Finite Group Databasebeta

← C2×#11733757 #13522048

Subgroups — C2×#11733757 #13522048

Order 1792.

3678 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6502C211yesmaximal, characteristic
2C22×#6448C211yesmaximal, characteristic, complemented
3C22×#6441C211yesmaximal, characteristic, complemented
4C22×C4×Dic14C211yesmaximal, characteristic, complemented
5C2×C7×#390C211yesmaximal, characteristic, complemented
6C2×#89994C211yesmaximal, characteristic, complemented
7C2×#89766C211yesmaximal, characteristic, complemented
8C2×#89744C211yesmaximal, characteristic, complemented
9C2×#89720C211yesmaximal, characteristic, complemented
10C2×#89733C211yesmaximal, characteristic, complemented
11C2×#89729C211yesmaximal, characteristic, complemented
12C2×#89729C211yesmaximal, characteristic, complemented
13C2×#89723C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
15C2×#89712C211yesmaximal, characteristic, complemented
16#11733757C2116yesmaximal, direct product factor
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C42×C7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C2×#6502—28no—
34C2×#6502C2218yes—
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×(C2×D7)⋊C4C2211yescharacteristic
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×C4⋊Dic7C2211yescharacteristic
41C22×C4⋊Dic7C2211yescharacteristic
42C22×Dic7⋊C4C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×Dic7⋊C4C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C22×C4×Dic7C2211yescharacteristic
49C22×C4×Dic7C2211yescharacteristic
50C2×#6448—28no—
51C2×#6448C2218yescomplemented
52C2×#6441—28no—
53C2×#6441C2218yescomplemented
54C2×C4×Dic14—28no—
55C2×C4×Dic14C2218yescomplemented
56C7×#390C2218yescomplemented
57#89994C2218yescomplemented
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61C2×C7⋊#95C2211yescharacteristic
62#89766C2218yescomplemented
63#89744C2218yescomplemented
64#89733C2218yescomplemented
65#89729C2218yescomplemented
66#89729C2218yescomplemented
67#89723C2218yescomplemented
68#89720C2218yescomplemented
69C22⋊C4×Dic7C2218yescomplemented
70#89712C2218yescomplemented
71C2×#2426—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—42no—
78C22×C7×D4C2314yes—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—24no—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7C2314yes—
91C22×C22⋊D7C2314yes—
92C23×Dic7—24no—
93C23×Dic7—24no—
94C23×Dic7—24no—
95C23×Dic7C2314yes—
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2311yescharacteristic
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C22×Dic14—24no—
104C22×Dic14—24no—
105C22×Dic14D418yescomplemented
106C22×Dic14C2314yes—
107C2×C7×C4⋊C4—42no—
108C2×C7×C4⋊C4C2314yes—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4—24no—
111C2×C7×C22⋊C4—24no—
112C2×C7×C22⋊C4—24no—
113C2×C7×C22⋊C4C2314yes—
114C2×C7×C22⋊C4C2314yes—
115C2×C7×C22⋊C4C2314yes—
116C2×C7×C22⋊C4C2314yes—
117C2×C42×C7—24no—
118C2×C42×C7C2314yes—
119C2×C22⋊Dic7—24no—
120C2×C22⋊Dic7—24no—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—42no—
124C2×C22⋊Dic7C2314yes—
125C2×C22⋊Dic7C2314yes—
