Finite Group Databasebeta

← C73×#59403 #32968807

Subgroups — C73×#59403 #32968807

Order 18688.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2781C212yesmaximal, complemented
2C73×#2756C212yesmaximal, complemented
3C73×#2603C212yesmaximal, complemented
4C73×#2559C212yesmaximal, complemented
5C73×#2543C212yesmaximal, complemented
6C73×#2537C211yesmaximal, characteristic, complemented
7C73×#2512C211yesmaximal, characteristic, complemented
8C73×#2507C211yesmaximal, characteristic, complemented
9C73×#2495C211yesmaximal, characteristic, complemented
10C73×#2456C212yesmaximal, complemented
11C73×#2428C211yesmaximal, characteristic, complemented
12C73×#2428C211yesmaximal, characteristic, complemented
13C73×#2420C211yesmaximal, characteristic, complemented
14C73×#2420C212yesmaximal, complemented
15C73×#2414C211yesmaximal, characteristic, complemented
16C73×#2366C211yesmaximal, characteristic, complemented
17C73×#2363C211yesmaximal, characteristic, complemented
18C73×#2353C212yesmaximal, complemented
19C73×#2349C211yesmaximal, characteristic, complemented
20C73×#2346C211yesmaximal, characteristic, complemented
21C4×#123×C73C211yesmaximal, characteristic, complemented
22C4×#121×C73C211yesmaximal, characteristic, complemented
23C4×#121×C73C211yesmaximal, characteristic, complemented
24C2×#127×C73C2211yescharacteristic
25C2×#126×C73C2212yes—
26C2×#123×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic
29C2×#121×C73C2211yescharacteristic
30C2×#121×C73C2212yes—
31C2×#121×C73C2212yes—
32C2×#121×C73C2212yes—
33C2×#121×C73C2211yescharacteristic
34C2×C4×D4×C73C2212yes—
35C2×C4×D4×C73C2211yescharacteristic
36C2×C4×D4×C73C2212yes—
37C2×C4×D4×C73C2211yescharacteristic
38C2×C4×D4×C73C2211yescharacteristic
39C2×C4×D4×C73C2212yes—
40C2×C4×D4×C73C2211yescharacteristic
41C2×C4×D4×C73C2211yescharacteristic
42C2×#117×C73C2211yescharacteristic
43C22×C42×C73C2211yescharacteristic
44#400×C73C2212yes—
45#398×C73C2212yes—
46#398×C73C2212yes—
47#397×C73C2212yes—
48#397×C73C2212yes—
49#397×C73C2212yes—
50#396×C73C2212yes—
51#394×C73C2212yes—
52#394×C73C2212yes—
53#394×C73C2212yes—
54#394×C73C2212yes—
55#394×C73C2212yes—
56#394×C73C2212yes—
57#392×C73C2212yes—
58#392×C73C2212yes—
59#392×C73C2212yes—
60#390×C73C2212yes—
61#390×C73C2212yes—
62#390×C73C2211yescharacteristic
63#390×C73C2211yescharacteristic
64#390×C73C2211yescharacteristic
65#390×C73C2211yescharacteristic
66#390×C73C2212yes—
67#389×C73C2211yescharacteristic
68#389×C73C2211yescharacteristic
69#389×C73C2211yescharacteristic
70#389×C73C2212yes—
71#389×C73C2211yescharacteristic
72#389×C73C2211yescharacteristic
73#389×C73C2211yescharacteristic
74#388×C73C2212yes—
75#388×C73C2212yes—
76#388×C73C2211yescharacteristic
77#388×C73C2212yes—
78#388×C73C2212yes—
79#388×C73C2212yes—
80#388×C73C2212yes—
81#388×C73C2212yes—
82#388×C73C2212yes—
83#388×C73C2211yescharacteristic
84#387×C73C2212yes—
85#387×C73C2211yescharacteristic
86#387×C73C2211yescharacteristic
87#386×C73C2212yes—
88#386×C73C2212yes—
89#386×C73C2212yes—
90#386×C73C2212yes—
91#386×C73C2212yes—
92#386×C73C2211yescharacteristic
93#386×C73C2212yes—
94#386×C73C2212yes—
95#386×C73C2212yes—
96#385×C73C2212yes—
97#385×C73C2211yescharacteristic
98#385×C73C2212yes—
