×D414yes—
299C22×C73—22no—
300C22×C73—22no—
301C22×C73—22no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73—41no—
306C22×C73—42no—
307C22×C73—42no—
308C22×C73—42no—
309C22×C73—81no—
310C22×C73—81no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73C2×C4×D411yescharacteristic
314C22×C73D4211yescharacteristic
315C22×C73#54711yescharacteristic
316C22×C73#57511yescharacteristic
317C22×C73#57511yescharacteristic
318C22×C73#57711yescharacteristic
319C22×C73#57711yescharacteristic
320C4×C73—22no—
321C4×C73—41no—
322C4×C73—41no—
323C4×C73—42no—
324C4×C73—42no—
325C4×C73—42no—
326C4×C73—41no—
327C4×C73—42no—
328C4×C73—42no—
329C4×C73—41no—
330C4×C73—81no—
331C4×C73—81no—
332C4×C73C2×C4×D411yescharacteristic
333C4×C73#52011yescharacteristic
334C4×C73#54811yescharacteristic
335C4×C73#55311yescharacteristic
336#23033C7311yesmaximal, characteristic, direct product factor, Sylow
337C2×C73—42no—
338C2×C73—82no—
339C2×C73#236111yescharacteristic
340C2×C73#294311yescharacteristic
341C2×C73#294911yescharacteristic
342C2×C73#326711yescharacteristic
343C2×C73#327111yescharacteristic
344C2×C73#334811yescharacteristic
345C2×C73#335011yescharacteristic
346C2×#465C2×C7311yescharacteristic
347C2×#440C2×C7311yescharacteristic, complemented
348C2×#427C2×C7311yescharacteristic, complemented
349#2363C2×C7311yescharacteristic
350#2362C2×C7311yescharacteristic, complemented
351#1973C2×C7311yescharacteristic, complemented
352#1944C2×C7311yescharacteristic, complemented
353#1927C2×C7311yescharacteristic, complemented
354#1926C2×C7311yescharacteristic, complemented
355#1875C2×C7311yescharacteristic
356#1873C2×C7311yescharacteristic, complemented
357#1865C2×C7311yescharacteristic, complemented
358#1864C2×C7311yescharacteristic, complemented
359#1776C2×C7311yescharacteristic, complemented
360#1752C2×C7311yescharacteristic, complemented
361C73#2303311yescharacteristic, direct product factor, Sylow
362C22×SD16C22×C7311yescharacteristic
363C23×C8C22×C7311yescharacteristic
364C2×C22⋊Q8C22×C7311yescharacteristic
365C2×#121C22×C7311yescharacteristic
366C2×C4×Q8C22×C7311yescharacteristic
367C2×C4×D4C22×C7311yescharacteristic
368C2×#117C22×C7311yescharacteristic
369C2×#117C22×C7311yescharacteristic
370#465C4×C7318yescomplemented
371#440—24no—
372#427—24no—
373C2×#107C22×C7311yescharacteristic
374C2×#107C22×C7311yescharacteristic
375C2×#106C22×C7311yescharacteristic
376C2×#106C22×C7311yescharacteristic
377C2×#106C22×C7311yescharacteristic
378C2×#103C22×C7311yescharacteristic
379C2×#103C22×C7311yescharacteristic
380C2×#103C22×C7311yescharacteristic
381C2×#102C22×C7311yescharacteristic
382C2×#102C22×C7311yescharacteristic
383C2×#102C22×C7311yescharacteristic
384C2×C22⋊C8C22×C7311yescharacteristic
385C2×#97C22×C7311yescharacteristic
386C2×#97C22×C7311yescharacteristic
387#391C22×C7311yescharacteristic
388#390—21no—
389#390C22×C7311yescharacteristic
390#389C22×C7311yescharacteristic
391#389C22×C7311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#387—21no—
396#386—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4C22×C7311yescharacteristic
399C4×C4⋊C4C22×C7311yescharacteristic
400C4×C22⋊C4—21no—
401C4×C22⋊C4C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#340C22×C7311yescharacteristic
404#340C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406#336C22×C7311yescharacteristic
407#336C22×C7311yescharacteristic
408C22×Q8C23×C7311yescharacteristic
409C22×D4—21no—
410C22×D4C23×C7311yescharacteristic
411C23×C4—21no—
412C23×C4C23×C7311yescharacteristic
413C2×SD16—22no—
414C2×SD16—22no—
415C2×SD16C2×C4×C7314yes—
416C22×C8—22no—
417C22×C8—22no—
418C22×C8C2×C4×C7314yescomplemented
419C22×C8C23×C7311yescharacteristic
420C22×C8C23×C7311yescharacteristic
421C22×C8C23×C7311yescharacteristic
422C22×C8C23×C7311yescharacteristic
423C22⋊Q8—22no—
424C22⋊Q8C2×C4×C7314yescomplemented
425#121—22no—
426#121C2×C4×C7314yes—
427C4×Q8—22no—
428C4×Q8—41no—
429C4×D4—22no—
430C4×D4—41no—
431#117—22no—
432#117—22no—
433#117—41no—
434#117—41no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4C23×C7311yescharacteristic
440C2×C4⋊C4C23×C7311yescharacteristic
441C2×C4⋊C4C23×C7311yescharacteristic
442C2×C4⋊C4C23×C7311yescharacteristic
443C2×C4⋊C4C23×C7311yescharacteristic