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129#6502—232no—
130C2×(C2×D7)⋊C4—24no—
131C2×(C2×D7)⋊C4—24no—
132C2×(C2×D7)⋊C4—24no—
133C2×(C2×D7)⋊C4—24no—
134C2×(C2×D7)⋊C4—42no—
135C2×(C2×D7)⋊C4C2314yes—
136C2×(C2×D7)⋊C4C2314yes—
137C2×(C2×D7)⋊C4C2314yes—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×C4⋊Dic7—24no—
141C2×C4⋊Dic7—24no—
142C2×C4⋊Dic7C2314yes—
143C2×C4⋊Dic7C2314yes—
144C2×Dic7⋊C4—24no—
145C2×Dic7⋊C4—24no—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4—42no—
148C2×Dic7⋊C4D418yes—
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2314yes—
151C2×Dic7⋊C4C2314yes—
152C2×Dic7⋊C4C2314yes—
153C2×Dic7⋊C4C2314yes—
154C2×C4×Dic7—24no—
155C2×C4×Dic7—24no—
156C2×C4×Dic7—24no—
157C2×C4×Dic7C2314yes—
158C2×C4×Dic7C2314yes—
159C2×C4×Dic7C2314yes—
160#6448—232no—
161#6441—232no—
162C4×Dic14—232no—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×#124—71no—
168C22×C22⋊Q8—71no—
169C22×#121—71no—
170C22×C4×Q8—71no—
171#2426—716no—
172C2×#396—71no—
173C2×#396—71no—
174C2×#394—71no—
175C2×#394—71no—
176C2×#390—71no—
177C2×#390—71no—
178C2×#390D711yescharacteristic, complemented
179C2×#389—71no—
180C2×#388—71no—
181C2×#388—71no—
182C2×C4×C22⋊C4—71no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7—22no—
196C24×C7#4114yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7—22no—
206C23×D7—22no—
207C23×D7C2412yes—
208C2×C7×D4—28no—
209C2×C7×D4—28no—
210C2×C7×D4—44no—
211C2×C7×D4—416no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7C2×D414yes—
225C22×C4×C7C2×D414yes—
226C22×C4×C7#4114yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C2×C22⋊D7—28no—
233C2×C22⋊D7—28no—
234C2×C22⋊D7—28no—
235C2×C22⋊D7—28no—
236C2×C22⋊D7—28no—
237C2×C22⋊D7—44no—
238C2×C22⋊D7—416no—
239C2×C22⋊D7—416no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—22no—
256C22×Dic7—28no—
257C22×Dic7—28no—
258C22×Dic7—28no—
259C22×Dic7—416no—
260C22×Dic7C2×D414yes—
261C22×Dic7C2×D414yes—
262C22×Dic7C2×D414yes—
263C22×Dic7C2×D414yes—
264C22×Dic7#4114yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C2×Dic14—232no—
273C2×Dic14—28no—
274C2×Dic14—28no—
275C2×Dic14C2×D4116yescomplemented
276C7×C4⋊C4—44no—
277C7×C22⋊C4—28no—
278C7×C22⋊C4—28no—
279C7×C22⋊C4—28no—
280C7×C22⋊C4—28no—
281C42×C7—28no—
282C22⋊Dic7—28no—
283C22⋊Dic7—28no—
284C22⋊Dic7—28no—
285C22⋊Dic7—28no—
286C22⋊Dic7—44no—
287(C2×D7)⋊C4—28no—
288(C2×D7)⋊C4—28no—
289(C2×D7)⋊C4—28no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—44no—
292C4⋊Dic7—28no—
293C4⋊Dic7—28no—
294Dic7⋊C4—28no—
295Dic7⋊C4—28no—
296Dic7⋊C4—28no—
297Dic7⋊C4—44no—
298Dic7⋊C4C2×D4116yes—
299C4×Dic7—28no—
300C4×Dic7—28no—
301C4×Dic7—28no—
302C23×Q8—71no—
303C23×D4—71no—
304C23×D4—71no—
305C23×D4C2×D711yescharacteristic
306C24×C4—71no—
307C2×#124—78no—
308C2×#124—148no—
309C2×C22⋊Q8—78no—
310C2×C22⋊Q8—148no—
311C2×#121—78no—
312C2×#121—148no—
313C2×C4×Q8—78no—
314C2×C4×Q8—148no—
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4C2×D711yescharacteristic
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4C2×D711yescharacteristic