99#384×C73C2211yescharacteristic
100#383×C73C2212yes—
101#382×C73C2211yescharacteristic
102#382×C73C2212yes—
103#381×C73C2211yescharacteristic
104#381×C73C2212yes—
105#380×C73C2211yescharacteristic
106#380×C73C2211yescharacteristic
107#380×C73C2212yes—
108#380×C73C2212yes—
109#380×C73C2211yescharacteristic
110C4×C4⋊C4×C73C2211yescharacteristic
111C4×C4⋊C4×C73C2211yescharacteristic
112C4×C4⋊C4×C73C2211yescharacteristic
113C4×C4⋊C4×C73C2211yescharacteristic
114C4×C4⋊C4×C73C2211yescharacteristic
115C4×C22⋊C4×C73C2211yescharacteristic
116C4×C22⋊C4×C73C2212yes—
117C4×C22⋊C4×C73C2212yes—
118C4×C22⋊C4×C73C2211yescharacteristic
119C4×C22⋊C4×C73C2211yescharacteristic
120C4×C22⋊C4×C73C2212yes—
121#376×C73C2212yes—
122C2×#95×C73C2212yes—
123C22×D4×C73C2311yescharacteristic
124C22×D4×C73C2312yes—
125C22×D4×C73C2312yes—
126C22×D4×C73C2311yescharacteristic
127C22×D4×C73C2312yes—
128C22×D4×C73C2311yescharacteristic
129C22×D4×C73C2312yes—
130C22×D4×C73C2312yes—
131C22×D4×C73C2312yes—
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2312yes—
136C23×C4×C73C2312yes—
137C23×C4×C73C2312yes—
138C23×C4×C73C2312yes—
139C23×C4×C73C2311yescharacteristic
140#127×C73—24no—
141#126×C73—44no—
142#123×C73—24no—
143#121×C73—24no—
144#121×C73—24no—
145#121×C73—24no—
146#121×C73—44no—
147#121×C73—44no—
148#121×C73—44no—
149#121×C73—42no—
150C4×D4×C73—24no—
151C4×D4×C73—28no—
152C4×D4×C73—42no—
153C4×D4×C73—42no—
154C4×D4×C73—42no—
155C4×D4×C73—42no—
156C4×D4×C73—44no—
157C4×D4×C73—44no—
158#117×C73—24no—
159C2×C4⋊C4×C73C2311yescharacteristic
160C2×C4⋊C4×C73C2311yescharacteristic
161C2×C4⋊C4×C73C2311yescharacteristic
162C2×C4⋊C4×C73C2311yescharacteristic
163C2×C4⋊C4×C73C2311yescharacteristic
164C2×C4⋊C4×C73C2311yescharacteristic
165C2×C4⋊C4×C73C2311yescharacteristic
166C2×C4⋊C4×C73C2311yescharacteristic
167C2×C4⋊C4×C73C2311yescharacteristic
168C2×C4⋊C4×C73C2312yes—
169C2×C4⋊C4×C73C2312yes—
170C2×C4⋊C4×C73C2312yes—
171C2×C4⋊C4×C73C2312yes—
172C2×C4⋊C4×C73C2312yes—
173C2×C4⋊C4×C73C2312yes—
174C2×C4⋊C4×C73C2312yes—
175C2×C4⋊C4×C73C2312yes—
176C2×C4⋊C4×C73C2311yescharacteristic
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C22⋊C4×C73C2312yes—
179C2×C22⋊C4×C73C2312yes—
180C2×C22⋊C4×C73C2312yes—
181C2×C22⋊C4×C73C2311yescharacteristic
182C2×C22⋊C4×C73C2311yescharacteristic
183C2×C22⋊C4×C73C2311yescharacteristic
184C2×C22⋊C4×C73C2312yes—
185C2×C22⋊C4×C73C2311yescharacteristic
186C2×C22⋊C4×C73C2312yes—
187C2×C22⋊C4×C73C2311yescharacteristic
188C2×C22⋊C4×C73C2312yes—
189C2×C22⋊C4×C73C2312yes—
190C2×C22⋊C4×C73C2312yes—
191C2×C22⋊C4×C73C2312yes—
192C2×C22⋊C4×C73C2311yescharacteristic
193C2×C22⋊C4×C73C2312yes—
194C2×C22⋊C4×C73C2312yes—
195C2×C22⋊C4×C73C2312yes—
196C2×C22⋊C4×C73C2312yes—
197C2×C22⋊C4×C73C2311yescharacteristic
198C2×C22⋊C4×C73C2312yes—
199C2×C22⋊C4×C73C2312yes—
200C2×C22⋊C4×C73C2312yes—
201C2×C22⋊C4×C73C2312yes—
202C2×C22⋊C4×C73C2312yes—
203C2×C22⋊C4×C73C2312yes—
204C2×C22⋊C4×C73C2311yescharacteristic
205C2×C22⋊C4×C73C2312yes—
206C2×C42×C73—42no—
207C2×C42×C73C2311yescharacteristic
208C2×C42×C73C2311yescharacteristic
209C2×C42×C73C2311yescharacteristic
210C2×C42×C73C2311yescharacteristic
211C2×C42×C73C2312yes—
212C2×C42×C73C2312yes—
213C2×C42×C73C2311yescharacteristic
214C2×C42×C73C2312yes—