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4D4×C7311yescharacteristic
453C2×C22⋊C4D4×C7311yescharacteristic
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42C23×C7311yescharacteristic
460C2×C42C23×C7311yescharacteristic
461#107—22no—
462#107D4×C7314yescomplemented
463#106—22no—
464#106—22no—
465#106C2×C4×C7314yescomplemented
466#103—22no—
467#103—41no—
468#103C2×C4×C7314yescomplemented
469#102—22no—
470#102—41no—
471#102C2×C4×C7314yes—
472C22⋊C8—22no—
473#97—22no—
474#97—22no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95D4×C7311yescharacteristic
482#95D4×C7311yescharacteristic
483C24—21no—
484C24C2×D4×C7311yescharacteristic
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C22×C4×C7312yes—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C22×C4×C7312yes—
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—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4C22×C4×C7312yes—
515C22×C4C2×D4×C7311yescharacteristic
516C22×C4C2×D4×C7311yescharacteristic
517C22×C4C2×D4×C7311yescharacteristic
518C22×C4C2×D4×C7311yescharacteristic
519C22×C4C2×D4×C7311yescharacteristic
520C22×C4#41×C7312yes—
521C22×C4C24×C7311yescharacteristic
522SD16—28no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—28no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8C22×C4×C7312yes—
533C2×C8C22×C4×C7312yes—
534C2×C8C2×D4×C7312yes—
535C2×C8#41×C7312yes—
536C4⋊C4—24no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—81no—
548C4⋊C4C22×C4×C7312yes—
549C4⋊C4C22×C4×C7312yes—
550C4⋊C4C2×D4×C7312yes—
551C4⋊C4C2×D4×C7312yes—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—42no—
567C42—42no—
568C42—42no—
569C42—81no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C4×D4×C7312yes—
584C23C22×D4×C7311yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—84no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
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×C4—84no—
634C2×C4C4×D4×C7312yes—
635C2×C4C23×C4×C7311yescharacteristic
636C2×C4C22×D4×C7311yescharacteristic
637C2×C4C2×#41×C7311yescharacteristic
638C2×C4C2×#41×C7311yescharacteristic
639C2×C4H(5,𝔽2)×C7311yescharacteristic
640C2×C42−1+4×C7311yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8C4×D4×C7314yes—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22C2×C4×D4×C7311yescharacteristic
660C22D42×C7311yescharacteristic
661C22#547×C7311yescharacteristic
662C22#575×C7311yescharacteristic
663C22#575×C7311yescharacteristic
664C22#577×C7311yescharacteristic
665C22#577×C7311yescharacteristic
666C4—22no—
667C4—41no—
668C4—42no—
669C4—42no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4C2×C4×D4×C7311yescharacteristic
679C4#520×C7311yescharacteristic
680C4#548×C7311yescharacteristic
681C4#553×C7311yescharacteristic
682C2—42no—
683C2—82no—
684C2C73×#236111yescharacteristic
685C2C73×#294311yescharacteristic
686C2C73×#294911yescharacteristic
687C2C73×#326711yescharacteristic
688C2C73×#327111yescharacteristic
689C2C73×#334811yescharacteristic
690C2C73×#335011yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C73C2semidirect
3. C2×#427×C73C2semidirect
5. C73×#2362C2semidirect
6. C73×#1973C2semidirect
7. C73×#1944C2semidirect
8. C73×#1927C2semidirect
9. C73×#1926C2semidirect
11. C73×#1873C2semidirect
12. C73×#1865C2semidirect
13. C73×#1864C2semidirect
14. C73×#1776C2semidirect
15. C73×#1752C2semidirect
24. #465×C73C4semidirect
72. C22×C8×C73C2×C4semidirect
78. C22⋊Q8×C73C2×C4semidirect
116. #107×C73D4semidirect
119. #106×C73C2×C4semidirect
122. #103×C73C2×C4semidirect
336. #23033C73direct (N × H)
347. C2×#440C2×C73semidirect
348. C2×#427C2×C73semidirect
350. #2362C2×C73semidirect
351. #1973C2×C73semidirect
352. #1944C2×C73semidirect
353. #1927C2×C73semidirect
354. #1926C2×C73semidirect
356. #1873C2×C73semidirect
357. #1865C2×C73semidirect
358. #1864C2×C73semidirect
359. #1776C2×C73semidirect
360. #1752C2×C73semidirect
361. C73#23033direct (N × H)
370. #465C4×C73semidirect
418. C22×C8C2×C4×C73semidirect
424. C22⋊Q8C2×C4×C73semidirect
462. #107D4×C73semidirect
465. #106C2×C4×C73semidirect
468. #103C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C732
C2×#440×C732
C2×#427×C732
C73×#23632
C73×#23622
C73×#19732
C73×#19442
C73×#19272
C73×#19262
C73×#18752
C73×#18732
C73×#18652
C73×#18642
C73×#17762
C73×#17522
#2303373