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C42—71no—
338C22×C42—71no—
339C22×C42—71no—
340C22×C42C2×D711yescharacteristic
341#396—78no—
342#396—78no—
343#394—78no—
344#394—78no—
345#390—78no—
346#390—78no—
347#390C2×D718yescomplemented
348#389—78no—
349#388—78no—
350#388—78no—
351C4×C22⋊C4—78no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C23×C7—28no—
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—44no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7C22×D412yes—
384C23×C7C22×D412yes—
385C23×C7C2×#4114yes—
386C23×C7C2×#4112yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7H(5,𝔽2)12yes—
390C23×C72−1+412yes—
391C23×C7C2511yescharacteristic
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—44no—
400C22×D7—44no—
401C22×D7—44no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C7×D4—416no—
407C2×C4×C7—28no—
408C2×C4×C7—28no—
409C2×C4×C7—28no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—44no—
423C2×C4×C7—44no—
424C2×C4×C7C22×D414yes—
425C2×C4×C7C22×D414yes—
426C2×C4×C7C2×#4114yes—
427C22⋊D7—416no—
428C22⋊D7—416no—
429C2×Dic7—28no—
430C2×Dic7—28no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—44no—
448C2×Dic7—44no—
449C2×Dic7—44no—
450C2×Dic7—44no—
451C2×Dic7—416no—
452C2×Dic7#121116yes—
453C2×Dic7C22×D414yes—
454C2×Dic7C22×D414yes—
455C2×Dic7C22×D414yes—
456C2×Dic7C22×D414yes—
457C2×Dic7C2×#4114yes—
458Dic14—232no—
459C25—71no—
460C25C22×D711yescharacteristic
461C25C22×D711yescharacteristic
462C22×Q8—78no—
463C22×Q8—74no—
464C22×Q8—144no—
465C22×Q8—144no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—42no—
469C22×D4—74no—
470C22×D4—74no—
471C22×D4—144no—
472C22×D4—144no—
473C22×D4—144no—
474C22×D4—144no—
475C22×D4—144no—
476C22×D4—282no—
477C22×D4C22×D714yes—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—74no—
482C23×C4—71no—
483C23×C4—71no—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—144no—
487C23×C4—144no—
488C23×C4—144no—
489C23×C4C22×D711yescharacteristic
490C23×C4C22×D711yescharacteristic
491C23×C4C22×D711yescharacteristic
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494#124—1432no—
495C22⋊Q8—1432no—
496#121—1432no—
497C4×Q8—1432no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—78no—
500C2×C4⋊C4—74no—
501C2×C4⋊C4—74no—
502C2×C4⋊C4—74no—
503C2×C4⋊C4—74no—
504C2×C4⋊C4—74no—
505C2×C4⋊C4—74no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—144no—
508C2×C4⋊C4—144no—
509C2×C4⋊C4—144no—
510C2×C4⋊C4—144no—
511C2×C4⋊C4—144no—
512C2×C4⋊C4—282no—
513C2×C4⋊C4C22×D714yes—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—74no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—144no—
529C2×C22⋊C4—144no—
530C2×C22⋊C4—144no—
531C2×C22⋊C4—144no—
532C2×C22⋊C4—144no—
533C2×C22⋊C4—144no—
534C2×C22⋊C4—144no—
535C2×C22⋊C4—144no—
536C2×C22⋊C4—282no—
537C2×C22⋊C4—282no—
538C2×C22⋊C4C22×D714yes—
539C2×C22⋊C4C22×D714yes—
540C2×C22⋊C4C22×D714yes—
541C2×C22⋊C4C22×D714yes—
542C2×C42—24no—
543C2×C42—74no—
544C2×C42—74no—
545C2×C42—74no—
546C2×C42—144no—
547C2×C42—144no—
548C2×C42—144no—
549C2×C42C22×D714yes—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554C22×C7—24no—