215C2×C42×C73C2311yescharacteristic
216C2×C42×C73C2312yes—
217C2×C42×C73C2311yescharacteristic
218#95×C73C2311yescharacteristic
219#95×C73C2312yes—
220#95×C73C2312yes—
221#95×C73C2311yescharacteristic
222#95×C73C2312yes—
223#95×C73C2311yescharacteristic
224#95×C73C2312yes—
225#95×C73C2311yescharacteristic
226#95×C73C2312yes—
227#95×C73C2311yescharacteristic
228#95×C73C2311yescharacteristic
229#95×C73C2311yescharacteristic
230#95×C73C2311yescharacteristic
231#95×C73C2312yes—
232#95×C73C2312yes—
233#95×C73C2311yescharacteristic
234#95×C73C2312yes—
235#95×C73C2311yescharacteristic
236#95×C73C2312yes—
237#95×C73C2312yes—
238#95×C73C2312yes—
239#95×C73C2312yes—
240#95×C73C2312yes—
241#95×C73C2312yes—
242C24×C73C2411yescharacteristic
243C24×C73C2412yes—
244C24×C73C2412yes—
245C24×C73C2411yescharacteristic
246C2×D4×C73—24no—
247C2×D4×C73—24no—
248C2×D4×C73—24no—
249C2×D4×C73—22no—
250C2×D4×C73—24no—
251C2×D4×C73—24no—
252C2×D4×C73—24no—
253C2×D4×C73—22no—
254C2×D4×C73—24no—
255C2×D4×C73—24no—
256C2×D4×C73—22no—
257C2×D4×C73—22no—
258C2×D4×C73—22no—
259C2×D4×C73—22no—
260C2×D4×C73—22no—
261C2×D4×C73—41no—
262C2×D4×C73—42no—
263C2×D4×C73—42no—
264C2×D4×C73—42no—
265C2×D4×C73—42no—
266C2×D4×C73—42no—
267C2×D4×C73—42no—
268C2×D4×C73—42no—
269C2×D4×C73—42no—
270C2×D4×C73—42no—
271C2×D4×C73—42no—
272C2×D4×C73#4114yes—
273C22×C4×C73—22no—
274C22×C4×C73—22no—
275C22×C4×C73—22no—
276C22×C4×C73—22no—
277C22×C4×C73—22no—
278C22×C4×C73—22no—
279C22×C4×C73—22no—
280C22×C4×C73—22no—
281C22×C4×C73—22no—
282C22×C4×C73—24no—
283C22×C4×C73—24no—
284C22×C4×C73—24no—
285C22×C4×C73—24no—
286C22×C4×C73—41no—
287C22×C4×C73—41no—
288C22×C4×C73—41no—
289C22×C4×C73—42no—
290C22×C4×C73—42no—
291C22×C4×C73—42no—
292C22×C4×C73—42no—
293C22×C4×C73—42no—
294C22×C4×C73—42no—
295C22×C4×C73—42no—
296C22×C4×C73—42no—
297C22×C4×C73C2411yescharacteristic
298C22×C4×C73C2411yescharacteristic
299C22×C4×C73C2411yescharacteristic
300C22×C4×C73C2412yes—
301C22×C4×C73C2411yescharacteristic
302C22×C4×C73C2412yes—
303C22×C4×C73C2412yes—
304C22×C4×C73C2411yescharacteristic
305C22×C4×C73C2411yescharacteristic
306C22×C4×C73C2411yescharacteristic
307C22×C4×C73C2412yes—
308C22×C4×C73C2412yes—
309C22×C4×C73C2411yescharacteristic
310C22×C4×C73C2411yescharacteristic
311C22×C4×C73C2411yescharacteristic
312C22×C4×C73C2412yes—
313C22×C4×C73C2411yescharacteristic
314C22×C4×C73C2411yescharacteristic
315C22×C4×C73C2411yescharacteristic
316C4⋊C4×C73—22no—
317C4⋊C4×C73—22no—
318C4⋊C4×C73—22no—
319C4⋊C4×C73—22no—
320C4⋊C4×C73—22no—
321C4⋊C4×C73—22no—
322C4⋊C4×C73—22no—
323C4⋊C4×C73—42no—
324C4⋊C4×C73—41no—
325C4⋊C4×C73—41no—
326C4⋊C4×C73—42no—
327C4⋊C4×C73—42no—
328C4⋊C4×C73—42no—
329C4⋊C4×C73—42no—
330C4⋊C4×C73—42no—
331C4⋊C4×C73—42no—
332C4⋊C4×C73—42no—
333C4⋊C4×C73#4114yes—
334C4⋊C4×C73#4114yes—
335C22⋊C4×C73—24no—
336C22⋊C4×C73—24no—
337C22⋊C4×C73—24no—
338C22⋊C4×C73—22no—
339C22⋊C4×C73—24no—
340C22⋊C4×C73—24no—
341C22⋊C4×C73—24no—
342C22⋊C4×C73—24no—
343C22⋊C4×C73—24no—
344C22⋊C4×C73—22no—
345C22⋊C4×C73—22no—
346C22⋊C4×C73—22no—
347C22⋊C4×C73—22no—
348C22⋊C4×C73—24no—
349C22⋊C4×C73—41no—
350C22⋊C4×C73—42no—
351C22⋊C4×C73—42no—
352C22⋊C4×C73—41no—
353C22⋊C4×C73—41no—
354C22⋊C4×C73—42no—
355C22⋊C4×C73—42no—
356C22⋊C4×C73—42no—
357C22⋊C4×C73—42no—
358C22⋊C4×C73—42no—
359C22⋊C4×C73—42no—
360C22⋊C4×C73—42no—
361C22⋊C4×C73—42no—
362C22⋊C4×C73—42no—
363C42×C73—24no—
364C42×C73—24no—
365C42×C73—22no—
366C42×C73—22no—
367C42×C73—22no—
368C42×C73—22no—
369C42×C73—22no—
370C42×C73—24no—
371C42×C73—41no—
372C42×C73—41no—
373C42×C73—42no—
374C23×C73—22no—
375C23×C73—22no—
376C23×C73—21no—
377C23×C73—21no—
378C23×C73—21no—
379C23×C73—21no—
380C23×C73—22no—
381C23×C73—21no—
382C23×C73—22no—
383C23×C73—22no—
384C23×C73—22no—
385C23×C73—21no—
386C23×C73—21no—
387C23×C73—21no—
388C23×C73—22no—
389C23×C73—22no—
390C23×C73—21no—
391C23×C73—22no—
392C23×C73—22no—
393C23×C73—21no—
394C23×C73—22no—
395C23×C73—22no—
396C23×C73—21no—
397C23×C73—21no—
398C23×C73—21no—
399C23×C73—22no—
400C23×C73C2×#4114yes—
401C23×C73H(5,𝔽2)12yes—
402C23×C73C2511yescharacteristic
403D4×C73—28no—
404D4×C73—48no—
405D4×C73—48no—
406D4×C73—44no—
407D4×C73—48no—
408D4×C73—44no—
409D4×C73—84no—
410D4×C73—84no—
411D4×C73—84no—
412C2×C4×C73—21no—
413C2×C4×C73—21no—
414C2×C4×C73—21no—
415C2×C4×C73—21no—
416C2×C4×C73—21no—
417C2×C4×C73—22no—
418C2×C4×C73—21no—
419C2×C4×C73—22no—
420C2×C4×C73—21no—
421C2×C4×C73—21no—
422C2×C4×C73—21no—
423C2×C4×C73—21no—
424C2×C4×C73—22no—
425C2×C4×C73—22no—
426C2×C4×C73—21no—
427C2×C4×C73—22no—
428C2×C4×C73—21no—
429C2×C4×C73—21no—
430C2×C4×C73—21no—
431C2×C4×C73—21no—
432C2×C4×C73—21no—
433C2×C4×C73—21no—
434C2×C4×C73—22no—
435C2×C4×C73—22no—
436C2×C4×C73—21no—
437C2×C4×C73—21no—
438C2×C4×C73—21no—
439C2×C4×C73—22no—
440C2×C4×C73—22no—
441C2×C4×C73—21no—
442C2×C4×C73—22no—
443C2×C4×C73—21no—
444C2×C4×C73—22no—
445C2×C4×C73—22no—
446C2×C4×C73—21no—
447C2×C4×C73—21no—
448C2×C4×C73—21no—
449C2×C4×C73—21no—
450C2×C4×C73—21no—
451C2×C4×C73—22no—
452C2×C4×C73—22no—
453C2×C4×C73—21no—
454C2×C4×C73—21no—
455C2×C4×C73—22no—
456C2×C4×C73—22no—
457C2×C4×C73—21no—
458C2×C4×C73—21no—
459C2×C4×C73—21no—
460C2×C4×C73—22no—
461C2×C4×C73—44no—
462C2×C4×C73—44no—
463C2×C4×C73—44no—
464C2×C4×C73—44no—
465C2×C4×C73—84no—
466C2×C4×C73—84no—
467C2×C4×C73—84no—
468C2×C4×C73—84no—
469C2×C4×C73C2×#4112yes—
470C2×C4×C73C2×#4114yes—
471C2×C4×C73C2×#4112yes—
472C2×C4×C73C2×#4112yes—
473C2×C4×C73C2×#4112yes—
474C2×C4×C73C2×#4112yes—
475C2×C4×C73H(5,𝔽2)12yes—
476C2×C4×C73H(5,𝔽2)12yes—
477C22×C73—24no—
478C22×C73—24no—
479C22×C73—22no—
480C22×C73—22no—
481C22×C73—22no—
482C22×C73—24no—
483C22×C73—41no—
484C22×C73—41no—
485C22×C73—42no—
486C22×C73—41no—
487C22×C73—42no—
488C22×C73—42no—
489C22×C73—41no—
490C22×C73—42no—
491C22×C73—41no—
492C22×C73—42no—
493C22×C73—42no—
494C22×C73—41no—
495C22×C73—41no—
496C22×C73—42no—
497C22×C73—42no—
498C22×C73—41no—
499C22×C73—42no—
500C22×C73—41no—
501C22×C73—41no—
502C22×C73—42no—
503C22×C73—41no—
504C22×C73—42no—
505C22×C73C22×#4111yescharacteristic
506C22×C73C22×#4111yescharacteristic
507C22×C73C22×#4111yescharacteristic
508C22×C73C2×H(5,𝔽2)11yescharacteristic
509C22×C73C2×H(5,𝔽2)11yescharacteristic
510C22×C73C2×H(5,𝔽2)11yescharacteristic
511C22×C73#58511yescharacteristic
512C4×C73—22no—
513C4×C73—24no—
514C4×C73—22no—
515C4×C73—22no—
516C4×C73—22no—
517C4×C73—41no—
518C4×C73—41no—
519C4×C73—42no—
520C4×C73—41no—
521C4×C73—41no—
522C4×C73—41no—
523C4×C73—42no—
524C4×C73—42no—
525C4×C73—42no—