555C22×C7—24no—
556C22×C7—24no—
557C22×C7—42no—
558C22×C7—416no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—42no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—88no—
570C22×C7C2×#12114yes—
571C22×C7#52914yes—
572C22×C7#54214yes—
573C22×C7#54614yes—
574C22×C7#54814yes—
575C22×C7#54814yes—
576C22×C7#55014yes—
577C22×C7C23×D411yescharacteristic
578C22×C7C23×D411yescharacteristic
579C22×C7C22×#4111yescharacteristic
580C22×C7C22×#4111yescharacteristic
581C22×C7C22×#4111yescharacteristic
582C22×C7C2×H(5,𝔽2)11yescharacteristic
583C22×C7C2×2−1+411yescharacteristic
584C2×D7—42no—
585C2×D7—42no—
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—88no—
592C4×C7—24no—
593C4×C7—24no—
594C4×C7—24no—
595C4×C7—42no—
596C4×C7—42no—
597Dic7—24no—
598Dic7—24no—
599Dic7—42no—
600Dic7—42no—
601Dic7—42no—
602Dic7—42no—
603Dic7C2×#12118yes—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—72no—
618C24—142no—
619C24—142no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24#115714yes—
626C24C23×D712yes—
627C24C23×D712yes—
628C24C23×D711yescharacteristic
629C2×Q8—716no—
630C2×Q8—148no—
631C2×Q8—1432no—
632C2×Q8—148no—
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—44no—
636C2×D4—416no—
637C2×D4—148no—
638C2×D4—148no—
639C2×D4—148no—
640C2×D4—148no—
641C2×D4—148no—
642C2×D4—2816no—
643C2×D4—284no—
644C2×D4—2816no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—74no—
658C22×C4—74no—
659C22×C4—74no—
660C22×C4—72no—
661C22×C4—74no—
662C22×C4—74no—
663C22×C4—72no—
664C22×C4—72no—
665C22×C4—72no—
666C22×C4—72no—
667C22×C4—72no—
668C22×C4—72no—
669C22×C4—148no—
670C22×C4—148no—
671C22×C4—148no—
672C22×C4—142no—
673C22×C4—142no—
674C22×C4—142no—
675C22×C4—142no—
676C22×C4—142no—
677C22×C4—142no—
678C22×C4—142no—
679C22×C4—142no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—2816no—
689C22×C4D4×D714yes—
690C22×C4D4×D714yes—
691C22×C4#115914yes—
692C22×C4C23×D712yes—
693C22×C4C23×D712yes—
694C22×C4C23×D712yes—
695C22×C4C23×D712yes—
696C22×C4C23×D712yes—
697C4⋊C4—44no—
698C4⋊C4—716no—
699C4⋊C4—148no—
700C4⋊C4—148no—
701C4⋊C4—148no—
702C4⋊C4—148no—
703C4⋊C4—148no—
704C4⋊C4—284no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—148no—
710C22⋊C4—148no—
711C22⋊C4—148no—
712C22⋊C4—148no—
713C22⋊C4—148no—
714C22⋊C4—148no—
715C22⋊C4—148no—
716C22⋊C4—148no—
717C22⋊C4—284no—
718C22⋊C4—284no—
719C42—28no—
720C42—148no—
721C42—148no—
722C42—148no—
723C2×C7—44no—
724C2×C7—82no—
725C2×C7#242618yescomplemented
726C2×C7C22×#12111yescharacteristic
727C2×C7C2×#52911yescharacteristic
728C2×C7C2×#54211yescharacteristic
729C2×C7C2×#54611yescharacteristic
730C2×C7C2×#54811yescharacteristic
731C2×C7C2×#54811yescharacteristic
732C2×C7C2×#55011yescharacteristic
733D7—82no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—142no—
762C23—142no—
763C23—142no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—284no—
769C23—284no—
770C23—284no—
771C23—284no—
772C23—284no—
773C23—284no—
774C23—284no—
775C23C2×#115714yes—
776C23C2×#115712yes—
777C23C2×D4×D712yes—
778C23C2×D4×D712yes—
779C23C2×#115912yes—
780C23#654812yes—
781C23D7×#4112yes—
782C23#655412yes—
783C23C24×D711yescharacteristic
784Q8—1432no—
785D4—416no—
786D4—2816no—
787D4—2816no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—716no—
806C2×C4—74no—
807C2×C4—74no—
808C2×C4—74no—
809C2×C4—74no—
810C2×C4—74no—
811C2×C4—148no—
812C2×C4—148no—
813C2×C4—142no—
814C2×C4—142no—
815C2×C4—142no—
816C2×C4—142no—
817C2×C4—142no—
818C2×C4—142no—
819C2×C4—142no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—2816no—
830C2×C4—284no—
831C2×C4—284no—
832C2×C4—284no—
833C2×C4—284no—
834C2×C4C2×D4×D714yes—
835C2×C4C2×D4×D714yes—
836C2×C4C2×#115914yes—
837C7C2×#242611yescharacteristic, complemented, Sylow
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—416no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—88no—
854C22—282no—
855C22—282no—
856C22—282no—
857C22—282no—
858C22—282no—
859C22—282no—
860C22—282no—
861C22—568no—
862C22#9018114yes—
863C22#9022914yes—
864C22#9024314yes—
865C22#9028914yes—
866C22D7×#12114yes—
867C22#9036014yes—
868C22#9040914yes—
869C22C22×#115711yescharacteristic
870C22C22×D4×D711yescharacteristic
871C22C22×D4×D711yescharacteristic
872C22C22×#115911yescharacteristic
873C22C2×#654811yescharacteristic
874C22C2×D7×#4111yescharacteristic
875C22C2×#655411yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—78no—
882C4—144no—
883C4—144no—
884C4—282no—
885C4—282no—
886C4—282no—
887C4—282no—
888C2—44no—
889C2—82no—
890C2—562no—
891C2#1173375718yesdirect product factor
892C2C2×#9018111yescharacteristic
893C2C2×#9022911yescharacteristic
894C2C2×#9024311yescharacteristic
895C2C2×#9028911yescharacteristic
896C2C2×D7×#12111yescharacteristic
897C2C2×#9036011yescharacteristic
898C2C2×#9040911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#390C2
socleC24×C7C24
prime radicalC22×#6502C2
hypercenterC2×#390D7
hypocenterC7C2×#2426
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×#6448C2semidirect
3. C22×#6441C2semidirect
4. C22×C4×Dic14C2semidirect
5. C2×C7×#390C2semidirect
6. C2×#89994C2semidirect
7. C2×#89766C2semidirect
8. C2×#89744C2semidirect
9. C2×#89720C2semidirect
10. C2×#89733C2semidirect
11. C2×#89729C2semidirect
12. C2×#89729C2semidirect
13. C2×#89723C2semidirect
14. C2×C22⋊C4×Dic7C2semidirect
15. C2×#89712C2semidirect
16. #11733757C2direct (N × H)
51. C2×#6448C22semidirect
53. C2×#6441C22semidirect
55. C2×C4×Dic14C22semidirect
56. C7×#390C22semidirect
57. #89994C22semidirect
62. #89766C22semidirect
63. #89744C22semidirect
64. #89733C22semidirect
65. #89729C22semidirect
66. #89729C22semidirect
67. #89723C22semidirect
68. #89720C22semidirect
69. C22⋊C4×Dic7C22semidirect
70. #89712C22semidirect
105. C22×Dic14D4semidirect
178. C2×#390D7semidirect
275. C2×Dic14C2×D4semidirect
347. #390C2×D7semidirect
725. C2×C7#2426semidirect
837. C7C2×#2426semidirect
891. C2#11733757direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#65022
C22×#64482
C22×#64412
C22×C4×Dic142
C2×C7×#3902
C2×#899942
C2×#897662
C2×#897442
C2×#897202
C2×#897332
C2×#897292
C2×#897232
C2×C22⋊C4×Dic72
C2×#897122
#117337572
C2×#24267