526C4×C73—41no—
527C4×C73—41no—
528C4×C73—41no—
529C4×C73—42no—
530C4×C73#55314yes—
531#59403C7311yesmaximal, characteristic, direct product factor, Sylow
532C2×C73—44no—
533C2×C73—42no—
534C2×C73—81no—
535C2×C73—82no—
536C2×C73C2×#55311yescharacteristic
537C2×C73#347511yescharacteristic
538C2×C73#348311yescharacteristic
539C2×C73#351311yescharacteristic
540C2×C73#351911yescharacteristic
541C2×C73#351911yescharacteristic
542C2×C73#354211yescharacteristic
543#2781C2×C7312yescomplemented
544#2756C2×C7312yescomplemented
545#2603C2×C7312yescomplemented
546#2559C2×C7312yescomplemented
547#2543C2×C7312yescomplemented
548#2537C2×C7311yescharacteristic, complemented
549#2512C2×C7311yescharacteristic, complemented
550#2507C2×C7311yescharacteristic, complemented
551#2495C2×C7311yescharacteristic, complemented
552#2456C2×C7312yescomplemented
553#2428C2×C7311yescharacteristic, complemented
554#2428C2×C7311yescharacteristic, complemented
555#2420C2×C7311yescharacteristic, complemented
556#2420C2×C7312yescomplemented
557#2414C2×C7311yescharacteristic, complemented
558#2366C2×C7311yescharacteristic, complemented
559#2363C2×C7311yescharacteristic, complemented
560#2353C2×C7312yescomplemented
561#2349C2×C7311yescharacteristic, complemented
562#2346C2×C7311yescharacteristic, complemented
563C4×#123C2×C7311yescharacteristic, complemented
564C4×#121C2×C7311yescharacteristic, complemented
565C4×#121C2×C7311yescharacteristic, complemented
566C73#5940311yescharacteristic, direct product factor, Sylow
567C2×#127C22×C7311yescharacteristic
568C2×#126C22×C7312yes—
569C2×#123C22×C7311yescharacteristic
570C2×#121C22×C7311yescharacteristic
571C2×#121C22×C7311yescharacteristic
572C2×#121C22×C7311yescharacteristic
573C2×#121C22×C7311yescharacteristic
574C2×#121C22×C7312yes—
575C2×#121C22×C7312yes—
576C2×#121C22×C7312yes—
577C2×C4×D4C22×C7311yescharacteristic
578C2×C4×D4C22×C7312yes—
579C2×C4×D4C22×C7312yes—
580C2×C4×D4C22×C7311yescharacteristic
581C2×C4×D4C22×C7311yescharacteristic
582C2×C4×D4C22×C7311yescharacteristic
583C2×C4×D4C22×C7311yescharacteristic
584C2×C4×D4C22×C7312yes—
585C2×#117C22×C7311yescharacteristic
586C22×C42C22×C7311yescharacteristic
587#400C22×C7312yes—
588#398C22×C7312yes—
589#398C22×C7312yes—
590#397C22×C7312yes—
591#397C22×C7312yes—
592#397C22×C7312yes—
593#396C22×C7312yes—
594#394C22×C7312yes—
595#394C22×C7312yes—
596#394C22×C7312yes—
597#394C22×C7312yes—
598#394C22×C7312yes—
599#394C22×C7312yes—
600#392C22×C7312yes—
601#392C22×C7312yes—
602#392C22×C7312yes—
603#390C22×C7312yes—
604#390C22×C7312yes—
605#390C22×C7311yescharacteristic
606#390C22×C7312yes—
607#390C22×C7311yescharacteristic
608#390C22×C7311yescharacteristic
609#390C22×C7311yescharacteristic
610#389C22×C7311yescharacteristic
611#389C22×C7311yescharacteristic
612#389C22×C7311yescharacteristic
613#389C22×C7311yescharacteristic
614#389C22×C7311yescharacteristic
615#389C22×C7312yes—
616#389C22×C7311yescharacteristic
617#388C22×C7312yes—
618#388C22×C7312yes—
619#388C22×C7312yes—
620#388C22×C7312yes—
621#388C22×C7312yes—
622#388C22×C7312yes—
623#388C22×C7311yescharacteristic
624#388C22×C7312yes—
625#388C22×C7312yes—
626#388C22×C7311yescharacteristic
627#387C22×C7311yescharacteristic
628#387C22×C7312yes—
629#387C22×C7311yescharacteristic
630#386C22×C7312yes—
631#386C22×C7312yes—
632#386C22×C7312yes—
633#386C22×C7312yes—
634#386C22×C7312yes—
635#386C22×C7312yes—
636#386C22×C7312yes—
637#386C22×C7312yes—
638#386C22×C7311yescharacteristic
639#385C22×C7311yescharacteristic
640#385C22×C7312yes—
641#385C22×C7312yes—
642#384C22×C7311yescharacteristic
643#383C22×C7312yes—
644#382C22×C7312yes—
645#382C22×C7311yescharacteristic
646#381C22×C7312yes—
647#381C22×C7311yescharacteristic
648#380C22×C7311yescharacteristic
649#380C22×C7312yes—
650#380C22×C7312yes—
651#380C22×C7311yescharacteristic
652#380C22×C7311yescharacteristic
653C4×C4⋊C4C22×C7311yescharacteristic
654C4×C4⋊C4C22×C7311yescharacteristic
655C4×C4⋊C4C22×C7311yescharacteristic
656C4×C4⋊C4C22×C7311yescharacteristic
657C4×C4⋊C4C22×C7311yescharacteristic
658C4×C22⋊C4C22×C7311yescharacteristic
659C4×C22⋊C4C22×C7312yes—
660C4×C22⋊C4C22×C7312yes—
661C4×C22⋊C4C22×C7312yes—
662C4×C22⋊C4C22×C7311yescharacteristic
663C4×C22⋊C4C22×C7311yescharacteristic
664#376C22×C7312yes—
665C2×#95C22×C7312yes—
666C22×D4C23×C7311yescharacteristic
667C22×D4C23×C7312yes—
668C22×D4C23×C7311yescharacteristic
669C22×D4C23×C7312yes—
670C22×D4C23×C7312yes—
671C22×D4C23×C7311yescharacteristic
672C22×D4C23×C7312yes—
673C22×D4C23×C7312yes—
674C22×D4C23×C7312yes—
675C23×C4C23×C7311yescharacteristic
676C23×C4C23×C7311yescharacteristic
677C23×C4C23×C7311yescharacteristic
678C23×C4C23×C7312yes—
679C23×C4C23×C7312yes—
680C23×C4C23×C7312yes—
681C23×C4C23×C7311yescharacteristic
682C23×C4C23×C7312yes—
683#127—24no—
684#126—44no—
685#123—24no—
686#121—24no—
687#121—24no—
688#121—24no—
689#121—44no—
690#121—44no—
691#121—44no—
692#121—42no—
693C4×D4—24no—
694C4×D4—28no—
695C4×D4—42no—
696C4×D4—42no—
697C4×D4—42no—
698C4×D4—42no—
699C4×D4—44no—
700C4×D4—44no—
701#117—24no—
702C2×C4⋊C4C23×C7311yescharacteristic
703C2×C4⋊C4C23×C7311yescharacteristic
704C2×C4⋊C4C23×C7311yescharacteristic
705C2×C4⋊C4C23×C7311yescharacteristic
706C2×C4⋊C4C23×C7311yescharacteristic
707C2×C4⋊C4C23×C7311yescharacteristic
708C2×C4⋊C4C23×C7311yescharacteristic
709C2×C4⋊C4C23×C7311yescharacteristic
710C2×C4⋊C4C23×C7312yes—
711C2×C4⋊C4C23×C7312yes—
712C2×C4⋊C4C23×C7312yes—
713C2×C4⋊C4C23×C7312yes—
714C2×C4⋊C4C23×C7312yes—
715C2×C4⋊C4C23×C7312yes—
716C2×C4⋊C4C23×C7312yes—
717C2×C4⋊C4C23×C7311yescharacteristic
718C2×C4⋊C4C23×C7312yes—
719C2×C4⋊C4C23×C7311yescharacteristic
720C2×C4⋊C4C23×C7311yescharacteristic
721C2×C22⋊C4C23×C7312yes—
722C2×C22⋊C4C23×C7312yes—
723C2×C22⋊C4C23×C7312yes—
724C2×C22⋊C4C23×C7312yes—
725C2×C22⋊C4C23×C7312yes—
726C2×C22⋊C4C23×C7311yescharacteristic
727C2×C22⋊C4C23×C7311yescharacteristic
728C2×C22⋊C4C23×C7312yes—
729C2×C22⋊C4C23×C7312yes—
730C2×C22⋊C4C23×C7312yes—
731C2×C22⋊C4C23×C7312yes—
732C2×C22⋊C4C23×C7311yescharacteristic
733C2×C22⋊C4C23×C7311yescharacteristic
734C2×C22⋊C4C23×C7311yescharacteristic
735C2×C22⋊C4C23×C7312yes—
736C2×C22⋊C4C23×C7312yes—
737C2×C22⋊C4C23×C7312yes—
738C2×C22⋊C4C23×C7311yescharacteristic
739C2×C22⋊C4C23×C7312yes—
740C2×C22⋊C4C23×C7312yes—
741C2×C22⋊C4C23×C7311yescharacteristic
742C2×C22⋊C4C23×C7312yes—
743C2×C22⋊C4C23×C7312yes—
744C2×C22⋊C4C23×C7312yes—
745C2×C22⋊C4C23×C7312yes—
746C2×C22⋊C4C23×C7312yes—
747C2×C22⋊C4C23×C7312yes—
748C2×C22⋊C4C23×C7311yescharacteristic
749C2×C42—42no—
750C2×C42C23×C7312yes—
751C2×C42C23×C7311yescharacteristic
752C2×C42C23×C7312yes—
753C2×C42C23×C7312yes—
754C2×C42C23×C7311yescharacteristic
755C2×C42C23×C7311yescharacteristic
756C2×C42C23×C7311yescharacteristic
757C2×C42C23×C7311yescharacteristic
758C2×C42C23×C7312yes—
759C2×C42C23×C7311yescharacteristic
760C2×C42C23×C7311yescharacteristic
761#95C23×C7311yescharacteristic
762#95C23×C7312yes—
763#95C23×C7312yes—
764#95C23×C7312yes—
765#95C23×C7311yescharacteristic
766#95C23×C7312yes—
767#95C23×C7312yes—
768#95C23×C7311yescharacteristic
769#95C23×C7312yes—
770#95C23×C7312yes—
771#95C23×C7311yescharacteristic
772#95C23×C7312yes—
773#95C23×C7311yescharacteristic
774#95C23×C7312yes—
775#95C23×C7311yescharacteristic
776#95C23×C7311yescharacteristic
777#95C23×C7311yescharacteristic
778#95C23×C7311yescharacteristic
779#95C23×C7312yes—
780#95C23×C7312yes—
781#95C23×C7311yescharacteristic
782#95C23×C7312yes—
783#95C23×C7312yes—
784#95C23×C7312yes—
785C24C24×C7311yescharacteristic
786C24C24×C7312yes—
787C24C24×C7312yes—
788C24C24×C7311yescharacteristic
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—22no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—22no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—41no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4#41×C7314yes—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4C24×C7311yescharacteristic
841C22×C4C24×C7311yescharacteristic
842C22×C4C24×C7311yescharacteristic
843C22×C4C24×C7312yes—
844C22×C4C24×C7311yescharacteristic
845C22×C4C24×C7312yes—
846C22×C4C24×C7312yes—
847C22×C4C24×C7311yescharacteristic
848C22×C4C24×C7311yescharacteristic
849C22×C4C24×C7311yescharacteristic
850C22×C4C24×C7312yes—
851C22×C4C24×C7312yes—
852C22×C4C24×C7311yescharacteristic
853C22×C4C24×C7311yescharacteristic
854C22×C4C24×C7311yescharacteristic
855C22×C4C24×C7312yes—
856C22×C4C24×C7311yescharacteristic
857C22×C4C24×C7311yescharacteristic
858C22×C4C24×C7311yescharacteristic
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—42no—
867C4⋊C4—41no—
868C4⋊C4—41no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4#41×C7314yes—
877C4⋊C4#41×C7314yes—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—22no—
882C22⋊C4—24no—
883C22⋊C4—24no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—24no—
892C22⋊C4—41no—
893C22⋊C4—42no—
894C22⋊C4—42no—
895C22⋊C4—41no—
896C22⋊C4—41no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—42no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C42—24no—
907C42—24no—
908C42—22no—
909C42—22no—
910C42—22no—
911C42—22no—
912C42—22no—
913C42—24no—
914C42—41no—
915C42—41no—
916C42—42no—
917C23—22no—
918C23—22no—
919C23—21no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—22no—
924C23—21no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—21no—
929C23—21no—
930C23—21no—
931C23—22no—
932C23—22no—
933C23—21no—
934C23—22no—
935C23—22no—
936C23—21no—
937C23—22no—
938C23—22no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—22no—
943C23C2×#41×C7314yes—
944C23H(5,𝔽2)×C7312yes—
945C23C25×C7311yescharacteristic
946D4—28no—
947D4—48no—
948D4—48no—
949D4—44no—
950D4—48no—
951D4—44no—
952D4—84no—
953D4—84no—
954D4—84no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—22no—
986C2×C4—21no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—44no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—84no—
1009C2×C4—84no—
1010C2×C4—84no—
1011C2×C4—84no—
1012C2×C4C2×#41×C7312yes—
1013C2×C4C2×#41×C7314yes—
1014C2×C4C2×#41×C7312yes—
1015C2×C4C2×#41×C7312yes—
1016C2×C4C2×#41×C7312yes—
1017C2×C4C2×#41×C7312yes—
1018C2×C4H(5,𝔽2)×C7312yes—
1019C2×C4H(5,𝔽2)×C7312yes—
1020C22—24no—
1021C22—24no—
1022C22—22no—
1023C22—22no—
1024C22—22no—
1025C22—24no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—41no—
1030C22—42no—
1031C22—42no—
1032C22—41no—
1033C22—42no—
1034C22—41no—
1035C22—42no—
1036C22—42no—
1037C22—41no—
1038C22—41no—
1039C22—42no—
1040C22—42no—
1041C22—41no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—42no—
1046C22—41no—
1047C22—42no—
1048C22C22×#41×C7311yescharacteristic
1049C22C22×#41×C7311yescharacteristic
1050C22C22×#41×C7311yescharacteristic
1051C22C2×H(5,𝔽2)×C7311yescharacteristic
1052C22C2×H(5,𝔽2)×C7311yescharacteristic
1053C22C2×H(5,𝔽2)×C7311yescharacteristic
1054C22#585×C7311yescharacteristic
1055C4—22no—
1056C4—24no—
1057C4—22no—
1058C4—22no—
1059C4—22no—
1060C4—41no—
1061C4—41no—
1062C4—42no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—42no—
1067C4—42no—
1068C4—41no—
1069C4—42no—
1070C4—41no—
1071C4—42no—
1072C4—41no—
1073C4#553×C7314yes—
1074C2—44no—
1075C2—42no—
1076C2—81no—
1077C2—82no—
1078C2C2×#553×C7311yescharacteristic
1079C2C73×#347511yescharacteristic
1080C2C73×#348311yescharacteristic
1081C2C73×#351311yescharacteristic
1082C2C73×#351911yescharacteristic
1083C2C73×#351911yescharacteristic
1084C2C73×#354211yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2781C2semidirect
2. C73×#2756C2semidirect
3. C73×#2603C2semidirect
4. C73×#2559C2semidirect
5. C73×#2543C2semidirect
6. C73×#2537C2semidirect
7. C73×#2512C2semidirect
8. C73×#2507C2semidirect
9. C73×#2495C2semidirect
10. C73×#2456C2semidirect
11. C73×#2428C2semidirect
12. C73×#2428C2semidirect
13. C73×#2420C2semidirect
14. C73×#2420C2semidirect
15. C73×#2414C2semidirect
16. C73×#2366C2semidirect
17. C73×#2363C2semidirect
18. C73×#2353C2semidirect
19. C73×#2349C2semidirect
20. C73×#2346C2semidirect
21. C4×#123×C73C2semidirect
22. C4×#121×C73C2semidirect
23. C4×#121×C73C2semidirect
531. #59403C73direct (N × H)
543. #2781C2×C73semidirect
544. #2756C2×C73semidirect
545. #2603C2×C73semidirect
546. #2559C2×C73semidirect
547. #2543C2×C73semidirect
548. #2537C2×C73semidirect
549. #2512C2×C73semidirect
550. #2507C2×C73semidirect
551. #2495C2×C73semidirect
552. #2456C2×C73semidirect
553. #2428C2×C73semidirect
554. #2428C2×C73semidirect
555. #2420C2×C73semidirect
556. #2420C2×C73semidirect
557. #2414C2×C73semidirect
558. #2366C2×C73semidirect
559. #2363C2×C73semidirect
560. #2353C2×C73semidirect
561. #2349C2×C73semidirect
562. #2346C2×C73semidirect
563. C4×#123C2×C73semidirect
564. C4×#121C2×C73semidirect
565. C4×#121C2×C73semidirect
566. C73#59403direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#27812
C73×#27562
C73×#26032
C73×#25592
C73×#25432
C73×#25372
C73×#25122
C73×#25072
C73×#24952
C73×#24562
C73×#24282
C73×#24202
C73×#24142
C73×#23662
C73×#23632
C73×#23532
C73×#23492
C73×#23462
C4×#123×C732
C4×#121×C732
#5940373